In the final chapter the authors introduce Support Vector Machines (SVM). What SVM do are generalize linear decision boundaries for classification. Like the other chapters, this one avoids math and simply shows you how to use SVM in R. It then analyzes the spam mail dataset from chapter 3 using SVM, kNN and regularized logistic regression and compares their performance.

The first section of the chapter demonstrates SVM using a toy dataset. The dataset has two predictors (X and Y) and a response (a classification of 0 or 1). The dataset looks like this plotted:


I show this figure because the book is printed in black and white and you can’t tell class 0 from class 1 in the picture on page 276. That’s a problem that plagues this entire chapter. Anyway, what we have here is data that require a non-linear decision boundary. In other words we can’t draw a single straight line through the picture to indicate a boundary between the blue and red dots. This is where SVM comes in handy. Here’s the SVM code they use to analyze this dataset. As you’ll see they play around with the svm function from the e1071 package to show how changing certain parameters affects the quality of predictions. I didn’t get anything new out of this section that I felt compelled to blog about. It’s basically an extended example of how to use the svm function similar to what you might see on a help page. They do make use of the melt function from the reshape package, which is very cool and useful, but I already wrote about that in the Chapter 8 post.

The second section is “Comparing Algorithms”. They resurrect the spam dataset from chapter 3 and analyze it using SVM, kNN and regularized logistic regression. Recall the spam dataset was converted to a term document matrix (TDM) where the emails are the rows and the columns are terms. So email #1 would be row 1. In that row we would see the number of times the words in the column headers appeared. For example. the word “banner” appears 0 times in email #1. Column 1 of the spam dataset indicates whether or not the email is spam. They create testing and training sets and use those to create models and compare the different classification methods. Again, there’s nothing too fancy here where R programming is concerned, or at least nothing I haven’t already covered. They determine logistic regression works best for classifying spam email.

Now here’s something interesting worth noting. Instead of prepping the spam data as they did in Chapter 3, they skip directly to loading it into R as follows:

load('data/dtm.RData')

But how did they save that data as dtm.Rdata? By doing something like this:

save(dtm, file="dtm.RData")

…where dtm was a matrix. I say “matrix” because that’s what dtm.RData is when it gets loaded.

Another snippet worth noting is how they create their training and test sets. First they randomly select numbers as the indices for selecting the training data from the number of rows from the spam matrix. Then they take whatever numbers were not selected and make those the indices for the test data:

training.indices <- sort(sample(1:nrow(dtm), round(0.5 * nrow(dtm))))
test.indices <- which(! 1:nrow(dtm) %in% training.indices)

The dtm dataset has 3249 rows. So the sample function selects (without replacement) from the numbers 1 through 3249. The second argument to the sample function says how many to sample, which in this case is \( 0.5 \times 3249 = 1624.5 \). That gets rounded to 1624 by the round function. So 1624 numbers are sampled without replacement from the numbers 1 through 3249. And then they get sorted in ascending order. Those are the indices for the training data. To get the test data, they use the value matching %in% operator to look for matches, but negate the matches to get all the numbers that were not selected with the sample function.

The code "1:nrow(dtm) %in% training.indices" returns a logical vector with 3249 elements. 1624 are TRUE, the rest are FALSE. The code "! 1:nrow(dtm) %in% training.indices" returns the opposite logical vector. Now 1624 are FALSE and the rest are TRUE. Finally, inserting that strip of code into the which function returns the indices of the vector that are FALSE. Therefore both training.indices and test.indices are vectors of numbers from 1:3249, with no overlap between them. For example:

> training.indices[1:10]
 [1] 1 2 6 9 11 12 15 16 18 19
> test.indices[1:10]
 [1] 3 4 5 7 8 10 13 14 17 24

These vectors of numbers are then used to select the training and test data as follows:

train.x <- dtm[training.indices, 3:ncol(dtm)]
train.y <- dtm[training.indices, 1]

test.x <- dtm[test.indices, 3:ncol(dtm)]
test.y <- dtm[test.indices, 1]

I thought that was good to go through and understand since all the functions in this section require data (or are capable of taking data) in this format. For example:

library('glmnet')
regularized.logit.fit <- glmnet(train.x, train.y, family = c('binomial'))
library('e1071')
linear.svm.fit <- svm(train.x, train.y, kernel = 'linear')
library('class')
knn.fit <- knn(train.x, test.x, train.y, k = 50)

And that does it for me! I'm ready to move on to another book.

Are you a heavy Twitter user? Would you like to build a custom recommendation system in R that will recommend new Twitter feeds for you to follow? If you answered “yes” to both questions then this is the chapter for you. Here’s the code. Have fun.

Now I don’t use Twitter, so this chapter was not very interesting for me. I should probably use Twitter and get with it and join the 2010’s. But at the moment I don’t, so building a Twitter recommendation system in R doesn’t do me any good. I guess I could have followed along and built the recommendation system in the book for one of the authors, but I just couldn’t motivate. It’s a lot of code that requires new packages. Plus there’s a section that requires using a program outside of R called Gephi. It’s an extremely specific case study. It’s not like some of the other chapters where they introduce a general machine learning method, like kNN or PCA, and show an example of how to use it. There is nothing general about this chapter. At one point they do make use of hierarchical clustering to find similarities between Twitter users. Clustering is a common machine learning tactic. But they only give it a couple of pages. I hate to sound down on the chapter. It’s well done and the authors put a lot of work into it. Personally, though, I just couldn’t get excited about it.

