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If you use one of these installations, we recommend that you consult the instructions for your operating system because there is considerable variance in the best practices among Linux distributions.

IDEs and Text Editors R is a scripting language, and therefore the majority of the work done in the case studies that follow will be done within an IDE or text editor, rather than directly inputted into the R console.

As we show in the next section, some tasks are well suited for the console, such as package installation, but primarily you will want to work within the IDE or text editor of your choice.

As a hacker, you likely already have an IDE or text editor of choice, and we recommend that you use whichever environment you are most comfortable in for the case studies.

There are simply too many options to enumerate here, and we have no intention of inserting ourselves in the infamous Emacs versus Vim debate.

Figure With respect to the case studies we will describe, there are packages for dealing with spatial data, text analysis, network structures, and interacting with web- based APIs, among many others.

As such, we will be relying heavily on the functionality built into several of these packages.

Loading packages in R is very straightforward. There are two functions to perform this: library and require.

There are some subtle differences between the two, but for the purposes of this book, the primary difference is that require will return a Boolean TRUE or FALSE value, indicating whether the package is installed on the machine after attempting to load it.

For example, in Chapter 6 we will use the tm package to tokenize text. To load these packages, we can use either the library or require functions.

In the following example, we use library to load tm but use require for XML. If you are working with a fresh installation of R, then you will have to install a number of packages to complete all of the case studies in this book.

There are two ways to install packages in R: either with the GUI or with the install. Given the intended audience for this book, we will be interacting with R exclusively from the console during the case studies, but it is worth pointing out how to use the GUI to install packages.

You can now select the package you wish to install and click Install Selected to install the packages.

R for Machine Learning 9 Figure One of the primary advantages of using install. In these cases you will need to install from source: install.

The tm provides a function used to do text mining, and we will use it in Chapter 3 to perform classifications on email text. One useful parameter in the install.

As a best practice, we recommend always setting this to TRUE, especially if you are working with a clean installation of R.

Alternatively, we can also install directly from compressed source files. Using the setwd function to make sure the R working directory is set to the directory where the source file has been saved, we can simply execute the command shown earlier to install directly from the source code.

Note the two parameters that have been altered in this case. The premier package for creating high- quality graphics.

Used for representing social networks. Used to import raw data from the Web. Used to parse data from web-based APIs.

Used to work with unstructured text data. Used to extract structured data from the Web. As mentioned, we will use several packages through the course of this book.

Table lists all of the packages used in the case studies and includes a brief description of their purpose, along with a link to additional information about each.

Given the number of prerequisite packages, to expedite the installation process we have created a short script that will check whether each required package is installed and, if R for Machine Learning 11 it is not, will attempt to install it from CRAN.

Once set, the script will run, and you will see the progress of any required package installation that you did not yet have.

We are now ready to begin exploring machine learning with R! Before we proceed to the case studies, however, we will review some R functions and operations that we will use frequently.

R Basics for Machine Learning As we stated at the outset, we believe that the best way to learn a new technical skill is to start with a problem you wish to solve or a question you wish to answer.

Being excited about the higher-level vision of your work makes learning from case studies effective. In this review of basic concepts in the R language, we will not be addressing a machine learning problem, but we will encounter several issues related to working with data and managing it in R.

As we will see in the case studies, quite often we will spend the bulk of our time getting the data formatted and organized in a way that suits the anal- ysis.

Usually very little time, in terms of coding, is spent running the analysis. For this case we will address a question with pure entertainment value.

Recently, the data service Infochimps. The data spans hundreds of years and has reports from all over the world.

Though it is international, the majority of sightings in the data come from the United States. With the time and spatial dimensions of the data, we might ask the following questions: are there seasonal trends in UFO sightings; and what, if any, variation is there among UFO sightings across the different states in the US?

This is a great data set to start exploring because it is rich, well-structured, and fun to work with.

It is also useful for this exercise because it is a large text file, which is typically the type of data we will deal with in this book.

In such text files there are often messy parts, and we will use base functions in R and some external libraries to clean and organize the raw data.

This section will bring you through, step by step, an entire simple analysis that tries to answer the questions we posed earlier.

We begin by loading the data and required libraries for the analysis. Both of these packages are used for manipulating and organizing data in R, and we will use plyr in this example to aggregate and organize the data.

Note that the file is tab-delimited hence the. Because R exploits defaults very heavily, we have to be particularly conscientious of the default parameter settings for the functions we use in our scripts.

To see how we can learn about parameters in R, suppose that we had never used the read. Alternatively, assume that we do not know that read.

R offers several useful functions for searching for help:? In the first example, we append a question mark to the beginning of the function.

We can also search for specific terms inside of packages by using a combination of?? The double question marks indicate a search for a specific term.

R also allows you to perform less structured help searches with help. The help. Al- ternatively, you can search the R website, which includes help files and the mailing lists archive, using the RSiteSearch function.

Please note that this is by no means meant to be an exhaustive review of R or the functions used in this section. For the UFO data there are several parameters in read.

First, we need to tell the function how the data is delimited. We know this is a tab-delimited file, so we set sep to the Tab character.

Next, when read. In our case, all of the columns are strings, but the default setting for all read. This class is meant for categorical variables, but we do not want this.

In fact, it is always a good prac- tice to switch off this default, especially when working with unfamiliar data.

Also, this data does not include a column header as its first row, so we will need to switch off that default as well to force R to not use the first row in the data as a header.

Finally, there are many empty elements in the data, and we want to set those to the special R value NA. R for Machine Learning 13 To do this, we explicitly define the empty string as the na.

In statistics, categorical variables are very important because we may be interested in what makes certain observations of a certain type.

In R we represent categorical variables as factor types, which essentially assigns numeric references to string la- bels.

We will repeat this process many times. We now have a data frame containing all of the UFO data! Whenever you are working with data frames, especially when they are from external data sources, it is always a good idea to inspect the data by hand.

Two great functions for doing this are head and tail. Man on Hwy 43 SW of Milwauk.. Man repts. Sheriff's office calls to re..

The first obvious issue with the data frame is that the column names are generic. Using the documentation for this data set as a reference, we can assign more meaningful labels to the columns.

Having meaningful column names for data frames is an important best practice. It makes your code and output easier to understand, both for you and other audiences.

We will use the names function, which can either access the column labels for a data structure or assign them. As in other languages, R treats dates as a special type, and we will want to convert the date strings to actual date types.

To do this, we will use the as. Date function, which will take the date string and attempt to convert it to a Date object.

As such, we will also have to specify a format string in as. Date so the function knows how to convert the strings. Why might this be the case?

We are dealing with a large text file, so perhaps some of the data was malformed in the original set.

Assuming this is the case, those data points will not be parsed correctly when loaded by read. Converting date strings and dealing with malformed data To address this problem, we first need to locate the rows with defective date strings, then decide what to do with them.

To find the problem rows, therefore, we simply need to find those that have strings with more than eight characters.

As a best practice, we first inspect the data to see what the malformed data looks like, in order to get a better understanding of what has gone wrong.

In this case, we will use the head function as before to examine the data returned by our logical statement.

This function is a vectorized version of the typical if-else logical switch for some Boolean test. We will see many examples of vectorized opera- tions in R.

We need to know the length of the string in each entry of DateOccurred and DateReported, so we use the nchar 1.

For a brief introduction to vectorized operations in R, see R help desk: How can I avoid this loop or make it faster?

R for Machine Learning 15 function to compute this. Once we have the vectors of Booleans, we want to see how many entries in the data frame have been malformed.

Next, we compute the length of that vector to find the number of bad entries. With only rows not conforming, the best option is to simply remove these entries and ignore them.

The latter portion, identifying those that do not conform, is particularly important because we are only interested in sighting variation in the United States and will use this information to isolate those entries.

Organizing location data To manipulate the data in this way, we will first construct a function that takes a string as input and performs the data cleaning.

Then we will run this function over the location data using one of the vectorized apply functions: get. The strsplit function will throw an error if the split character is not matched; therefore, we have to catch this error.

In our case, when there is no comma to split, we will return a vector of NA to indicate that this entry is not valid.

Finally, we add an additional check to ensure that only those location vectors of length two are returned.

Many non-US entries have multiple com- mas, creating larger vectors from the strsplit function. In this case, we will again return an NA vector.

As mentioned, members of the apply family of functions in R are extremely useful. They are constructed of the form apply vector, function and return results of the vectorized application of the function to the vector in a specific form.

In our case, we are using lapply, which always returns a list: city. In our case the keys are simply integers, but lists can also have strings as keys.

