## K-means Clustering (from "R in Action")

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:

1. Selects K centroids (K rows chosen at random)
2. Assigns each data point to its closest centroid
3. 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)
4. Assigns data points to their closest centroids
5. 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,xij is the value of the jth variable for the ith observation, and xkj-bar is the mean of the jth variable for the kth cluster.

## Interactive Graphics with the iplots Package (from “R in Action”)

The followings introductory post is intended for new users of R.  It deals with interactive visualization using R through the iplots package.

This is a guest article by Dr. Robert I. Kabacoff, the founder of (one of) the first online R tutorials websites: Quick-R. Kabacoff has recently published the book ”R in Action“, providing a detailed walk-through for the R language based on various examples for illustrating R’s features (data manipulation, statistical methods, graphics, and so on…). In previous guest posts by Kabacoff we introduced data.frame objects in R and dealt with the Aggregation and Restructuring of data (using base R functions and the reshape package).

For readers of this blog, there is a 38% discount off the “R in Action” book (as well as all other eBooks, pBooks and MEAPs at Manning publishing house), simply by using the code rblogg38 when reaching checkout.

Let us now talk about Interactive Graphics with the iplots Package:

### Interactive Graphics with the iplots Package

The base installation of R provides limited interactivity with graphs. You can modify graphs by issuing additional program statements, but there’s little that you can do to modify them or gather new information from them using the mouse. However, there are contributed packages that greatly enhance your ability to interact with the graphs you create—playwith, latticist, iplots, and rggobi. In this article, we’ll focus on functions provided by the iplots package. Be sure to install it before first use.

While playwith and latticist allow you to interact with a single graph, the iplots package takes interaction in a different direction. This package provides interactive mosaic plots, bar plots, box plots, parallel plots, scatter plots, and histograms that can be linked together and color brushed. This means that you can select and identify observations using the mouse, and highlighting observations in one graph will automatically highlight the same observations in all other open graphs. You can also use the mouse to obtain information about graphic objects such as points, bars, lines, and box plots.

The iplots package is implemented through Java and the primary functions are listed in table 1.

Table 1 iplot functions

 Function Description ibar() Interactive bar chart ibox() Interactive box plot ihist() Interactive histogram imap() Interactive map imosaic() Interactive mosaic plot ipcp() Interactive parallel coordinates plot iplot() Interactive scatter plot

To understand how iplots works, execute the code provided in listing 1.

Listing 1 iplots demonstration

 1 2 3 4 5 6 7 8 9 10 11 12 library(iplots) attach(mtcars) cylinders <- factor(cyl) gears <- factor(gear) transmission <- factor(am) ihist(mpg) ibar(gears) iplot(mpg, wt) ibox(mtcars[c("mpg", "wt", "qsec", "disp", "hp")]) ipcp(mtcars[c("mpg", "wt", "qsec", "disp", "hp")]) imosaic(transmission, cylinders) detach(mtcars)

Six windows containing graphs will open. Rearrange them on the desktop so that each is visible (each can be resized if necessary). A portion of the display is provided in figure 1.

Figure 1 An iplots demonstration created by listing 1. Only four of the six windows are displayed to save room. In these graphs, the user has clicked on the three-gear bar in the bar chart window.

Now try the following:

• Click on the three-gear bar in the Barchart (gears) window. The bar will turn red. In addition, all cars with three-gear engines will be highlighted in the other graph windows.
• Mouse down and drag to select a rectangular region of points in the Scatter plot (wt vs mpg) window. These points will be highlighted and the corresponding observations in every other graph window will also turn red.
• Hold down the Ctrl key and move the mouse pointer over a point, bar, box plot, or line in one of the graphs. Details about that object will appear in a pop-up window.
• Right-click on any object and note the options that are offered in the context menu. For example, you can right-click on the Boxplot (mpg) window and change the graph to a parallel coordinates plot (PCP).
• You can drag to select more than one object (point, bar, and so on) or use Shift-click to select noncontiguous objects. Try selecting both the three- and five-gear bars in the Barchart (gears) window.

