In R’s partitioning approach, observations are divided into K groups and reshuffled to form the most cohesive clusters possible according to a given criterion. There are two methods—K-means and partitioning around mediods (PAM). In this article, based on chapter 16 of R in Action, Second Edition, author Rob Kabacoff discusses K-means clustering.

In R’s partitioning approach, observations are divided into K groups and reshuffled to form the most cohesive clusters possible according to a given criterion. There are two methods—K-means and partitioning around mediods (PAM). In this article, based on chapter 16 of R in Action, Second Edition, author Rob Kabacoff discusses K-means clustering.

Until Aug 21, 2013, you can buy the book: R in Action, Second Edition with a 44% discount, using the code: “mlria2bl”.

K-means clustering

The most common partitioning method is the K-means cluster analysis. Conceptually, the K-means algorithm:

Selects K centroids (K rows chosen at random)

Assigns each data point to its closest centroid

Recalculates the centroids as the average of all data points in a cluster (i.e., the centroids are p-length mean vectors, where p is the number of variables)

Assigns data points to their closest centroids

Continues steps 3 and 4 until the observations are not reassigned or the maximum number of iterations (R uses 10 as a default) is reached.

Implementation details for this approach can vary.

R uses an efficient algorithm by Hartigan and Wong (1979) that partitions the observations into k groups such that the sum of squares of the observations to their assigned cluster centers is a minimum. This means that in steps 2 and 4, each observation is assigned to the cluster with the smallest value of:

Where k is the cluster,x_{ij} is the value of the j^{th} variable for the i^{th} observation, and x_{kj}-bar is the mean of the j^{th} variable for the k^{th} cluster.

Disclaimer: This post is not intended to be a comprehensive review, but more of a “getting started guide”. If I did not mention an important tool or package I apologize, and invite readers to contribute in the comments.

Introduction

I have recently had the delight to participate in a “Brain Hackathon” organized as part of the OHBM2013 conference. Being supported by Amazon, the hackathon participants were provided with Amazon credit in order to promote the analysis using Amazon’s Web Services (AWS). We badly needed this computing power, as we had 14*10^{9} p-values to compute in order to localize genetic associations in the brain leading to Figure 1.

Figure 1- Brain volumes significantly associated to genotype.

While imaging genetics is an interesting research topic, and the hackathon was a great idea by itself, it is the AWS I wish to present in this post. Starting with the conclusion:

Storing your data and analyzing it on the cloud, be it AWS, Azure, Rackspace or others, is a quantum leap in analysis capabilities. I fell in love with my new cloud powers and I strongly recommend all statisticians and data scientists get friendly with these services. I will also note that if statisticians do not embrace these new-found powers, we should not be surprised if data analysis becomes synonymous with Machine Learning and not with Statistics (if you have no idea what I am talking about, read this excellent post by Larry Wasserman).

As motivation for analysis in the cloud consider:

The ability to do your analysis from any device, be it a PC, tablet or even smartphone.

The ability to instantaneously augment your CPU and memory to any imaginable configuration just by clicking a menu. Then scaling down to save costs once you are done.

The ability to instantaneously switch between operating systems and system configurations.

The ability to launch hundreds of machines creating your own cluster, parallelizing your massive job, and then shutting it down once done.

Here is a quick FAQ before going into the setup stages.

Since its first introduction on this blog, stargazer, a package for turning R statistical output into beautiful LaTeX and ASCII text tables, has made a great deal of progress. Compared to available alternatives (such as apsrtable or texreg), the latest version (4.0) of stargazer supports the broadest range of model objects. In particular, it can create side-by-side regression tables from statistical model objects created by packages AER, betareg, dynlm, eha, ergm, gee, gmm, lme4, MASS, mgcv, nlme, nnet, ordinal, plm, pscl, quantreg, relevent, rms, robustbase, spdep, stats, survey, survival and Zelig. You can install stargazer from CRAN in the usual way:

install.packages(“stargazer”)

New Features: Text Output and Confidence Intervals

In this blog post, I would like to draw attention to two new features of stargazer that make the package even more useful:

stargazer can now produce ASCII text output, in addition to LaTeX code. As a result, users can now create beautiful tables that can easily be inserted into Microsoft Word documents, published on websites, or sent via e-mail. Sharing your regression results has never been easier. Users can also use this feature to preview their LaTeX tables before they use the stargazer-generated code in their .tex documents.

In addition to standard errors, stargazer can now report confidence intervals at user-specified confidence levels (with a default of 95 percent). This possibility might be especially appealing to researchers in public health and biostatistics, as the reporting of confidence intervals is very common in these disciplines.

In the reproducible example presented below, I demonstrate these two new features in action.