Having said that, I did see some interesting things in the R code that I wanted to file away and remember. The first was creating an empty vector. In a loop they run, they sometimes get a null result and want to store an empty vector for that pass. They do this as follows:

y <- c(integer(0), integer(0))

What caught my eye was the way rbind handles those vectors. It ignores them. I could see that being potentially useful. Here's a toy demonstration:

x <- c(5, 4)
y <- c(integer(0), integer(0))
z <- c(3, 2)
rbind(x,y,z)
   [,1] [,2]
x     5    4
z     3    2

Another snippet I wanted to note was how to identify unique values in a matrix. You use the unique function, which I was familiar with. What I didn't know was that you can do it for a matrix by calling the columns of the matrix, like this:

mat <- matrix(floor(runif(10,2,8)),5,2)
mat
           [,1] [,2]
[1,]        4      3
[2,]        2      7
[3,]        7      2
[4,]        3      7
[5,]        5      7
> unique(c(mat[,1],mat[,2]))
[1] 4 2 7 3 5

This chapter also used a base function that I had never seen before called duplicated. It returns a vector of True/False values that tells you whether or not the value occurs previously in the vector. I was surprised I hadn't heard of it before. Here's a demo of duplicated:

x <- c(1:5,2:6)
x
[1] 1 2 3 4 5 2 3 4 5 6
duplicated(x)
[1] FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE
!duplicated(x)
[1] TRUE TRUE TRUE TRUE TRUE FALSE FALSE FALSE FALSE TRUE
x[duplicated(x)]
[1] 2 3 4 5
x[!duplicated(x)]
[1] 1 2 3 4 5 6

Finally they make use of sapply in one of their functions and I wanted to document its use. The suite of apply functions always give me trouble for some reason. I get the gist of what they do, I just have a hard time remember why I would want to use one over the other. Anyway, what they do is use sapply to run a function over each row of a matrix. That seems like a useful thing to remember. First let's create a 100 x 3 data frame of values:

a <- rnorm(100,2,4)
b <- rnorm(100,3,4)
c <- rnorm(100,5,4)
df <- data.frame(a,b,c)

Now, let's say I wanted to create a True/False vector indicating which rows contained a value less than 0. Here's how I can do that using sapply:

sapply(1:nrow(df), function(i) ifelse(any(df[i,]<0),1,0))

The authors did something similar to that and then used the vector of T/F values to subset another vector. Of course if I wanted to subset my example data frame above to show only rows that contain a value less than o, then I could do this:

subset(df, a < 0 | b <0 | c < 0)

So that's the helpful R code I gleaned from Chapter 11. I feel like there should be more. It's a long chapter with a lot of code. But much of it either involves functions from specific packages or uses common R functions I've already documented or know about. Next up is chapter 12, the final chapter.

k-nearest neighbors (kNN) is the topic of chapter 10. The authors say it’s the most intuitive of the machine learning algorithms covered in the book and I guess I would agree, provided you understand the euclidean distance formula, understand what a distance matrix is, and know a little about how R works.

They provide a toy dataset (named “df”) to demonstrate how kNN works. It looks like this:

         X        Y Label
1 2.373546 5.398106     0
2 3.183643 4.387974     0
3 2.164371 5.341120     0
4 4.595281 3.870637     0
5 3.329508 6.433024     0
6 2.179532 6.980400     0

Think of the rows as points lying in an XY plane. Notice they also have labels. The dataset has 100 rows, with 50 labeled 0 and 50 labeled 1. To run the kNN algorithm, we need to create a distance matrix that stores the distance between all the points. So row 1 of the distance matrix would have the distances of all points from the first point (2.373546, 5.398106). Row 2 would have the distances of all points from (3.183643, 4.387974). And so on. The authors actually write a function to create the distance matrix, which is good for illustrating how the distance matrix is created, but I want to note you can use the built-in “dist” function for this:

distance <- as.matrix(dist(df, diag=TRUE, upper=TRUE))

I set the "diag" and "upper" parameters to TRUE in order to match the matrix they create. The result is this:

 distance[1:3,1:3]
          1        2         3
1 0.0000000 1.294845 0.2167983
2 1.2948454 0.000000 1.3954937
3 0.2167983 1.395494 0.0000000

That's just a portion of the matrix. The full matrix is 100 x 100. The first row (or first column) refers to point 1 (2.373546, 5.398106). distance[1,1] is 0 because that's how far point 1 is from itself. distance[1,2] is 1.294845 because that's how far point 2 (3.183643, 4.387974) is from point 1. The distance between two points A() and B() is calculated using the Euclidean distance formula:

$$ AB = \sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2}}$$

$$ 1.294845 = \sqrt{(2.373546-3.183643)^{2} + (5.398106-4.387974)^{2}}$$

Once we have our distance matrix, we can find the k-nearest neighbors for a particular point by sorting the row from smallest to greatest distance. We can use the order function to help us do this. For example, let's find the 5 nearest neighbors for the first point:

indices <- order(distance[1,])[2:6]
indices
[1] 46 3 36 13 29
distance[1,indices]
46        3         36        13        29 
0.1796931 0.2167983 0.2212696 0.2916801 0.3561144