To do this, we will need to convert this long list into a two-column matrix, with the city data as the leading column: location. Similar to the apply functions, do.

We will often use the com- bination of lapply and do. To get this into the data frame, we use the transform function.

Finally, the state abbreviations are inconsistent, with some uppercase and others lowercase, so we use the tolower function to make them all lowercase.

Specifically, the data includes several UFO sightings from Canada, which also take this form. Fortunately, none of the Canadian province abbreviations match US state abbreviations.

We can use this information to identify non-US entries by constructing a vector of US state abbreviations and keeping only those entries in the USState column that match an entry in this vector: us.

This function takes two arguments: first, the values to be matched, and second, those to be matched against.

The function returns a vector of the same length as the first argument in which the values are the index of entries in that vector that match some value in the second vector.

If no match is found, the function returns NA by default. In our case, we are only interested in which entries are NA, as these are the entries that do not match a US state.

We then use the is. Our original data frame now has been manipulated to the point that we can extract from it only the data we are interested in.

By replacing entries that did not meet this criteria in the previous steps, we can use the subset command to create a new data frame of only US incidents: ufo.

Milwaukee wi 3 Telephoned Report:CA woman v Shelton wa 4 Man repts. Columbia mo 5 Anonymous caller repts. Seattle wa 6 Sheriff's office calls to re In the previous section we spent a lot of time getting the data properly formatted and identi- fying the relevant entries for our analysis.

In this section we will explore the data to further narrow our focus. This data has two primary dimensions: space where the sighting happened and time when a sighting occurred.

We focused on the former in the previous section, but here we will focus on the latter. First, we use the summary function on the DateOccurred column to get a sense of this chronological range of the data: summary ufo.

Median Mean 3rd Qu. Given this outlier, the next question is: how is this data distributed over time? And is it worth analyzing the entire time series?

A quick way to look at this visually is to construct a histogram. We will discuss histograms in more detail in the next chapter, but for now you should know that histograms allow you to bin your data by a given dimension and observe the frequency with which your data falls into those bins.

The dimension of interest here is time, so we construct a histogram that bins the data over time: quick. There are several things to note here.

This is our first use of the ggplot2 package, which we use throughout this book for all of our data visualizations. In this case, we are constructing a very simple histogram that requires only a single line of code.

First, we create a ggplot object and pass it the UFO data frame as its initial argument. Next, we set the x-axis aesthetic to the DateOccurred column, as this is the frequency we are interested in examining.

With ggplot2 we must always work with data frames, and the first argument to create a ggplot object must always be a data frame.

This means the package adheres to this particular philosophy for data visualization, and all visualiza- tions will be built up as a series of layers.

For this histogram, shown in Figure , the initial layer is the x-axis data, namely the UFO sighting dates. In this case, we will use the default settings for this function, but as we will see later, this default often is not a good choice.

Once the ggplot object has been constructed, we use the ggsave function to output the visualization to a file. Note the warning message that is printed when you draw the R for Machine Learning 19 visualization.

There are many ways to bin data in a histogram, and we will discuss this in detail in the next chapter, but this warning is provided to let you know exactly how ggplot2 does the binning by default.

We are now ready to explore the data with this visualization. Exploratory histogram of UFO data over time The results of this analysis are stark.

The vast majority of the data occur between and , with the majority of UFO sightings occurring within the last two decades. For our purposes, therefore, we will focus on only those sightings that occurred between and This will allow us to exclude the outliers and compare relatively similar units during the analysis.

As before, we will use the subset function to create a new data frame that meets this criteria: ufo. Date "" nrow ufo. To see the difference, we regenerate the histogram of the subset data in Figure We see that there is much more variation when looking at this sample.

But which way of aggregating our data is most appropriate here? The DateOccurred column provides UFO sighting information by the day, but there is considerable inconsistency in terms of the coverage throughout the entire set.

We need to aggregate the data in a way that puts the amount of data for each state on relatively level planes. In this case, doing so by year-month is the best option.

This aggregation also best addresses the core of our question, as monthly ag- gregation will give good insight into seasonal variations.

First, we will need to create a new column in the data that corresponds to the years and months present in the data. As before, we will set the format parameter accordingly to get the strings: ufo.

Rather, we simply referenced a column name that did not exist, and R R for Machine Learning 21 automatically added it.

Both methods for adding new columns to a data frame are useful, and we will switch between them depending on the particular task.

Next, we want to count the number of times each state and year-month combination occurs in the data. For the first time we will use the ddply function, which is part of the extremely useful plyr library for manipulating data.

The plyr family of functions work a bit like the map-reduce-style data aggregation tools that have risen in popularity over the past several years.

They attempt to group data in some specific way that was meaningful to all observations, and then do some calcula- tion on each of these groups and return the results.

For this task we want to group the data by state abbreviations and the year-month column we just created. Once the data is grouped as such, we count the number of entries in each group and return that as a new column.

Here we will simply use the nrow function to reduce the data by the number of rows in each group: sightings.

USState,YearMonth , nrow head sightings. From the head call in the example, however, we can see that there may be a problem with using the data as is because it contains a lot of missing values.

Presumably, there were no UFO sightings in these months, but the data does not include entries for nonsightings, so we have to go back and add these as zeros.

We need a vector of years and months that spans the entire data set. From this we can check to see whether they are already in the data, and if not, add them as zeros.

To do this, we will create a sequence of dates using the seq. Date function, and then format them to match the data in our data frame: date.

Date min ufo. Date max ufo. We will use this to perform the matching with the UFO sighting data. As before, we will use the lapply function to create the columns and the do.

Note that there are now entries from February and March for Alaska. To add in the missing zeros to the UFO sighting data, we need to merge this data with our original data frame.

To do this, we will use the merge func- tion, which takes two ordered data frames and attempts to merge them by common columns. In our case, we have two data frames ordered alphabetically by US state abbreviations and chronologically by year and month.

We need to tell the function which columns to merge these data frames by. We will set the by. Finally, we set the all parameter to TRUE, which instructs the function to include entries that do not match and to fill them with NA.

Those entries in the V1 column will be those state, year, and month entries for which no UFOs were sighted: all. First, we will set the column names in the new all.

This is done in exactly the same way as we did it at the outset. Next, we will convert the NA entries to zeros, again using the is.

Finally, we will convert the YearMonth and State columns to the appropriate types. Using the date. Likewise, the state abbreviations are better represented as categorical variables than strings, so we convert these to factor types.

We will describe factors and other R data types in more detail in the next chapter: names all. Date rep date.

R for Machine Learning 23 Analyzing the data For this data, we will address the core question only by analyzing it visually. For the remainder of the book, we will combine both numeric and visual analyses, but as this example is only meant to introduce core R programming paradigms, we will stop at the visual component.

Unlike the previous histogram visualization, however, we will take greater care with ggplot2 to build the visual layers explicitly.

This will allow us to create a visualization that directly addresses the question of seasonal variation among states over time and produce a more professional-looking visualization.

We will construct the visualization all at once in the following example, then explain each layer individually: state. Here we are using the all.

Again, we need to build an aesthetic layer of data to plot, and in this case the x-axis is the YearMonth column and the y-axis is the Sightings data.

Next, to show seasonal variation among states, we will plot a line for each state. This will allow us to observe any spikes, lulls, or oscillation in the number of UFO sightings for each state over time.

As we have seen throughout this case, the UFO data is fairly rich and includes many sightings across the United States over a long period of time.

Knowing this, we need to think of a way to break up this visualization such that we can observe the data for each state, but also compare it to the other states.

If we plot all of the data in a single panel, it will be very difficult to discern variation. A better approach would be to plot the data for each state individually and order them in a grid for easy comparison.

We also explicitly define the number of rows and columns in the grid, which is easier in our case because we know we are creating 50 different plots.

The ggplot2 package has many plotting themes. The default theme is the one we used in the first example and has a gray background with dark gray gridlines.

Once you become more comfortable with ggplot2, we recommend experi- menting with different defaults to find the one you prefer. Though not formally required, paying attention to these details is what can separate amateurish plots from professional-looking data visualiza- tions.

In fact, ggplot2 tends to think of colors as a way of distinguishing among different types or categories of data and, as such, prefers to have a factor type used to specify color.

Because this data spans 20 years, we will set these to be at regular five-year intervals. Then we set the tick labels to be the year in a full four-digit format.

Finally, we use the opts function to give the plot a title. There are many more options available in the opts function, and we will see some of them in later chapters, but there are many more that are beyond the scope of this book.

With all of the layers built, we are now ready to render the image with ggsave and analyze the data. There are many interesting observations that fall out of this analysis see Figure We see that California and Washington are large outliers in terms of the number of UFO sightings in these states compared to the others.

