Running a k-Means Cluster Analysis in SAS, pt. 1

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来自 Wesleyan University 的课程

使用机器学习进行数据分析

202 个评分

Wesleyan University

使用机器学习进行数据分析

202 个评分

课程 4（共 5 门，Specialization Data Analysis and Interpretation）

Are you interested in predicting future outcomes using your data? This course helps you do just that! Machine learning is the process of developing, testing, and applying predictive algorithms to achieve this goal. Make sure to familiarize yourself with course 3 of this specialization before diving into these machine learning concepts. Building on Course 3, which introduces students to integral supervised machine learning concepts, this course will provide an overview of many additional concepts, techniques, and algorithms in machine learning, from basic classification to decision trees and clustering. By completing this course, you will learn how to apply, test, and interpret machine learning algorithms as alternative methods for addressing your research questions.

从本节课中

K-Means Cluster Analysis

Cluster analysis is an unsupervised machine learning method that partitions the observations in a data set into a smaller set of clusters where each observation belongs to only one cluster. The goal of cluster analysis is to group, or cluster, observations into subsets based on their similarity of responses on multiple variables. Clustering variables should be primarily quantitative variables, but binary variables may also be included. In this session, we will show you how to use k-means cluster analysis to identify clusters of observations in your data set. You will gain experience in interpreting cluster analysis results by using graphing methods to help you determine the number of clusters to interpret, and examining clustering variable means to evaluate the cluster profiles. Finally, you will get the opportunity to validate your cluster solution by examining differences between clusters on a variable not included in your cluster analysis. You can use the same variables that you have used in past weeks as clustering variables. If most or all of your previous explanatory variables are categorical, you should identify some additional quantitative clustering variables from your data set. Ideally, most of your clustering variables will be quantitative, although you may also include some binary variables. In addition, you will need to identify a quantitative or binary response variable from your data set that you will not include in your cluster analysis. You will use this variable to validate your clusters by evaluating whether your clusters differ significantly on this response variable using statistical methods, such as analysis of variance or chi-square analysis, which you learned about in Course 2 of the specialization (Data Analysis Tools). Note also that if you are working with a relatively small data set, you do not need to split your data into training and test data sets.

Running a k-Means Cluster Analysis in SAS, pt. 18:14

Running a k-Means Cluster Analysis in SAS, pt. 26:08

与讲师见面

Jen Rose
Research Professor
Psychology
Lisa Dierker
Professor
Psychology

So, let's run a K-means cluster analysis in Sass.

Following my Libname statement and

data step which we are using to call in the data set,

we can delete the observations with missing data on the clustering variables.

We'll first create a dataset that includes only my clustering variables and

the GPA variable.

which I'm going to use to externally validate the clusters.

Then, we will assign each observation a unique identifier.

So, that we can merge the cluster assignment variable back with the main

dataset later on.

We will use the cmiss command to tell Sass to delete observations with missing data.

And of underscore all underscore, in parentheses, to tell Sass to do this for

every variable in the dataset.

I will also turn on ODS graphics with the statement ODS graphics on.

ODS stands for Output Delivery System.

Which manages the output and display such as those in HTML.

Sass will not print any plots if ODS graphics is not turned on.

Then, I will use the surveyselect procedure to randomly split my data set

into a training data set consisting of 70% of the total observations in the data set.

And a test dataset consisting of the other 30% of the observations.

Data equals, specifies the name of my managed dataset, called clust.

And out equals the name of the randomly split output dataset,

which I will call traintest.

With it, we include the seed option.

Which allows us to specify a random number seed to ensure that the data

are randomly split the same way if I run the code again.

The SAMP rate command tells Sass to split the input data set.

So, that 70% of the observations are designated as training observations.

And the remaining 30% are designated as test observations.

Method equals SRS specifies that the data are to be split

using simple random sampling.

And the out all option tells staffs to include both the training and test

observations in a single output data set that has a new variable called selected.

The selected variable indicates whether an observation belongs to the training data

set or the test data set.

Training set observations are coded one on the selected variable and

test observations are coded zero.

In cluster analysis,

variables with large values contribute more to the distance calculations.

Variables measured on different scales should be standardized prior to

clustering.

So, that the solution is not driven by variables measured on larger scales.

We use the following code to standardize the clustering variables to have a mean of

zero and a standard deviation of one.

We use the proc standard procedure.

Data equals is where we provide the name

of our clus under score train training data set.