Reproducible Example

I begin by creating model objects for two Ordinary Least Squares (OLS) models (using the lm() command) and a probit model (using glm() ). Note that I use data from attitude, one of the standard data frames that should be provided with your installation of R.

I then use stargazer to create a ‘traditional’ LaTeX table with standard errors. With the sole exception of the argument no.space – which I use to save space by removing all empty lines in the table – both the command call and the resulting table should look familiar from earlier versions of the package:

stargazer(linear.1, linear.2, probit.model, title="Regression Results", align=TRUE, dep.var.labels=c("Overall Rating","High Rating"), covariate.labels=c("Handling of Complaints","No Special Privileges", "Opportunity to Learn","Performance-Based Raises","Too Critical","Advancement"), omit.stat=c("LL","ser","f"), no.space=TRUE)

Currently I am doing my master thesis on multi-state models. Survival analysis was my favourite course in the masters program, partly because of the great survival package which is maintained by Terry Therneau. The only thing I am not so keen on are the default plots created by this package, by using plot.survfit. Although the plots are very easy to produce, they are not that attractive (as are most R default plots) and legends has to be added manually. I come across them all the time in the literature and wondered whether there was a better way to display survival. Since I was getting the grips of ggplot2 recently I decided to write my own function, with the same functionality as plot.survfitbut with a result that is much better looking. I stuck to the defaults of plot.survfit as much as possible, for instance by default plotting confidence intervals for single-stratum survival curves, but not for multi-stratum curves. Below you’ll find the code of the ggsurv function. Just as plot.survfit it only requires a fitted survival object to produce a default plot. We’ll use the lung data set from the survival package for illustration. First we load in the function to the console (see at the end of this post).

Once the function is loaded, we can get going, we use the lung data set from the survival package for illustration.

What are the top 100 (most downloaded) R packages in 2013? Thanks to the recent release of RStudio of their “0-cloud” CRAN log files (but without including downloads from the primary CRAN mirror or any of the 88 other CRAN mirrors), we can now answer this question (at least for the months of Jan till May)!

By relying on the nice code that Felix Schonbrodt recently wrote for tracking packages downloads, I have updated my installr R package with functions that enables the user to easily download and visualize the popularity of R packages over time. In this post I will share some nice plots and quick insights that can be made from this great data. The code for this analysis is given at the end of this post.

Top 8 most downloaded R packages – downloads over time

Let’s first have a look at the number of downloads per day for these 5 months, of the top 8 most downloaded packages (click the image for a larger version):

We can see the strong weekly seasonality of the downloads, with Saturday and Sunday having much fewer downloads than other days. This is not surprising since we know that the countries which uses R the most have these days as rest days (see James Cheshire’s world map of R users). It is also interesting to note how some packages had exceptional peaks on some dates. For example, I wonder what happened on January 23rd 2013 that the digest package suddenly got so many downloads, or that colorspace started getting more downloads from April 15th 2013.

“Family tree” of the top 100 most downloaded R packages

We can extract from this data the top 100 most downloaded R packages. Moreover, we can create a matrix showing for each package which of our unique ids (censored IP addresses), has downloaded which package. Using this indicator matrix, we can thing of the “similarity” (or distance) between each two packages, and based on that we can create a hierarchical clustering of the packages – showing which packages “goes along” with one another.

With this analysis, you can locate package on the list which you often use, and then see which other packages are “related” to that package. If you don’t know that package – consider having a look at it – since other R users are clearly finding the two packages to be “of use”.

Such analysis can (and should!) be extended. For example, we can imagine creating a “suggest a package” feature based on this data, utilizing the package which you use, the OS that you use, and other parameters. But such coding is beyond the scope of this post.

Here is the “family tree” (dendrogram) of related packages:

To make it easier to navigate, here is a table with links to the top 100 R packages, and their links:

The question “How many people use my R package?” is a natural question that (I imagine) every R package developer asks himself at some point or another. After many years in the dark, a silver lining has now emerged thanks to the good people at RStudio. Just yesterday, a blog post by Hadley Wickham was written about the newly released CRAN log files of the RStudio cloud CRAN!

And here is the code to allow you to make a similar plot for the package which interests you:

# if (!require('devtools')) install.packages('devtools'); require('devtools')# make sure you have Rtools installed first! if not, then run:#install_Rtools()#install_github('installr', 'talgalili') # get the latest installr R package# or run the code from here:# https://github.com/talgalili/installr/blob/master/R/RStudio_CRAN_data.rif(packageVersion("installr")%in%c("0.8","0.9","0.9.2"))install.packages('installr')#If you have one of the older installr versions, install the latest one....require(installr)# The first two functions might take a good deal of time to run (depending on the date range)
RStudio_CRAN_data_folder <- download_RStudio_CRAN_data(START ='2013-04-02', END ='2013-04-05')# around the time R 3.0.0 was released
my_RStudio_CRAN_data <- read_RStudio_CRAN_data(RStudio_CRAN_data_folder)# barplots: (more functions can easily be added in the future)
barplot_package_users_per_day("plyr", my_RStudio_CRAN_data)
barplot_package_users_per_day("installr", my_RStudio_CRAN_data)

If you (the reader) are interested in helping me extend (/improve) these functions, please do so – I’d be happy to accept pull requests (or comments/e-mails).

