Download Comparison Of Enterprise Miner And SAS/STAT For Data Mining

Paper DM100
Comparison of Enterprise Miner and SAS/Stat for Data Mining
Patricia B. Cerrito, University of Louisville, Louisville, KY
ABSTRACT
There are many definitions of data mining: the discovery of spurious relationships in the data; automated data
analysis; examination of large data sets; exploratory data analysis. Early methods of data mining included stepwise
regression, cluster analysis, and discriminant analysis. Data mining should be thought of as a process that includes
data cleaning, investigation of the data using models, and validation of potential results. In particular, practical
significance should be emphasized over statistical significance. Also, decision making and the cost of
misclassification is important. SAS/Stat contains methods that can be used to investigate data using a data mining
process. These methods can complement those developed specifically for Enterprise Miner, and can be used in
conjunction with Enterprise Miner. This paper will examine data mining in SAS/Stat, contrasting it with Enterprise
Miner.
INTRODUCTION
The term “data mining” has now come into public use with little understanding of what it is or does. In the past,
statisticians have thought little of data mining because data were examined without the final step of model validation.
Data mining differs from standard statistical practice in that the process
Assumes large data samples
Assumes large numbers of variables
Has Validation as a routine, automatic part of the process
Examines the cost of misclassification
Emphasizes decision-making over inference
And yet there remains overlap between statistics and data mining in both technique and practice. Since many of the
techniques, such as cluster analysis, overlap both statistics and data mining, it is the purpose of this paper to
examine some of the differences and similarities in the use of these overlapping techniques from a statistical
perspective versus a data mining perspective.
To demonstrate the different techniques, a dataset consisting of responses to a survey concerning student
expectations in mathematics courses was used throughout. A list of questions asked in the survey is given in the
appendix. The data were coded ordinally and variable names were coded to represent the questions. The data
analysis was performed to investigate the relationship between variables and responses in the dataset. A total of 192
responses were collected from this survey. The basic survey questions are
The areas of mathematics which interest me are (Check all that apply):
_____Pure mathematics
_____Applied mathematics
_____Abstract Algebra
_____Number Theory
_____Topology
_____Real analysis
_____Discrete mathematics
_____Differential equations
_____Actuarial Science
_____Probability
_____Statistics
The students were also asked whether they were graduate or undergraduate, and how many hours per week they
estimated they studied mathematics.
CLUSTER ANALYSIS
As a data mining process, clustering is considered to be unsupervised learning, meaning that there is no specific
outcome variable. Clustering involves the following process:
Group observations or group variables
Choice of type-hierarchical or non-hierarchical
Number of clusters
Cluster identity
Validation
1
Hierarchical clustering involves the grouping of observations based upon the distance between observations.
Distance can be defined using different criteria available in PROC CLUSTER. The clusters are built based on a
hierarchical tree structure. The closest observations are grouped together initially followed by the next closest match.
The other method of clustering is based upon the selection of random seed values as the centers of spheres
containing all observations closest to that center (PROC FASTCLUS). Then the centers are re-defined based upon
the outcomes. In Enterprise Miner, PROC FASTCLUS is used to perform clustering. This is the same procedure
available in SAS/Stat. SAS/Stat has the additional hierarchical clustering techniques available. The variables in the
dataset dealing with preferences for mathematics subject were first clustered in SAS/Stat using the hierarchical
procedure in PROC CLUSTER. Several distance criteria were used for comparison purposes. In addition, course
level (200,300,400, 500 and above) was included.
proc cluster data=sasuser.studentsurvey method=density r=2 ;
var courselevel pure applied abstractalgebra numbertheory topology realanalysis
discretemathematics differentialequations actuarialscience probability statistics;
id id;
run;
proc tree horizontal spaces=2;
id id;
In addition to density, Ward’s method, centroid, and two stage methods were used to determine clusters with very
different results (Figure 1).
Figure 1. Methods of Clustering
Density
Ward’s Method
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Di st ance Bet ween Cl ust er Cent r oi ds
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Cl ust er Fusi on Densi t y
The number of clusters defined range from 2 to many. With so many different possible clustering results, it is difficult
to make a judgment as to which is optimal. Instead, the question must become, “Is the result reasonable, and does
the result enhance decision-making?”