Between these outliers, there are also interesting differences. In California, the number of reported UFO sightings seems to be somewhat random over time, but steadily increasing since , whereas in Washington, the seasonal variation seems to be very consistent over time, with regular peaks and valleys in UFO sightings starting from about We can also notice that many states experience sudden spikes in the number of UFO sightings reported.

For example, Arizona, Florida, Illinois, and Montana seem to have experienced spikes around mid, and Michigan, Ohio, and Oregon experienced similar spikes in late Only Michigan and Ohio are geographically close among these groups.

If we do not believe that these are actually the result of extraterrestrial visitors, what are some alternative explanations?

Perhaps there was increased vigilance 3. R for Machine Learning 25 Figure If, however, you are sympathetic to the notion that we may be regularly hosting visitors from outer space, there is also evidence to pique your curiosity.

In fact, there is sur- prising regularity of these sightings in many states in the US, with evidence of regional clustering as well.

It is almost as if the sightings really contain a meaningful pattern. Further Reading on R This introductory case is by no means meant to be an exhaustive review of the language.

Rather, we used this data set to introduce several R paradigms related to loading, cleaning, organizing, and analyzing data.

We will revisit many of these functions and processes in the following chapters, along with many others. For those readers inter- ested in gaining more practice and familiarity with R before proceeding, there are many excellent resources.

These resources can roughly be divided into either reference books and texts or online resources, as shown in Table In the next chapter, we review exploratory data analysis.

Much of the case study in this chapter involved exploring data, but we moved through these steps rather quickly. In the next chapter we will consider the process of data exploration much more deliberately.

R references Title Author Reference Description Text references Data Manipulation with R Phil Spector [Spe08] A deeper review of many of the data manip- ulation topics covered in the previous section, and an introduction to several techniques not covered.

This book takes the R manual and adds several practical examples. The distinction between exploratory data analysis and confirmatory data analysis comes down to us from the famous John Tukey, 1 who emphasized the importance of designing simple tools for practical data analysis.

In this chapter, we describe some of the basic tools that R provides for summa- rizing your data numerically, and then we teach you how to make sense of the results.

After that, we show you some of the tools that exist in R for visualizing your data, and at the same time, we give you a whirlwind tour of the basic visual patterns that you should keep an eye out for in any gization.

The human mind is designed to find patterns in the world and will do so even when those patterns are just quirks of chance.

Because confirmatory data analysis requires more math than exploratory data analysis, this chapter is exclusively concerned with exploratory tools.

The numerical summaries we describe are the stuff of introductory statistics courses: means and modes, percentiles and medians, and standard deviations and variances.

We think simple visualizations are often underappreciated, and we hope we can convince you that you can often learn a lot about your data using only these basic tools.

Much more sophisticated techniques will come up in the later chapters of this book, but the intuitions for analyzing data are best built up while working with the simplest of tools.

What Is Data? For example, you often want to know how the data you have was generated and whether the data can reasonably be expected to be representative of the population you truly want to study.

The interpretation of data requires that you know something about the source of your data. This viewpoint is clearly a substantial simplification, but it will let us motivate many of the big ideas of data analysis visually, which we hope makes what are otherwise very abstract ideas a little more tangible.

An example of this type of data summary is shown in Figure An example of a visual summary of a single column is shown in Figure Summarizing one column in one image Beyond the tools you can use for analyzing isolated columns, there are lots of tools you can use to understand the relationships between multiple columns in your data set.

An example of this is shown in Figure Correlation: summarizing two columns in one number And there are other tools that go further.

An example of what dimensionality reduction techniques achieve is shown in Figure Dimensionality reduction: summarizing many columns in one column As Figures through suggest, summary statistics and dimensionality reduction move along opposite directions: summary statistics tell you something about how all What Is Data?

Inferring the Types of Columns in Your Data Before you do anything else with a new data set, you should try to find out what each column in your current table represents.

Some people like to call this information a data dictionary, by which they mean that you might be handed a short verbal descrip- tion of every column in the data set.

For example, imagine that you had the unlabeled data set in Table given to you. Unlabeled data Indeed, as a starting point you should figure out the type of each column: is the first column really a string, even though it looks like it contains only 0s and 1s?

In the UFO example in the first chapter, we immediately labeled all of the columns of the data set we were given.

Three of the most important of these functions are shown in Table Type determination in R R function Description is.

R does not provide a single-character data type. It differs from a character vector in both its hidden internal representation and semantics: most statistical functions in R work on numeric vectors or factor vectors, but not on character vectors.

Having basic type information about each column can be very important as we move forward because a single R function will often do different things depending on the type of its inputs.

In part, this tendency to move back and forth between types comes from a general tradition in machine learning for dealing with categorical distinctions.

Many variables that really work like labels or categories are encoded mathematically as 0 and 1. You can think of these numbers as if they were Boolean values: 0 might indicate that an email is not spam, a 1 might indicate that the email is spam.

This specific use of 0s and 1s to describe qualitative properties of an object is often called dummy coding in machine learning and statistics.

Factors in R can be thought of as labels, but the labels are actually en- coded numerically in the background: when the programmer accesses the label, the numeric values are translated into the character labels specified in an indexed array of character strings.

Tables through show the same data, but the data has been described with three different encoding schemes. In practice, it might be loaded as a factor or as a string, depending on the data loading function you use see the stringsAsFactors Inferring the Types of Columns in Your Data 35 parameter that was described in Chapter 1 for details.

If you are unsure, it is often better to begin by loading things as strings. You can always convert a string column to a factor column later.

This style of numeric coding is actually required by some machine learning algorithms. Finally, in Table , we show another type of numeric encoding for the same qualitative concept.

This style of encoding qualitative distinctions is very popular with physicists, so you will even- tually see it as you read more about machine learning.

Determining what an unlabeled table of numbers describes can be sur- prisingly difficult. In those cases, human intuition, aided by liberally by searching through Google, is often the only tool that we can suggest to you.

Numeric Summaries One of the best ways to start making sense of a new data set is to compute simple numeric summaries of all of the columns.

R is very well suited to doing this. If you have just one column from a data set as a vector, summary will spit out the most obvious values you should look at first: data.

The minimum value in the vector 2. The median aka the 50th percentile 4. The mean 5. The 3rd quartile aka the 75th percentile 6. The maximum value This is close to everything you should ask for when you want a quick numeric summary of a data set.

For most hackers, code is a more natural language to express ideas than mathematical symbols, so we think that rolling your own functions to compute means and medians will probably make more sense than showing you the defining equations for those two statistics.

Computing the mean is incredibly easy. In R, you would normally use the mean function. The median is just the opposite: it entirely depends upon the relative position of the numbers in your list.

To get the 25th percentile also known as the 1st quartile , you can split the list at one quarter of its length. The code we wrote in the previous example handles the even-length vector case by taking the average of the two entries that would have been the median if the list had contained an odd number of entries.

To make that point clear, here is a simple example in which the median has to be invented by averaging entries and another case in which the median is exactly equal to the middle entry of the vector: my.

This will also give us an opportunity to test our code: my. For that reason, modes are only really defined visually for many kinds of data sets.

To get a better sense of the range of your data, you might want to know what value is the lowest point in your data.

The answer to that question is to use the quantile function in R. And the mean customer might be even less informative if your data has a strange shape.

But central tendencies are only one thing you might want to know about your data. You can imagine defining the range of your data in a lot of ways.

As we already said, you could use the definition that the range function implements: the range is defined by the min and max values. The min and max will match the outliers perfectly, which makes them fairly brittle definitions of spread.

In other words, the definition of range based on min and max effectively depends on only two of your data points, regardless of whether you have two data points or two million data points.

Standard Deviations and Variances 41 Now, there are a lot of ways you could try to meet the requirements we described earlier for a good numeric summary of data.

When you work with more advanced statistical methods, these sorts of ranges will come up again and again. Roughly, the idea is to measure how far, on average, a given number in your data set is from the mean value.

In theory, there could be a few reasons for this, most of which are examples of how things can go wrong when you assume floating-point arithmetic is perfectly accurate.

This is done because the variance that you can estimate from empirical data turns out, for fairly subtle reasons, to be biased downward from its true value.

To put everything back on the original scale, we need to replace the variance with the standard deviation, which is just the square root of the variance: my.

Still, it would be nice to get a sense of how tightly inside the data we are. This is quite typical, especially for data with the shape that our heights data has.

But to finally make that idea about the shape of our data precise, we need to start visualizing our data and define some formal terms for describing the shape of data.