The functions in the iplots package allow you to explore the variable distributions and relationships among variables in subgroups of observations that you select interactively. This can provide insights that would be difficult and time-consuming to obtain in other ways. For more information on the iplots package, visit the project website at http://rosuda.org/iplots/.

### Summary

In this article, we explored one of the several packages for dynamically interacting with graphs, iplots. This package allows you to interact directly with data in graphs, leading to a greater intimacy with your data and expanded opportunities for developing insights.

This article first appeared as chapter 16.4.4 from the “R in action book, and is published with permission from Manning publishing house.  Other books in this serious which you might be interested in are (see the beginning of this post for a discount code):

## data.frame objects in R (via “R in Action”)

The followings introductory post is intended for new users of R.  It deals with R data frames: what they are, and how to create, view, and update them. This is a guest article by Dr. Robert I. Kabacoff, the founder of (one of) the first online R tutorials websites: Quick-R.  Kabacoff has recently published the book ”R […]

The followings introductory post is intended for new users of R.  It deals with R data frames: what they are, and how to create, view, and update them.

This is a guest article by Dr. Robert I. Kabacoff, the founder of (one of) the first online R tutorials websites: Quick-R.  Kabacoff has recently published the book ”R in Action“, providing a detailed walk-through for the R language based on various examples for illustrating R’s features (data manipulation, statistical methods, graphics, and so on…)

For readers of this blog, there is a 38% discount off the “R in Action” book (as well as all other eBooks, pBooks and MEAPs at Manning publishing house), simply by using the code rblogg38 when reaching checkout.

Let us now talk about data frames:

### Data Frames

A data frame is more general than a matrix in that different columns can contain different modes of data (numeric, character, and so on). It’s similar to the datasets you’d typically see in SAS, SPSS, and Stata. Data frames are the most common data structure you’ll deal with in R.

The patient dataset in table 1 consists of numeric and character data.

Table 1: A patient dataset

 PatientID AdmDate Age Diabetes Status 1 10/15/2009 25 Type1 Poor 2 11/01/2009 34 Type2 Improved 3 10/21/2009 28 Type1 Excellent 4 10/28/2009 52 Type1 Poor

Because there are multiple modes of data, you can’t contain this data in a matrix. In this case, a data frame would be the structure of choice.

A data frame is created with the data.frame() function:

 1 mydata <- data.frame(col1, col2, col3,…)

where col1, col2, col3, … are column vectors of any type (such as character, numeric, or logical). Names for each column can be provided with the names function.

The following listing makes this clear.

Listing 1 Creating a data frame

 1 2 3 4 5 6 7 8 9 10 11 > patientID <- c(1, 2, 3, 4) > age <- c(25, 34, 28, 52) > diabetes <- c("Type1", "Type2", "Type1", "Type1") > status <- c("Poor", "Improved", "Excellent", "Poor") > patientdata <- data.frame(patientID, age, diabetes, status) > patientdata patientID age diabetes status 1 1 25 Type1 Poor 2 2 34 Type2 Improved 3 3 28 Type1 Excellent 4 4 52 Type1 Poor

Each column must have only one mode, but you can put columns of different modes together to form the data frame. Because data frames are close to what analysts typically think of as datasets, we’ll use the terms columns and variables interchangeably when discussing data frames.

There are several ways to identify the elements of a data frame. You can use the subscript notation or you can specify column names. Using the patientdata data frame created earlier, the following listing demonstrates these approaches.

Listing 2 Specifying elements of a data frame

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 > patientdata[1:2] patientID age 1 1 25 2 2 34 3 3 28 4 4 52 > patientdata[c("diabetes", "status")] diabetes status 1 Type1 Poor 2 Type2 Improved 3 Type1 Excellent 4 Type1 Poor > patientdata\$age #age variable in the patient data frame [1] 25 34 28 52

The \$ notation in the third example is used to indicate a particular variable from a given data frame. For example, if you want to cross-tabulate diabetes type by status, you could use the following code:

 1 2 3 4 5 > table(patientdata\$diabetes, patientdata\$status)   Excellent Improved Poor Type1 1 0 2 Type2 0 1 0

It can get tiresome typing patientdata\$ at the beginning of every variable name, so shortcuts are available. You can use either the attach() and detach() or with() functions to simplify your code.