2
0
In contrast, k-means clustering, which is used in Enterprise Miner, uses the following code:
proc fastclus data=sasuser.studentsurveyimputed maxclusters=4 list out=sasuser.fastclusresults ;
var courselevel pure applied abstractalgebra numbertheory topology realanalysis
discretemathematics differentialequations actuarialscience probability statistics;
id id;
It is important to save the cluster values. The option out=sasuser.fastclusresults preserves the original data plus the
variables CLUSTER and DISTANCE. CLUSTER gives the cluster number to the observation; DISTANCE gives the
Euclidean distance from the observation to the center of the cluster.
Note that the investigator needs to specify the maximum number of clusters to be examined. It is possible to create a
list identifying which observation is classified into which cluster. A labeled list is not possible with the hierarchical
procedure since the final clustering is uncertain. Once the hierarchy is established and the number of clusters is
chosen, the final clusters can be labeled by the investigator. For the Fastclus results, Table 1 gives the means of
each variable by cluster.
Table 1. Cluster by Variable
Pure
Cluster
.68
1
.28
2
.36
3
1.00
4
Applied
.36
.92
.08
1.00
Algebra
.32
.05
.08
.76
Topology
.02
.08
.04
.56
Probability
.18
.43
.88
.41
Statistics
.06
.69
.92
.35
In this program, the maximum number of possible clusters is given by the user. To validate the results, it is
extremely important to give each cluster a meaningful identity. Given the proportion of values in each cluster, it is
possible to define labels for each cluster (Table 2).
Table 2. Cluster Labels
Cluster
1
2
3
4
Label
Pure Math
Applied Math
Statistics
Math Generally
Table 3. 5 Clusters in FASTCLUS
Pure
Applied Algebra
Cluster
1
2
3
4
5
Cluster
1
2
3
4
5
.36
.30
.05
1.00
1.00
.46
.80
.44
.50
.90
.07
.48
.02
.40
.70
Label
Pure Math
Applied Math
Statistics
Somewhat
Ambivalent
Math Generally
Five clusters are summarized in Table 3.
Topology
.03
.14
.05
.05
.60
Probabilit
y
.09
.22
.65
1.00
.60
Statistic
s
.04
.32
.98
.75
.40
In contrast, Enterprise Miner does not require a specification of a
maximum number of clusters, although it is an available option. It
also provides some graphics to examine the data that are not readily
available in SAS/Stat (Figure 3). The coding for Enterprise Miner is
given in Figure 2. Although defined using icons, the Fastclus
procedure is the same.
Figure 2. Enterprise Miner Clustering
3
Figure 3. Visualization of 5 clusters in Enterprise Miner
In addition, a
multidimensional
scaling (PROC MDS)
is performed in
Enterprise Miner to
examine the
separation between
clusters (Figure 4). The
scaling is based upon
distance within and
between clusters.
Figure 4. Graphical Representation of Distance Between Clusters
The centers of each cluster are well
separated but there is considerable
overlap. Once the clusters are defined,
specific variables can be examined (Table
4).
Note also in Figure 2 that Enterprise Miner will automatically divide the dataset, creating a holdout sample that can
be used to test the results. That capability does not automatically exist in SAS/Stat. It is useful to have such a
holdout sample so that the clustering results can be validated. To create such a sample, the following code is used:
PROC SQL;
CREATE VIEW WORK.SORT6649
AS SELECT * FROM sasuser.REVISEDSTUDENTSURVEY;
QUIT;
PROC SURVEYSELECT DATA=sasuser.surveysample
OUT=SASUSER.RAND8956(LABEL="Random sample of sasuser.revisedstudentsurvey")
METHOD=SRS
RATE=0.2
Creates the random sample
;
of 20% of the data.
RUN;
Adds a pointer to the random
sample, of numeric value 1.
data sasuser.surveysampleadd;
set sasuser.surveysample;
sample=1;
run;
4
proc sort data=Sasuser.Revisedstudentsurvey out=WORK._TABLE1_;
by ID;
run;
proc sort data=Sasuser.Surveysampleadd out=WORK._TABLE2_;
by ID;
run;
data sasuser.merged;
length id 8 Student_Type $ 16 CourseLevel 8 Course 8 Section 8 Pure 8
Applied 8 AbstractAlgebra 8 NumberTheory 8 Topology 8 RealAnalysis 8
DiscreteMathematics 8 DifferentialEquations 8 ActuarialScience 8
Probability 8 Statistics 8 sample 8;
merge WORK._TABLE1_ (in=TABLE1) WORK._TABLE2_ (in=TABLE2) ;
by ID;
run;
Merges the random sample into
the original dataset.