Standard Deviations and Variances 43 Exploratory Data Visualization Computing numerical summaries of your data is clearly valuable. Visualizing your data is often a more effective way to discover patterns in it.

These idealized shapes, also called distributions, are standard patterns that statisticians have studied over the years.

When you find one of these shapes in your data, you can often make broad inferences about your data: how it originated, what sort of abstract prop- erties it will have, and so on.

Even when you think the shape you see is only a vague approximation to your data, the standard distributional shapes can provide you with building blocks that you can use to construct more complex shapes that match your data more closely.

The most typical single-column visualization technique that people use is the histogram. In a histogram, you divide your data set into bins and then count the number of entries in your data that fall into each of the bins.

For instance, in Figure , we create a histogram with one-inch bins to visualize our height data. We can do that in R as follows: library 'ggplot2' data.

Most of the entries are in the middle of your data, near the mean and median height. One way to check this is to try using several other binwidths.

This is something you should always keep in mind when working with histograms: the binwidths you use impose external structure on your data at the same time that they reveal internal struc- ture in your data.

In Figure , we recreate the histogram using five-inch bins with the following R code: ggplot heights. And the opposite problem, called undersmoothing, is just as danger- ous.

In Figure , we again adjust the binwidth, this time to a much smaller 0. Because we have so much data, you can still learn something from this histogram, but a data set with points would be basically worthless if you had used this sort of bindwidth.

Because setting bindwidths can be tedious and because even the best histogram is too jagged for our taste, we prefer an alternative to histograms called kernel density esti- mates KDE or density plots.

Although density plots suffer from most of the same problems of oversmoothing and undersmoothing that plague histograms, we generally Figure Additionally, density plots have some theoretical superiority over histograms: in theory, using a den- sity plot should require fewer data points to reveal the underlying shape of your data than a histogram.

And, thankfully, density plots are just as easy to generate in R as histograms. In Figure , we create our first density plot of the height data: ggplot heights.

Here the density plot suggests that the data is suspiciously flat at the peak value. Here we use the gender of each point to split up our data into two parts.

Next, in Figure we create a density plot in which there are two densities that get superimposed, but are colored in differently to indicate the gender they represent: ggplot heights.

We might expect to see the same bell curve structure in the weights for both genders. In Figure , we make a new density plot for the weights column of our data set: Figure We can easily see an example of the normal distribution by simply splitting up the plot into two pieces, called facets.

In R, we can build this sort of faceted plot as follows: ggplot heights. But the normal distribution is very important in the Figure On a more abstract level, a normal distribution is just a type of bell curve.

It might be any of the bell curves shown in Figures through In these graphs, two parameters vary: the mean of the distribution, which determines the center of the bell curve, and the variance of the distribution, which determines the width of the bell curve.

You should play around with visualizing various versions of the bell curve by playing with the parameters in the following code until you feel comfortable with how the bell curve looks.

To do that, play with the values of m and s in the code shown here: Figure As you can see from Figures through , the exact shape of the curves will vary, but their overall shape is consistent.

But the mode has a clear visual interpretation: when you make a density plot, the mode of the data is the peak of the bell. For an example, look at Figure Estimating modes visually is much easier to do with a density plot than with a histo- gram, which is one of the reasons we prefer density plots over histograms.

And modes make sense almost immediately when you look at density plots, whereas they often make very little sense if you try to work with the numbers directly.

In contrast, a graph like the one shown in Figure has two modes, and the graph in Figure has three modes.

Figures and show images of symmetric and skewed data to make these terms clear. A symmetric distribution has the same shape whether you move to the left of the mode or to the right of the mode.

The normal distribution has this property, which tells us Figure In contrast, another bell-shaped distribution called the Cauchy distribution produces Figure The canonical images that are usually used to explain this distinction between the thin- tailed normal and the heavy-tailed Cauchy are shown in Figures and R makes this quite easy, so you should try the following: Figure Normal distribution with its mode highlighted Exploratory Data Visualization 55 set.

The Cauchy is unimodal and sym- metric, and it has a bell shape with heavy tails. After the normal distribution, there are two more canonical images we want to show you before we bring this section on density plots to a close: a mildly skewed distribution called the gamma and a very skewed distribution called the exponential.

Mixture of three normal distributions with three modes highlighted Exploratory Data Visualization 57 gamma. As you can see, the gamma distribution is skewed to the right, which means that the median and the mean can sometimes be quite different.

This real data set looks remarkably like data that could have been produced by a the- oretical gamma distribution. When we describe how to use stochastic optimization tools near the end of this book, having an all-positive distribution will come in very handy.

An example data set drawn from the exponential distribution is shown in Figure This distribution comes up quite a lot when the most frequent value in your data set is zero and only Figure Skewed distribution Exploratory Data Visualization 59 positive values can ever occur.

For example, corporate call centers often find that the length of time between the calls they receive looks like an exponential distribution.

For right now, what you really take away from this section are the simple qual- itative terms that you can use to describe your data to others: unimodal versus multimodal, symmetric versus skewed, and thin-tailed versus heavy-tailed.

This is clearly worth doing: often just seeing a familiar shape in your data tells you a lot about your data.

To do real machine learning, we need Figure Facetted plot of heavy-tailed Cauchy and thin-tailed Normal Visualizing the Relationships Between Columns 61 to find relationships between multiple columns in our data and use those relationships to make sense of our data and to predict things about the future.

The first is the stereotypical regression picture. This is intuitively obvious, but de- scribing general strategies for finding these sorts of patterns will take up the rest of this book.

In this case, the predictions are simply a line, which is shown in blue. As you get more data, these guesses become more accurate and the shaded region shrinks.

Because we already used all of the data, the best way to see this effect is to go in the opposite Figure Scatterplot of heights versus weights Visualizing the Relationships Between Columns 65 direction: remove some of our data, and see how the pattern gets weaker and weaker.

The results are shown in Figures through For classification, Figure is the image you should keep in mind. That makes it clear that we see two distinct groups of people in our data.

To generate this image in ggplot2, we run the following code: ggplot heights. In the classification picture, we make a scatterplot of our data but use a third column to color in the points with different labels.

For our height and weight data, we added a third column, which is the gender Figure Scatterplot of heights versus weights with 20 observations Visualizing the Relationships Between Columns 67 of each person in our data set.

This data set just happens to be particularly easy to work with, which is why we started with it. As you can see, you need almost no code at all to get pretty impressive results.

We used heights and weights to predict whether a person was a man or a woman. For example, imagine that your data looked like the data set shown in Example This plot might depict people who are at risk for a certain ailment and those who are not.

Above and below the black horizontal lines we might predict that a person is at risk, but inside we would predict good health.

These black lines are thus our decision boundary. Suppose that the blue dots represent healthy people and the red dots rep- resent people who suffer from a disease.

If that were the case, the two black lines would work quite well as a decision boundary for classifying people as either healthy or sick.

At the unprocessed stage, the features are simply the contents of the raw email as plain text. This raw text provides us with our first problem.

We need to transform our raw text data into a set of features that describe qualitative concepts in a quantitative way.

Fortunately, the general-purpose text-mining packages available in R will do much of this work for us. For that reason, much of this chapter will focus on building up your intuition for the types of features that people have used in the past when working with text data.

Feature generation is a major topic in current machine learning research and is still very far from being automated in a general-purpose way.

Just as learning the words of a new language builds up an intuition for what could realistically be a word, learning about the features people have used in the past builds up an intuition for what features could reasonably be helpful in the future.

Table shows the results. This sort of problem comes up quite often when you work with data that contains only a few unique values for one or more of your variables.

As this is a recurring problem, there is a standard graphical solution: we simply add random noise This or That: Binary Classification 75 to the values before we plot.

This addition of noise is called jittering, and is very easy to produce in ggplot2 see Figure Before we can proceed, we should review some basic concepts of conditional proba- bility and discuss how they relate to classifying a message based on its text.

Moving Gently into Conditional Probability At its core, text classification is a 20th-century application of the 18th-century concept of conditional probability.

A conditional probability is the likelihood of observing one thing given some other thing that we already know about. This is something we can look up in survey results.

When a word is noticeably more likely to occur in one context rather than the other, its occurrence can be diagnostic of whether a new message is spam or ham.

If you see many words that are more likely to occur in spam than ham and very few words that are more likely to occur in ham than spam, that should be strong evidence that the email as a whole is spam.

How much more likely a message needs to be to merit being labeled spam depends upon an additional piece of information: the base rate of seeing spam messages.

This base rate information is usually called the prior. When working with email, the prior comes into play because the majority of email sent is spam, which means that even weak evidence that an email is spam can be sufficient to justify labeling it as spam.