With the unstandardized clustering variables.

Out equals clustvar, produces a data set called clustvar that

includes the standardized clustering variables.

Mean equals zero and std equals one, tells Sass to standardize the clustering

variables to have a mean of zero and a standard deviation of one.

Then we list the clustering variables that we want to be standardized.

Next, because we don't know how many clusters actually exist in the population,

we will run a series of cluster analyses.

For a range of values for the number of clusters.

Rather than run new Sass code for each value of K,

there's a macro called knean that we can use to automate the process.

The % macro code here, indicates that the code is part of a Sass macro.

The name of the macro is knean and the K in parenthesis indicates that the macro

will run the procedure code for number of different values of K.

Which we specify later.

We will this fastclus procedure to conduct the K means cluster analysis.

The fastclus procedure uses the standardized training data equals

clustvar as input.

In L equals data ampersand K dot,

creates an output data set called outdata for a range of values of K.

This data set contains a variable for cluster assignment for each observation.

And the distance of each observation from the cluster centroid.

The ampersand K dot, tells Sass to add a numeric value to the name of the data set.

So for example, the alpha data set for

K equals one cluster will be called outdata1.

The alpha data set for

K equals two clusters will be called outdata2 and so on.

Outstat equals clusterstat ampersand K dot, creates an output dataset for

the cluster analysis statistics for range of values of K.

Maxclusters equals ampersand K dot, tells Sass to run the cluster analysis.

Specifying the maximum number of clusters for a range of values of K.

And maxiter equals 300,

as to up to 300 iterations be used to find the cluster solution.

Then, we list the standardized clustering variables, then type run, to run the code.

Percent mend tells Sass to stop running the macro.

Following that, we asked Sass to print the output and

create the output data sets for K equals 1 to 9 clusters.

We do this by typing % knean which is the name of the macro and

in parenthesis, the value of K.

You'll do this from 1 to 9 clusters.

We can then create an elbow plot by plotting the r squared values for

each of the k equals one to nine cluster solutions.

To help us determine how many clusters to retain and interpret.

To do this though, we first have to extract the r squared value from

the output For each of the 1 to 9 cluster solutions.

And merge them together using the following code,

data clus1 tells sass to create a dataset called clus1.

Set cluststat1 tells Sass to use the cluster analysis

to a statistics dataset for K=1 to create this dataset.

We are then going to create a variable called nclust.

Which will be the variable that identifies the value of K for the r square.

So we will set nclust=1.

Then we select r-square statistics, which is quoted RSQ and the underscore type,

underscore variable using quotes because it is a string variable.

Finally, we'll keep the nclust variable and the variable label over_all.

Which is the variable that contains the actual r-square value.

Then we do the same for K equals two through nine.

We'll then create one dataset called clusrsquare,that

contains the rsquare values for all nine cluster solutions.

By adding together these nine rsquare data.

Data clusrsquare is the name of our new data set.

Now, we type set and list the nine data sets that we want to add together.

Then we type run to run the code.

Now we can plot the elbow curve using the clusrsquare data set,

with the gplot procedure.

The first line of code provides some display parameters for the plot.

Color equals blue tells Sass to plot the r-square in blue.

And I-N-T-E-R-P-O-L equals join,

tells Sass i to connect each of the plotted r-square values with a line.

Then we type proc gplot and the name of the data set,

which is clusrsquare followed by a semicolon.

In the next line of code, we type the plot command to plot the name of the variable

that has the R2 values over_all on the Y axis.

And the variable that has the number of clusters nclust

on the x axis followed by semi colon.

Then we type run to generate the plot.

So, what this plot shows is the increase in the proportion advantage in

the clustering variables, explained by each of the cluster solutions.

We start with the K equals 1R squared which is zero

because there's no clustering yet.

Then we can see that the two cluster solution accounts for

about 20% of the variance.

The R-square value increases as more clusters are specified.

What we're looking for here is a bend in the elbow that

kind of shows where the R-square value might be leveling off.

Sets the adding more cluster doesn't increase the r-square is much.

We can see how subjective this is though.

There appears to be a couple of bends in the line at 2 clusters,

4 clusters, and again at 8 clusters.

To help us figure out which solutions is best,

we should further examine the results for the 2, 4, and 8 cluster solutions.

To see whether the clusters overlap.

Or the patterns of means on the clustering variables are unique and meaningful.

And whether there are significant differences between the clusters

on our external validation variable, GPA.

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