PROC SQL;
CREATE TABLE SASUSER.studentsurveytrain AS SELECT studentsurveymerged.id
FORMAT=BEST12.,
studentsurveymerged.Student_Type FORMAT=$F16.,
studentsurveymerged.Pure FORMAT=BEST12.,
Filters out the random sample
studentsurveymerged.Applied FORMAT=BEST12.,
leaving all values not in the
studentsurveymerged.AbstractAlgebra FORMAT=BEST12.,
sample.
studentsurveymerged.NumberTheory FORMAT=BEST12.,
studentsurveymerged.Topology FORMAT=BEST12.,
studentsurveymerged.RealAnalysis FORMAT=BEST12.,
studentsurveymerged.DiscreteMathematics FORMAT=BEST12.,
studentsurveymerged.DifferentialEquations FORMAT=BEST12.,
studentsurveymerged.ActuarialScience FORMAT=BEST12.,
studentsurveymerged.Probability FORMAT=BEST12.,
studentsurveymerged.Statistics FORMAT=BEST12.,
studentsurveymerged.sample FORMAT=BEST12.
FROM sasuser.studentsurveymerged AS studentsurveymerged
WHERE studentsurveymerged.sample NOT = 1;
QUIT;
In this code, SURVEYSAMPLEADD is used to test the data; STUDENTSURVEYTRAIN is used to define the model.
Once the clusters are defined using the training set, PROC DISCRIM can be used to examine the clusters that would
be defined on the holdout sample:
proc discrim data=sasuser.studentsurveytrain testdata=sasuser.surveysampleadd list testlist;
class student_type;
id id;
var Pure Applied AbstractAlgebra NumberTheory RealAnalysis DiscreteMathematics DifferentialEquations
ActuarialScience Probability Statistics;;
run;
In the above code, data=sasuser.studentsurvey train is used to define the discriminant function (which will fit the
training set almost perfectly). Test data (defined by testdata=sasuser.surveysampleadd) are used to define cluster
values on a set not used to define them. Once these are defined, cluster means can be computed on the test data
set and compared to those in the initial set. Once the clusters are defined, they can be used in other types of
analyses for comparison purposes. Table 4 gives a chi-square analysis to examine clusters by types of students.
Table 4. Clusters by Student Type
Undergraduat Graduate
Cluster
e
53 (41%) 14 (23%)
1
35 (27%)
15
2
(25%)
20 (15%) 23 (38%)
3
16 (12%)
4 (7%)
4
5 (5%)
4 (7%)
5
Undergraduates are more likely than graduate student to
prefer pure mathematics. This trend is even more
noticeable when clusters are examined by course level
(Table 5).
5
Table 5. Clusters by Course Level
200
300
400
Cluster
41
12
6 (21%)
1
(42%)
(36%)
24
11
11
2
(25%)
(33%)
(39%)
14
6 (18%)
8 (28%)
3
(14%)
13
3 (9%)
2 (7%)
4
(13%)
5 (5%)
1 (3%)
1 (4%)
5
In contrast to tables, Enterprise Miner allows this
information to be depicted graphically in the
CLUSTER NODE (Figure 5).
500
8 (25%)
4 (13%)
15
(47%)
2 (6%)
3 (9%)
Figure 5. Enterprise Miner Comparisons
CLASSIFICATION AND PREDICTIVE MODELING
Classification is considered to be supervised data mining since it is possible to compare a predicted value to an
actual value. In SAS/Stat, discriminant analysis and logistic are the primary means of classification. In Enterprise
Miner, neural networks, decision trees, and logistic regression are used. However, the two components of SAS
approach classification with different perspectives. In Enterprise Miner, the dataset is large enough to partition it so
that the classification model can be validated through the use of a holdout sample. Misclassification is one of the
means of determining the strength of the model. Another is to define a profit/loss function to determine the cost (or
benefit) of a correct or incorrect classification.