### attach, detach, and with

The attach() function adds the data frame to the R search path. When a variable name is encountered, data frames in the search path are checked in order to locate the variable. Using a sample (mtcars) data frame, you could use the following code to obtain summary statistics for automobile mileage (mpg), and plot this variable against engine displacement (disp), and weight (wt):

 1 2 3 summary(mtcars\$mpg) plot(mtcars\$mpg, mtcars\$disp) plot(mtcars\$mpg, mtcars\$wt)

This could also be written as

 1 2 3 4 5 attach(mtcars) summary(mpg) plot(mpg, disp) plot(mpg, wt) detach(mtcars)

The detach() function removes the data frame from the search path. Note that detach() does nothing to the data frame itself. The statement is optional but is good programming practice and should be included routinely.

The limitations with this approach are evident when more than one object can have the same name. Consider the following code:

 1 2 3 4 5 6 7 8 9 > mpg <- c(25, 36, 47) > attach(mtcars)   The following object(s) are masked _by_ ‘.GlobalEnv’: mpg > plot(mpg, wt) Error in xy.coords(x, y, xlabel, ylabel, log) : ‘x’ and ‘y’ lengths differ > mpg [1] 25 36 47

Here we already have an object named mpg in our environment when the mtcars data frame is attached. In such cases, the original object takes precedence, which isn’t what you want. The plot statement fails because mpg has 3 elements and disp has 32 elements. The attach() and detach() functions are best used when you’re analyzing a single data frame and you’re unlikely to have multiple objects with the same name. In any case, be vigilant for warnings that say that objects are being masked.

An alternative approach is to use the with() function. You could write the previous example as

 1 2 3 4 5 with(mtcars, { summary(mpg, disp, wt) plot(mpg, disp) plot(mpg, wt) })

In this case, the statements within the {} brackets are evaluated with reference to the mtcars data frame. You don’t have to worry about name conflicts here. If there’s only one statement (for example, summary(mpg)), the {} brackets are optional.

The limitation of the with() function is that assignments will only exist within the function brackets. Consider the following:

 1 2 3 4 5 6 7 8 > with(mtcars, { stats <- summary(mpg) stats }) Min. 1st Qu. Median Mean 3rd Qu. Max. 10.40 15.43 19.20 20.09 22.80 33.90 > stats Error: object ‘stats’ not found

If you need to create objects that will exist outside of the with() construct, use the special assignment operator <<- instead of the standard one (<-). It will save the object to the global environment outside of the with() call. This can be demonstrated with the following code:

 1 2 3 4 5 6 7 8 9 > with(mtcars, { nokeepstats <- summary(mpg) keepstats <<- summary(mpg) }) > nokeepstats Error: object ‘nokeepstats’ not found > keepstats Min. 1st Qu. Median Mean 3rd Qu. Max. 10.40 15.43 19.20 20.09 22.80 33.90

Most books on R recommend using with() over attach(). I think that ultimately the choice is a matter of preference and should be based on what you’re trying to achieve and your understanding of the implications.

### Case identifiers

In the patient data example, patientID is used to identify individuals in the dataset. In R, case identifiers can be specified with a rowname option in the data frame function. For example, the statement

 1 2 patientdata <- data.frame(patientID, age, diabetes, status, row.names=patientID)

specifies patientID as the variable to use in labeling cases on various printouts and graphs produced by R.

### Summary

One of the most challenging tasks in data analysis is data preparation. R provides various structures for holding data and many methods for importing data from both keyboard and external sources. One of those structures is data frames, which we covered here. Your ability to specify elements of these structures via the bracket notation is particularly important in selecting, subsetting, and transforming data.

R offers a wealth of functions for accessing external data. This includes data from flat files, web files, statistical packages, spreadsheets, and databases. Note that you can also export data from R into these external formats. We showed you how to use either the attach() and detach() or with() functions to simplify your code.

This article first appeared as chapter 2.2.4 from the “R in action book, and is published with permission from Manning publishing house.