This is a guest article by Nina Zumel and John Mount, authors of the new book Practical Data Science with R. For readers of this blog, there is a 50% discount offthe “Practical Data Science with R” book, simply by using the code pdswrblo when reaching checkout (until the 30th this month). Here is the post:

Normalizing data by mean and standard deviation is most meaningful when the data distribution is roughly symmetric. In this article, based on chapter 4 of Practical Data Science with R, the authors show you a transformation that can make some distributions more symmetric.

The need for data transformation can depend on the modeling method that you plan to use. For linear and logistic regression, for example, you ideally want to make sure that the relationship between input variables and output variables is approximately linear, that the input variables are approximately normal in distribution, and that the output variable is constant variance (that is, the variance of the output variable is independent of the input variables). You may need to transform some of your input variables to better meet these assumptions.

In this article, we will look at some log transformations and when to use them.

Monetary amounts—incomes, customer value, account or purchase sizes—are some of the most commonly encountered sources of skewed distributions in data science applications. In fact, as we discuss in Appendix B: Important Statistical Concepts, monetary amounts are often lognormally distributed—that is, the log of the data is normally distributed. This leads us to the idea that taking the log of the data can restore symmetry to it. We demonstrate this in figure 1.

For the purposes of modeling, which logarithm you use—natural logarithm, log base 10 or log base 2—is generally not critical. In regression, for example, the choice of logarithm affects the magnitude of the coefficient that corresponds to the logged variable, but it doesn’t affect the value of the outcome. I like to use log base 10 for monetary amounts, because orders of ten seem natural for money: $100, $1000, $10,000, and so on. The transformed data is easy to read.

An aside on graphing

The difference between using the ggplot layer scale_x_log10 on a densityplot of income and plotting a densityplot of log10(income) is primarily axis labeling. Using scale_x_log10 will label the x-axis in dollars amounts, rather than in logs.

It’s also generally a good idea to log transform data with values that range over several orders of magnitude. First, because modeling techniques often have a difficult time with very wide data ranges, and second, because such data often comes from multiplicative processes, so log units are in some sense more natural.

For example, when you are studying weight loss, the natural unit is often pounds or kilograms. If I weigh 150 pounds, and my friend weighs 200, we are both equally active, and we both go on the exact same restricted-calorie diet, then we will probably both lose about the same number of pounds—in other words, how much weight we lose doesn’t (to first order) depend on how much we weighed in the first place, only on calorie intake. This is an additive process.

On the other hand, if management gives everyone in the department a raise, it probably isn’t by giving everyone $5000 extra. Instead, everyone gets a 2 percent raise: how much extra money ends up in my paycheck depends on my initial salary. This is a multiplicative process, and the natural unit of measurement is percentage, not absolute dollars. Other examples of multiplicative processes: a change to an online retail site increases conversion (purchases) for each item by 2 percent (not by exactly two purchases); a change to a restaurant menu increases patronage every night by 5 percent (not by exactly five customers every night). When the process is multiplicative, log-transforming the process data can make modeling easier.

Of course, taking the logarithm only works if the data is non-negative. There are other transforms, such as arcsinh, that you can use to decrease data range if you have zero or negative values. I don’t like to use arcsinh, because I don’t find the values of the transformed data to be meaningful. In applications where the skewed data is monetary (like account balances or customer value), I instead use what I call a “signed logarithm”. A signed logarithm takes the logarithm of the absolute value of the variable and multiplies by the appropriate sign. Values with absolute value less than one are mapped to zero. The difference between log and signed log are shown in figure 2.

Clearly this isn’t useful if values below unit magnitude are important. But with many monetary variables (in US currency), values less than a dollar aren’t much different from zero (or one), for all practical purposes. So, for example, mapping account balances that are less than a dollar to $1 (the equivalent every account always having a minimum balance of one dollar) is probably okay.

Once you’ve got the data suitably cleaned and transformed, you are almost ready to start the modeling stage.

Summary

At some point, you will have data that is as good quality as you can make it. You’ve fixed problems with missing data, and performed any needed transformations. You are ready to go on the modeling stage. Remember, though, that data science is an iterative process. You may discover during the modeling process that you have to do additional data cleaning or transformation.