The order function returns the index positions of the nearest neighbors in the distance matrix. The index position can also be thought of as the identifying point number. So the closest neighbor of point 1 is point 46. The second-closest neighbor of point 1 is point 3. The command "distance[1,indices]" shows us the 5 closest points and their distances. What are their labels?

df[indices,'Label']
[1] 0 0 0 0 0

They're all 0's. If we wanted to predict the label of point 1, we could use majority rule. In this case since the 5-nearest neighbors are all labeled "0", we would predict point 1 is also labeled "0". (In truth, it is.) The authors carry this out for the entire dataset of 100 points and correctly predict the label for 93 of them given their 5-nearest neighbors.

The case study in this chapter is recommending R packages. The dataset is a list of 2487 packages, listed 50 times over for 50 programmers, with an indicator of whether or not that package is installed for the programmer. Using kNN they build a list of 25 recommendations for each programmer. Here's the code.

Next up is Chapter 11, Analyzing Social Graphs. It looks like the case study will involve building an engine to recommend people to follow on Twitter. I guess I'm a poopy stick-in-the-mud because this doesn't appeal to me. I'm not really into the Twitter. But I'll keep an open mind, slog through it and learn as much as I can.

In this chapter we learn a little about Multidimensional Scaling, or MDS for short. Like PCA in Chapter 8, MDS is a topic usually taught in multivariate statistics classes. I guess it’s classified as machine learning because of the computing required to do it, though the same can be said of almost any statistical method. The MDS that is presented is the classical type (as opposed to the non-metric type). The case study is exploring similarity in the US Senate based on votes. As it turns out, a proper MDS analysis shows Democrats and Republicans indeed vote differently and are quite polarized. Not surprising but better than anecdotal evidence from some political pundit.

Now if you’ve been following my series of posts on this book (and I’m pretty sure you haven’t) then you know I don’t summarize the chapter but rather highlight the R code that I found interesting and new. But for the first time I really don’t have much to highlight. It’s a short chapter and the data for the case study required very little preparation. I was actually able to follow all the R code without running to the help pages and Google. Still, though, I feel like I should document something from this chapter.

How about reading in a bunch of files. I feel like this something I will forget how to do one day, so I should probably write about it to help form some memory. First they define a variable that stores a path and then they call the list.files function to create a vector of file names:

data.dir <- "data/roll_call/"
data.files <- list.files(data.dir)

Next they use the lapply function to create one big list object that contains the contents of all those files, which happen to be Stata data sets:

rollcall.data <- lapply(data.files, function(f) 
read.dta(paste(data.dir, f, sep=""), convert.factors=FALSE))

So the lapply function applies the read.dta function to each element in the data.files vector, which is file name. But in the read.dta function you'll notice the paste function is called to create a full path with the file name. Just dandy. That never fails to impress.

If you want to inspect some of the data, you can't just do head(rollcall.data). Since it's a list object you have to do something like this:

head(rollcall.data[[1]])

That shows the first 6 rows of the data stored in the first list element.

Later on they use the strsplit function to split first and last names of senators by comma. I'm pretty sure I've posted about this before, but it doesn't hurt to mention it again. Running a vector through strplit returns a list. For example:

 strsplit(congress$name[1], "[, ]")
[[1]]
[1] "SHELBY" ""       "RIC"

If I just want the last name, I can do this:

 strsplit(congress$name[1], "[, ]")[[1]][1]
[1] "SHELBY"

Now the authors use the strsplit function in an sapply function, like this:

congress.names <- sapply(congress$name, function(n) 
strsplit(n, "[, ]")[[1]][1])

That gives us this:

 head(congress.names)
SHELBY, RIC HEFLIN, HOW STEVENS, TH MURKOWSKI,  DECONCINI,  MCCAIN, JOH 
"SHELBY"    "HEFLIN"   "STEVENS" "MURKOWSKI" "DECONCINI"    "MCCAIN"

Notice each element in the vector has a "name". Ugly, I think, though it doesn't matter in the context of what they do. But what if you wanted a clean vector of last names without the "names"? You can do this:

congress.names <- sapply(congress$name, function(n) 
strsplit(n, "[, ]")[[1]][1],USE.NAMES = FALSE)
head(congress.names)
[1] "SHELBY"    "HEFLIN"    "STEVENS"   "MURKOWSKI" "DECONCINI" "MCCAIN"

Much better. Notice the USE.NAMES = FALSE setting. Pretty self-explanatory what it does.

If you want to see the rest of their code including how they carry out the MDS analysis and MDS clustering plots, see their git hub page. For more on how exactly MDS works, see Chapter 14 of A Handbook of Statistical Analyses Using R.