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The worst thing about R is that R is an extremely powerful language for manipulating and analyzing data.

Its meteoric rise in popularity within the data science and machine learning communities has made it the de facto lingua franca for analytics.

There are many technical advantages afforded by a language designed specifically for statistical computing.

As the description from the R Project notes, the language pro- vides an open source bridge to S, which contains many highly specialized statistical operations as base functions.

This data can then be visualized by passing the results to the plot function, which is designed to visualize the results of this analysis.

In other languages with large scientific computing communities, such as Python, du- plicating the functionality of lm requires the use of several third-party libraries to rep- resent the data NumPy , perform the analysis SciPy , and visualize the results mat- plotlib.

As we will see in the following chapters, such sophisticated analyses can be performed with a single line of code in R.

In addition, as in other scientific computing environments, the fundamental data type in R is a vector. Vectors can be aggregated and organized in various ways, but at the core, all data is represented this way.

This relatively rigid perspective on data structures can be limiting, but is also logical given the application of the language. Fundamentally, a data frame is simply a column-wise aggregation of vectors that R affords specific functionality to, which makes it ideal for working with any manner of data.

For all of its power, R also has its disadvantages. R does not scale well with large data, and although there have been many efforts to address this problem, it remains a serious issue.

For the purposes of the case studies we will review, however, this will not be an issue. The data sets we will use are relatively small, and all of the systems we will build are prototypes or proof-of-concept models.

This distinction is important because if your intention is to build enterprise-level machine learning systems at the Google or Facebook scale, then R is not the right solution.

If one of those experiments bears fruit, then the engineers will attempt to replicate the functionality designed in R in a more appropri- ate language, such as C.

This ethos of experimentation has also engendered a great sense of community around the language. The social advantages of R hinge on this large and growing community of experts using and contributing to the language.

Many R users, therefore, are experts in their various fields. This includes an extremely diverse set of disciplines, including mathematics, statistics, biology, chemistry, physics, psychology, economics, and political science, to name a few.

This community of experts has built a massive collection of packages on top of the extensive base functions in R.

In the case studies that follow, we will use many of the most popular packages, but this will only scratch the surface of what is possible with R.

But all grammatical grievances with a language can eventually be overcome, especially for persistent hackers.

What is more difficult for nonstatisti- cians is the liberal assumption of familiarity with statistical and mathematical methods built into R functions.

Using the lm function as an example, if you had never performed a linear regression, you would not know to look for coefficients, standard errors, or residual values in the results.

Nor would you know how to interpret those results. But because the language is open source, you are always able to look at the code of a function to see exactly what it is doing.

Part of what we will attempt to accomplish with this book is to explore many of these functions in the context of machine learning, but that exploration will ultimately address only a tiny subset of what you can do in R.

Fortunately, the R community is full of people willing to help you understand not only the language, but also the methods implemented in it.

Table lists some of the best places to start. Table This specialized search tool at- tempts to alleviate this problem by providing a focused portal to R documentation and information.

Thanks to the efforts of several prominent R community members, there is an active and vibrant col- lection of experts adding and answering R questions on StackOverflow.

The Rchive attempts to document the pre- sentations and tutorials given at these meetings by posting videos and slides, and now contains presentations from community members all over the world.

This includes downloading and installing R, as well as installing R packages. This includes issues of loading, cleaning, organizing, and analyzing data.

Downloading and Installing R Like many open source projects, R is distributed by a series of regional mirrors. If you do not have R already installed on your machine, the first step is to download it.

Once you have selected a mirror, you will need to download the appropriate distribution of R for whichever operating system you are running.

R relies on several legacy libraries compiled from C and Fortran. As such, depending on your operating system and your familiarity with installing software from source code, you may choose to install R from either a compiled binary distribution or the source.

Next, we present instructions for installing R on Windows, Mac OS X, and Linux distributions, with notes on installing from either source or binaries when avail- able.

Finally, R is available in both and bit versions. Depending on your hardware and operating system combination, you should install the appropriate version.

Windows For Windows operating systems, there are two subdirectories available to install R: base and contrib. The latter is a directory of compiled Windows binary versions of all of the contributed R packages in CRAN, whereas the former is the basic installation.

Select the base installation, and download the latest compiled binary. Installing con- tributed packages is easy to do from R itself and is not language-specific; therefore, it is not necessary to to install anything from the contrib directory.

Follow the on-screen instructions for the installation. Once the installation has successfully completed, you will have an R application in your Start menu, which will open the RGui and R Console, as pictured in Figure For most standard Windows installations, this process should proceed without any issues.

If you have a customized installation or encounter errors during the installation, consult the R for Windows FAQ at your mirror of choice.

R for Machine Learning 5 Figure You can check this by opening Terminal. You are now ready to begin! For some users, however, it will be useful to have a GUI ap- plication to interact with the R Console.

For this you will need to install separate soft- ware. With Mac OS X, you have the option of installing from either a compiled binary or the source.

Once the installation is complete, you will have both R. As with the Windows installation, if you are installing from a binary, this process should proceed without any problems.

When you open your new R application, you will see a console similar to the one pictured in Figure The R Console on a bit version of the Mac OS X installation If you have a custom installation of Mac OS X or wish to customize the installation of R for your particular configuration, we recommend that you install from the source code.

Installing R from source on Mac OS X requires both the C and Fortran compilers, which are not included in the standard installation of the operating system.

Once you have all of the necessary compilers to install from source, the process is the typical configure, make, and install procedure used to install most software at the command line.

Using Terminal. If you encounter any errors during the installation, using either the compiled binary distribution or the source code, consult the R for Mac OS X FAQ at the mirror of your choice.

Simply type R at the command line, and the R console will be loaded. You can now begin program- ming!

If you use one of these installations, we recommend that you consult the instructions for your operating system because there is considerable variance in the best practices among Linux distributions.

IDEs and Text Editors R is a scripting language, and therefore the majority of the work done in the case studies that follow will be done within an IDE or text editor, rather than directly inputted into the R console.

As we show in the next section, some tasks are well suited for the console, such as package installation, but primarily you will want to work within the IDE or text editor of your choice.

As a hacker, you likely already have an IDE or text editor of choice, and we recommend that you use whichever environment you are most comfortable in for the case studies.

There are simply too many options to enumerate here, and we have no intention of inserting ourselves in the infamous Emacs versus Vim debate.

Figure With respect to the case studies we will describe, there are packages for dealing with spatial data, text analysis, network structures, and interacting with web- based APIs, among many others.

As such, we will be relying heavily on the functionality built into several of these packages. Loading packages in R is very straightforward.

There are two functions to perform this: library and require. There are some subtle differences between the two, but for the purposes of this book, the primary difference is that require will return a Boolean TRUE or FALSE value, indicating whether the package is installed on the machine after attempting to load it.

For example, in Chapter 6 we will use the tm package to tokenize text. To load these packages, we can use either the library or require functions.

In the following example, we use library to load tm but use require for XML. If you are working with a fresh installation of R, then you will have to install a number of packages to complete all of the case studies in this book.

There are two ways to install packages in R: either with the GUI or with the install. Given the intended audience for this book, we will be interacting with R exclusively from the console during the case studies, but it is worth pointing out how to use the GUI to install packages.

You can now select the package you wish to install and click Install Selected to install the packages. R for Machine Learning 9 Figure One of the primary advantages of using install.

In these cases you will need to install from source: install. The tm provides a function used to do text mining, and we will use it in Chapter 3 to perform classifications on email text.

One useful parameter in the install. As a best practice, we recommend always setting this to TRUE, especially if you are working with a clean installation of R.

Alternatively, we can also install directly from compressed source files. Using the setwd function to make sure the R working directory is set to the directory where the source file has been saved, we can simply execute the command shown earlier to install directly from the source code.

Note the two parameters that have been altered in this case. The premier package for creating high- quality graphics.

Used for representing social networks. Used to import raw data from the Web. Used to parse data from web-based APIs. Used to work with unstructured text data.

Used to extract structured data from the Web. As mentioned, we will use several packages through the course of this book.

Table lists all of the packages used in the case studies and includes a brief description of their purpose, along with a link to additional information about each.

Given the number of prerequisite packages, to expedite the installation process we have created a short script that will check whether each required package is installed and, if R for Machine Learning 11 it is not, will attempt to install it from CRAN.

Once set, the script will run, and you will see the progress of any required package installation that you did not yet have. We are now ready to begin exploring machine learning with R!

Before we proceed to the case studies, however, we will review some R functions and operations that we will use frequently.

R Basics for Machine Learning As we stated at the outset, we believe that the best way to learn a new technical skill is to start with a problem you wish to solve or a question you wish to answer.

Being excited about the higher-level vision of your work makes learning from case studies effective.

In this review of basic concepts in the R language, we will not be addressing a machine learning problem, but we will encounter several issues related to working with data and managing it in R.

As we will see in the case studies, quite often we will spend the bulk of our time getting the data formatted and organized in a way that suits the anal- ysis.

Usually very little time, in terms of coding, is spent running the analysis. For this case we will address a question with pure entertainment value.

Recently, the data service Infochimps. The data spans hundreds of years and has reports from all over the world. Though it is international, the majority of sightings in the data come from the United States.

With the time and spatial dimensions of the data, we might ask the following questions: are there seasonal trends in UFO sightings; and what, if any, variation is there among UFO sightings across the different states in the US?

This is a great data set to start exploring because it is rich, well-structured, and fun to work with. It is also useful for this exercise because it is a large text file, which is typically the type of data we will deal with in this book.

In such text files there are often messy parts, and we will use base functions in R and some external libraries to clean and organize the raw data.

This section will bring you through, step by step, an entire simple analysis that tries to answer the questions we posed earlier.

We begin by loading the data and required libraries for the analysis. Both of these packages are used for manipulating and organizing data in R, and we will use plyr in this example to aggregate and organize the data.

Note that the file is tab-delimited hence the. Because R exploits defaults very heavily, we have to be particularly conscientious of the default parameter settings for the functions we use in our scripts.

To see how we can learn about parameters in R, suppose that we had never used the read. Alternatively, assume that we do not know that read.

R offers several useful functions for searching for help:? In the first example, we append a question mark to the beginning of the function.

We can also search for specific terms inside of packages by using a combination of?? The double question marks indicate a search for a specific term.

R also allows you to perform less structured help searches with help. The help. Al- ternatively, you can search the R website, which includes help files and the mailing lists archive, using the RSiteSearch function.

Please note that this is by no means meant to be an exhaustive review of R or the functions used in this section.

For the UFO data there are several parameters in read. First, we need to tell the function how the data is delimited.

We know this is a tab-delimited file, so we set sep to the Tab character. Next, when read. In our case, all of the columns are strings, but the default setting for all read.

This class is meant for categorical variables, but we do not want this. In fact, it is always a good prac- tice to switch off this default, especially when working with unfamiliar data.

Also, this data does not include a column header as its first row, so we will need to switch off that default as well to force R to not use the first row in the data as a header.

Finally, there are many empty elements in the data, and we want to set those to the special R value NA. R for Machine Learning 13 To do this, we explicitly define the empty string as the na.

In statistics, categorical variables are very important because we may be interested in what makes certain observations of a certain type.

In R we represent categorical variables as factor types, which essentially assigns numeric references to string la- bels.

We will repeat this process many times. We now have a data frame containing all of the UFO data!

Whenever you are working with data frames, especially when they are from external data sources, it is always a good idea to inspect the data by hand.

Two great functions for doing this are head and tail. Man on Hwy 43 SW of Milwauk.. Man repts.

Sheriff's office calls to re.. The first obvious issue with the data frame is that the column names are generic.

Using the documentation for this data set as a reference, we can assign more meaningful labels to the columns.

Having meaningful column names for data frames is an important best practice. It makes your code and output easier to understand, both for you and other audiences.

We will use the names function, which can either access the column labels for a data structure or assign them.

As in other languages, R treats dates as a special type, and we will want to convert the date strings to actual date types.

To do this, we will use the as. Date function, which will take the date string and attempt to convert it to a Date object.

As such, we will also have to specify a format string in as. Date so the function knows how to convert the strings. Why might this be the case?

We are dealing with a large text file, so perhaps some of the data was malformed in the original set. Assuming this is the case, those data points will not be parsed correctly when loaded by read.

Converting date strings and dealing with malformed data To address this problem, we first need to locate the rows with defective date strings, then decide what to do with them.

To find the problem rows, therefore, we simply need to find those that have strings with more than eight characters. As a best practice, we first inspect the data to see what the malformed data looks like, in order to get a better understanding of what has gone wrong.

In this case, we will use the head function as before to examine the data returned by our logical statement. This function is a vectorized version of the typical if-else logical switch for some Boolean test.

We will see many examples of vectorized opera- tions in R. We need to know the length of the string in each entry of DateOccurred and DateReported, so we use the nchar 1.

For a brief introduction to vectorized operations in R, see R help desk: How can I avoid this loop or make it faster?

R for Machine Learning 15 function to compute this. Once we have the vectors of Booleans, we want to see how many entries in the data frame have been malformed.

Next, we compute the length of that vector to find the number of bad entries. With only rows not conforming, the best option is to simply remove these entries and ignore them.

The latter portion, identifying those that do not conform, is particularly important because we are only interested in sighting variation in the United States and will use this information to isolate those entries.

Organizing location data To manipulate the data in this way, we will first construct a function that takes a string as input and performs the data cleaning.

Then we will run this function over the location data using one of the vectorized apply functions: get. The strsplit function will throw an error if the split character is not matched; therefore, we have to catch this error.

In our case, when there is no comma to split, we will return a vector of NA to indicate that this entry is not valid. Finally, we add an additional check to ensure that only those location vectors of length two are returned.

Many non-US entries have multiple com- mas, creating larger vectors from the strsplit function. In this case, we will again return an NA vector.

As mentioned, members of the apply family of functions in R are extremely useful. They are constructed of the form apply vector, function and return results of the vectorized application of the function to the vector in a specific form.

In our case, we are using lapply, which always returns a list: city. In our case the keys are simply integers, but lists can also have strings as keys.

To do this, we will need to convert this long list into a two-column matrix, with the city data as the leading column: location.

Similar to the apply functions, do. We will often use the com- bination of lapply and do. To get this into the data frame, we use the transform function.

Finally, the state abbreviations are inconsistent, with some uppercase and others lowercase, so we use the tolower function to make them all lowercase.

Specifically, the data includes several UFO sightings from Canada, which also take this form. Fortunately, none of the Canadian province abbreviations match US state abbreviations.

We can use this information to identify non-US entries by constructing a vector of US state abbreviations and keeping only those entries in the USState column that match an entry in this vector: us.

This function takes two arguments: first, the values to be matched, and second, those to be matched against. The function returns a vector of the same length as the first argument in which the values are the index of entries in that vector that match some value in the second vector.

If no match is found, the function returns NA by default. In our case, we are only interested in which entries are NA, as these are the entries that do not match a US state.

We then use the is. Our original data frame now has been manipulated to the point that we can extract from it only the data we are interested in.

By replacing entries that did not meet this criteria in the previous steps, we can use the subset command to create a new data frame of only US incidents: ufo.

Milwaukee wi 3 Telephoned Report:CA woman v Shelton wa 4 Man repts. Columbia mo 5 Anonymous caller repts. Seattle wa 6 Sheriff's office calls to re In the previous section we spent a lot of time getting the data properly formatted and identi- fying the relevant entries for our analysis.

In this section we will explore the data to further narrow our focus. This data has two primary dimensions: space where the sighting happened and time when a sighting occurred.

We focused on the former in the previous section, but here we will focus on the latter. First, we use the summary function on the DateOccurred column to get a sense of this chronological range of the data: summary ufo.

Median Mean 3rd Qu. Given this outlier, the next question is: how is this data distributed over time? And is it worth analyzing the entire time series?

A quick way to look at this visually is to construct a histogram. We will discuss histograms in more detail in the next chapter, but for now you should know that histograms allow you to bin your data by a given dimension and observe the frequency with which your data falls into those bins.

The dimension of interest here is time, so we construct a histogram that bins the data over time: quick.

There are several things to note here. This is our first use of the ggplot2 package, which we use throughout this book for all of our data visualizations.

In this case, we are constructing a very simple histogram that requires only a single line of code. First, we create a ggplot object and pass it the UFO data frame as its initial argument.

Next, we set the x-axis aesthetic to the DateOccurred column, as this is the frequency we are interested in examining.

With ggplot2 we must always work with data frames, and the first argument to create a ggplot object must always be a data frame.

This means the package adheres to this particular philosophy for data visualization, and all visualiza- tions will be built up as a series of layers.

For this histogram, shown in Figure , the initial layer is the x-axis data, namely the UFO sighting dates.

In this case, we will use the default settings for this function, but as we will see later, this default often is not a good choice.

Once the ggplot object has been constructed, we use the ggsave function to output the visualization to a file.

Note the warning message that is printed when you draw the R for Machine Learning 19 visualization.

There are many ways to bin data in a histogram, and we will discuss this in detail in the next chapter, but this warning is provided to let you know exactly how ggplot2 does the binning by default.

We are now ready to explore the data with this visualization. Exploratory histogram of UFO data over time The results of this analysis are stark.

The vast majority of the data occur between and , with the majority of UFO sightings occurring within the last two decades. For our purposes, therefore, we will focus on only those sightings that occurred between and This will allow us to exclude the outliers and compare relatively similar units during the analysis.

As before, we will use the subset function to create a new data frame that meets this criteria: ufo. Date "" nrow ufo.

To see the difference, we regenerate the histogram of the subset data in Figure We see that there is much more variation when looking at this sample.

But which way of aggregating our data is most appropriate here? The DateOccurred column provides UFO sighting information by the day, but there is considerable inconsistency in terms of the coverage throughout the entire set.

We need to aggregate the data in a way that puts the amount of data for each state on relatively level planes.

In this case, doing so by year-month is the best option. This aggregation also best addresses the core of our question, as monthly ag- gregation will give good insight into seasonal variations.

First, we will need to create a new column in the data that corresponds to the years and months present in the data. As before, we will set the format parameter accordingly to get the strings: ufo.

Rather, we simply referenced a column name that did not exist, and R R for Machine Learning 21 automatically added it. Both methods for adding new columns to a data frame are useful, and we will switch between them depending on the particular task.

Next, we want to count the number of times each state and year-month combination occurs in the data.

For the first time we will use the ddply function, which is part of the extremely useful plyr library for manipulating data.

The plyr family of functions work a bit like the map-reduce-style data aggregation tools that have risen in popularity over the past several years.

They attempt to group data in some specific way that was meaningful to all observations, and then do some calcula- tion on each of these groups and return the results.

For this task we want to group the data by state abbreviations and the year-month column we just created.

Once the data is grouped as such, we count the number of entries in each group and return that as a new column.

Here we will simply use the nrow function to reduce the data by the number of rows in each group: sightings.

USState,YearMonth , nrow head sightings. From the head call in the example, however, we can see that there may be a problem with using the data as is because it contains a lot of missing values.

Presumably, there were no UFO sightings in these months, but the data does not include entries for nonsightings, so we have to go back and add these as zeros.

We need a vector of years and months that spans the entire data set. From this we can check to see whether they are already in the data, and if not, add them as zeros.

To do this, we will create a sequence of dates using the seq. Date function, and then format them to match the data in our data frame: date.

Date min ufo. Date max ufo. We will use this to perform the matching with the UFO sighting data. As before, we will use the lapply function to create the columns and the do.

Note that there are now entries from February and March for Alaska. To add in the missing zeros to the UFO sighting data, we need to merge this data with our original data frame.

To do this, we will use the merge func- tion, which takes two ordered data frames and attempts to merge them by common columns. In our case, we have two data frames ordered alphabetically by US state abbreviations and chronologically by year and month.

We need to tell the function which columns to merge these data frames by. We will set the by. Finally, we set the all parameter to TRUE, which instructs the function to include entries that do not match and to fill them with NA.

Those entries in the V1 column will be those state, year, and month entries for which no UFOs were sighted: all.

First, we will set the column names in the new all. This is done in exactly the same way as we did it at the outset. Next, we will convert the NA entries to zeros, again using the is.

Finally, we will convert the YearMonth and State columns to the appropriate types. Using the date. Likewise, the state abbreviations are better represented as categorical variables than strings, so we convert these to factor types.

We will describe factors and other R data types in more detail in the next chapter: names all. Date rep date. R for Machine Learning 23 Analyzing the data For this data, we will address the core question only by analyzing it visually.

For the remainder of the book, we will combine both numeric and visual analyses, but as this example is only meant to introduce core R programming paradigms, we will stop at the visual component.

Unlike the previous histogram visualization, however, we will take greater care with ggplot2 to build the visual layers explicitly.

This will allow us to create a visualization that directly addresses the question of seasonal variation among states over time and produce a more professional-looking visualization.

We will construct the visualization all at once in the following example, then explain each layer individually: state.

Here we are using the all. Again, we need to build an aesthetic layer of data to plot, and in this case the x-axis is the YearMonth column and the y-axis is the Sightings data.

Next, to show seasonal variation among states, we will plot a line for each state. This will allow us to observe any spikes, lulls, or oscillation in the number of UFO sightings for each state over time.

As we have seen throughout this case, the UFO data is fairly rich and includes many sightings across the United States over a long period of time.

Knowing this, we need to think of a way to break up this visualization such that we can observe the data for each state, but also compare it to the other states.

If we plot all of the data in a single panel, it will be very difficult to discern variation. A better approach would be to plot the data for each state individually and order them in a grid for easy comparison.

We also explicitly define the number of rows and columns in the grid, which is easier in our case because we know we are creating 50 different plots.

The ggplot2 package has many plotting themes. The default theme is the one we used in the first example and has a gray background with dark gray gridlines.

Once you become more comfortable with ggplot2, we recommend experi- menting with different defaults to find the one you prefer.

Though not formally required, paying attention to these details is what can separate amateurish plots from professional-looking data visualiza- tions.

In fact, ggplot2 tends to think of colors as a way of distinguishing among different types or categories of data and, as such, prefers to have a factor type used to specify color.

Because this data spans 20 years, we will set these to be at regular five-year intervals. Then we set the tick labels to be the year in a full four-digit format.

Finally, we use the opts function to give the plot a title. There are many more options available in the opts function, and we will see some of them in later chapters, but there are many more that are beyond the scope of this book.

With all of the layers built, we are now ready to render the image with ggsave and analyze the data. There are many interesting observations that fall out of this analysis see Figure We see that California and Washington are large outliers in terms of the number of UFO sightings in these states compared to the others.

Between these outliers, there are also interesting differences. In California, the number of reported UFO sightings seems to be somewhat random over time, but steadily increasing since , whereas in Washington, the seasonal variation seems to be very consistent over time, with regular peaks and valleys in UFO sightings starting from about We can also notice that many states experience sudden spikes in the number of UFO sightings reported.

For example, Arizona, Florida, Illinois, and Montana seem to have experienced spikes around mid, and Michigan, Ohio, and Oregon experienced similar spikes in late Only Michigan and Ohio are geographically close among these groups.

If we do not believe that these are actually the result of extraterrestrial visitors, what are some alternative explanations?

Perhaps there was increased vigilance 3. R for Machine Learning 25 Figure If, however, you are sympathetic to the notion that we may be regularly hosting visitors from outer space, there is also evidence to pique your curiosity.

In fact, there is sur- prising regularity of these sightings in many states in the US, with evidence of regional clustering as well.

It is almost as if the sightings really contain a meaningful pattern. Further Reading on R This introductory case is by no means meant to be an exhaustive review of the language.

Rather, we used this data set to introduce several R paradigms related to loading, cleaning, organizing, and analyzing data.

We will revisit many of these functions and processes in the following chapters, along with many others. For those readers inter- ested in gaining more practice and familiarity with R before proceeding, there are many excellent resources.

These resources can roughly be divided into either reference books and texts or online resources, as shown in Table In the next chapter, we review exploratory data analysis.

Much of the case study in this chapter involved exploring data, but we moved through these steps rather quickly.

In the next chapter we will consider the process of data exploration much more deliberately. R references Title Author Reference Description Text references Data Manipulation with R Phil Spector [Spe08] A deeper review of many of the data manip- ulation topics covered in the previous section, and an introduction to several techniques not covered.

This book takes the R manual and adds several practical examples. The distinction between exploratory data analysis and confirmatory data analysis comes down to us from the famous John Tukey, 1 who emphasized the importance of designing simple tools for practical data analysis.

In this chapter, we describe some of the basic tools that R provides for summa- rizing your data numerically, and then we teach you how to make sense of the results.

After that, we show you some of the tools that exist in R for visualizing your data, and at the same time, we give you a whirlwind tour of the basic visual patterns that you should keep an eye out for in any gization.

The human mind is designed to find patterns in the world and will do so even when those patterns are just quirks of chance.

Because confirmatory data analysis requires more math than exploratory data analysis, this chapter is exclusively concerned with exploratory tools.

The numerical summaries we describe are the stuff of introductory statistics courses: means and modes, percentiles and medians, and standard deviations and variances.

We think simple visualizations are often underappreciated, and we hope we can convince you that you can often learn a lot about your data using only these basic tools.

Much more sophisticated techniques will come up in the later chapters of this book, but the intuitions for analyzing data are best built up while working with the simplest of tools.

What Is Data? For example, you often want to know how the data you have was generated and whether the data can reasonably be expected to be representative of the population you truly want to study.

The interpretation of data requires that you know something about the source of your data. This viewpoint is clearly a substantial simplification, but it will let us motivate many of the big ideas of data analysis visually, which we hope makes what are otherwise very abstract ideas a little more tangible.

An example of this type of data summary is shown in Figure An example of a visual summary of a single column is shown in Figure Summarizing one column in one image Beyond the tools you can use for analyzing isolated columns, there are lots of tools you can use to understand the relationships between multiple columns in your data set.

An example of this is shown in Figure Correlation: summarizing two columns in one number And there are other tools that go further.

An example of what dimensionality reduction techniques achieve is shown in Figure Dimensionality reduction: summarizing many columns in one column As Figures through suggest, summary statistics and dimensionality reduction move along opposite directions: summary statistics tell you something about how all What Is Data?

Inferring the Types of Columns in Your Data Before you do anything else with a new data set, you should try to find out what each column in your current table represents.

Some people like to call this information a data dictionary, by which they mean that you might be handed a short verbal descrip- tion of every column in the data set.

For example, imagine that you had the unlabeled data set in Table given to you. Unlabeled data Indeed, as a starting point you should figure out the type of each column: is the first column really a string, even though it looks like it contains only 0s and 1s?

In the UFO example in the first chapter, we immediately labeled all of the columns of the data set we were given. Three of the most important of these functions are shown in Table Type determination in R R function Description is.

R does not provide a single-character data type. It differs from a character vector in both its hidden internal representation and semantics: most statistical functions in R work on numeric vectors or factor vectors, but not on character vectors.

Having basic type information about each column can be very important as we move forward because a single R function will often do different things depending on the type of its inputs.

In part, this tendency to move back and forth between types comes from a general tradition in machine learning for dealing with categorical distinctions.

Many variables that really work like labels or categories are encoded mathematically as 0 and 1.

You can think of these numbers as if they were Boolean values: 0 might indicate that an email is not spam, a 1 might indicate that the email is spam.

This specific use of 0s and 1s to describe qualitative properties of an object is often called dummy coding in machine learning and statistics.

Factors in R can be thought of as labels, but the labels are actually en- coded numerically in the background: when the programmer accesses the label, the numeric values are translated into the character labels specified in an indexed array of character strings.

Tables through show the same data, but the data has been described with three different encoding schemes. In practice, it might be loaded as a factor or as a string, depending on the data loading function you use see the stringsAsFactors Inferring the Types of Columns in Your Data 35 parameter that was described in Chapter 1 for details.

If you are unsure, it is often better to begin by loading things as strings. You can always convert a string column to a factor column later.

This style of numeric coding is actually required by some machine learning algorithms. Finally, in Table , we show another type of numeric encoding for the same qualitative concept.

This style of encoding qualitative distinctions is very popular with physicists, so you will even- tually see it as you read more about machine learning.

Determining what an unlabeled table of numbers describes can be sur- prisingly difficult. In those cases, human intuition, aided by liberally by searching through Google, is often the only tool that we can suggest to you.

Numeric Summaries One of the best ways to start making sense of a new data set is to compute simple numeric summaries of all of the columns.

R is very well suited to doing this. If you have just one column from a data set as a vector, summary will spit out the most obvious values you should look at first: data.

The minimum value in the vector 2. The median aka the 50th percentile 4. The mean 5. The 3rd quartile aka the 75th percentile 6.

The maximum value This is close to everything you should ask for when you want a quick numeric summary of a data set.

For most hackers, code is a more natural language to express ideas than mathematical symbols, so we think that rolling your own functions to compute means and medians will probably make more sense than showing you the defining equations for those two statistics.

Computing the mean is incredibly easy. In R, you would normally use the mean function. The median is just the opposite: it entirely depends upon the relative position of the numbers in your list.

To get the 25th percentile also known as the 1st quartile , you can split the list at one quarter of its length. The code we wrote in the previous example handles the even-length vector case by taking the average of the two entries that would have been the median if the list had contained an odd number of entries.

To make that point clear, here is a simple example in which the median has to be invented by averaging entries and another case in which the median is exactly equal to the middle entry of the vector: my.

This will also give us an opportunity to test our code: my. For that reason, modes are only really defined visually for many kinds of data sets.

To get a better sense of the range of your data, you might want to know what value is the lowest point in your data. The answer to that question is to use the quantile function in R.

And the mean customer might be even less informative if your data has a strange shape. But central tendencies are only one thing you might want to know about your data.

You can imagine defining the range of your data in a lot of ways. As we already said, you could use the definition that the range function implements: the range is defined by the min and max values.

The min and max will match the outliers perfectly, which makes them fairly brittle definitions of spread. In other words, the definition of range based on min and max effectively depends on only two of your data points, regardless of whether you have two data points or two million data points.

Standard Deviations and Variances 41 Now, there are a lot of ways you could try to meet the requirements we described earlier for a good numeric summary of data.

When you work with more advanced statistical methods, these sorts of ranges will come up again and again. Roughly, the idea is to measure how far, on average, a given number in your data set is from the mean value.

In theory, there could be a few reasons for this, most of which are examples of how things can go wrong when you assume floating-point arithmetic is perfectly accurate.

This is done because the variance that you can estimate from empirical data turns out, for fairly subtle reasons, to be biased downward from its true value.

To put everything back on the original scale, we need to replace the variance with the standard deviation, which is just the square root of the variance: my.

Still, it would be nice to get a sense of how tightly inside the data we are. This is quite typical, especially for data with the shape that our heights data has.

But to finally make that idea about the shape of our data precise, we need to start visualizing our data and define some formal terms for describing the shape of data.

Standard Deviations and Variances 43 Exploratory Data Visualization Computing numerical summaries of your data is clearly valuable.

Visualizing your data is often a more effective way to discover patterns in it. These idealized shapes, also called distributions, are standard patterns that statisticians have studied over the years.

When you find one of these shapes in your data, you can often make broad inferences about your data: how it originated, what sort of abstract prop- erties it will have, and so on.

Even when you think the shape you see is only a vague approximation to your data, the standard distributional shapes can provide you with building blocks that you can use to construct more complex shapes that match your data more closely.

The most typical single-column visualization technique that people use is the histogram. In a histogram, you divide your data set into bins and then count the number of entries in your data that fall into each of the bins.

For instance, in Figure , we create a histogram with one-inch bins to visualize our height data. We can do that in R as follows: library 'ggplot2' data.

Most of the entries are in the middle of your data, near the mean and median height. One way to check this is to try using several other binwidths.

This is something you should always keep in mind when working with histograms: the binwidths you use impose external structure on your data at the same time that they reveal internal struc- ture in your data.

In Figure , we recreate the histogram using five-inch bins with the following R code: ggplot heights. And the opposite problem, called undersmoothing, is just as danger- ous.

In Figure , we again adjust the binwidth, this time to a much smaller 0. Because we have so much data, you can still learn something from this histogram, but a data set with points would be basically worthless if you had used this sort of bindwidth.

Because setting bindwidths can be tedious and because even the best histogram is too jagged for our taste, we prefer an alternative to histograms called kernel density esti- mates KDE or density plots.

Although density plots suffer from most of the same problems of oversmoothing and undersmoothing that plague histograms, we generally Figure Additionally, density plots have some theoretical superiority over histograms: in theory, using a den- sity plot should require fewer data points to reveal the underlying shape of your data than a histogram.

And, thankfully, density plots are just as easy to generate in R as histograms. In Figure , we create our first density plot of the height data: ggplot heights.

Here the density plot suggests that the data is suspiciously flat at the peak value. Here we use the gender of each point to split up our data into two parts.

Next, in Figure we create a density plot in which there are two densities that get superimposed, but are colored in differently to indicate the gender they represent: ggplot heights.

We might expect to see the same bell curve structure in the weights for both genders. In Figure , we make a new density plot for the weights column of our data set: Figure We can easily see an example of the normal distribution by simply splitting up the plot into two pieces, called facets.

In R, we can build this sort of faceted plot as follows: ggplot heights. But the normal distribution is very important in the Figure On a more abstract level, a normal distribution is just a type of bell curve.

It might be any of the bell curves shown in Figures through In these graphs, two parameters vary: the mean of the distribution, which determines the center of the bell curve, and the variance of the distribution, which determines the width of the bell curve.

You should play around with visualizing various versions of the bell curve by playing with the parameters in the following code until you feel comfortable with how the bell curve looks.

To do that, play with the values of m and s in the code shown here: Figure Deinen Artikel finde ich sehr interessant.

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