In SAS/Stat, datasets are often small so that partitioning is not possible. The strength of a logistic regression is
measured by the odds ratios, the receiver operating curve, and the p-value. Similarly, the strength of discriminant
analysis is measured by the proportion of correct classifications without the use of a holdout sample, although there
is an option for cross validation that is not available for logistic regression.
For logistic regression, however, the two data sets should remain merged. However, the coding given in the previous
section should be modified to allow for differences in procedures.
data sasuser.surveysampleadd;
set sasuser.surveysample;
sample=1;
student_type1=student_type;
student_type=’.’
run;
proc sort data=Sasuser.Revisedstudentsurvey out=WORK._TABLE1_;
Merges the random sample into
by ID;
the original dataset.
run;
proc sort data=Sasuser.Surveysampleadd out=WORK._TABLE2_;
by ID;
run;
data sasuser.merged;
length id 8 Student_Type $ 16 student_type1 $ 16 CourseLevel 8 Course 8 Section 8 Pure 8
Applied 8 AbstractAlgebra 8 NumberTheory 8 Topology 8 RealAnalysis 8
6
DiscreteMathematics 8 DifferentialEquations 8 ActuarialScience 8
Probability 8 Statistics 8 sample 8;
merge WORK._TABLE1_ (in=TABLE1) WORK._TABLE2_ (in=TABLE2) ;
by ID;
run;
Then, using the merged datasets, the outcome values are removed from the smaller partition. The logistic procedure
will predict the values that can then be compared to accuracy. In this example, the holdout sample had a 22%
misclassification rate compared to 13% for the initial sample.
Similarly, PROC DISCRIM uses the following code, where the partitioned dataset can be used as a holdout sample.
Note that it is very similar to the code used to validate the clustering in the previous section.
proc discrim data=sasuser.trainingset testdata=sasuser.partition list testlist;
class student_type;
id id;
var pure applied abstractalgebra numbertheory topology realanalysis discretemathematics
differentialequations actuarialscience probability statistics;
run;
The summary table on the test data is given in Table 6 below.
Graduate
Student Type
4 (67%)
Graduate
6 (30%)
Undergraduate
Undergraduate
2 (33%)
14 (70%)
Nonparametric discriminant analysis can also be used:
proc discrim data=sasuser.trainingset testdata=sasuser.partition list testlist
method=npar r=1 kernel=epa;
class student_type;
id id;
var pure applied abstractalgebra numbertheory topology realanalysis discretemathematics
differentialequations actuarialscience probability statistics;
run;
with a strong likelihood of correctly classifying undergraduates (Table 7).
Student Type
Graduate
Undergraduate
Graduate
3 (50%)
4 (20%)
Undergraduate
3 (50%)
16 (80%)
Instead of a holdout sample, cross validation is the standard method to correct for the inflation of results (Table 8):
proc discrim data=sasuser.revisedstudentsurvey list
method=npar k=5 crossvalidate;
class student_type;
id id;
var pure applied abstractalgebra numbertheory topology realanalysis discretemathematics
differentialequations actuarialscience probability statistics;
run;
Student Type
Graduate
Undergraduate
Graduate
28 (47%)
46 (35%)
Undergraduate
31 (52%)
83 (64%)
Note that while the cross validation technique can correctly classify undergraduates 64% of the time, the
classification of graduate students is poor. In comparison, a standard discriminant analysis without cross validation
shows a much more accurate result (Table 9).
Graduate
Undergraduate
Student Type
43 (72%)
17 (28%)
Graduate
43 (33%)
87 (67%)
Undergraduate
In contrast, Enterprise Miner has the capability to partition easily (Figure 6).
7
Figure 6. Code in Enterprise Miner for Classification
Neural networks act like “black boxes” in that the model is not presented in a nice, concise format that is provided by
regression. Its accuracy is examined in a way similar to the diagnostics of the regression curve. The simplest neural
network contains a single input (independent variable) and a single target (dependent variable) with a single output
unit. It increases in complexity with the addition of hidden layers, and additional input variables. With no hidden
layers, the results of a neural network analysis will resemble those of regression. Each input variable is
connected to each variable in the hidden layer, and each hidden variable is connected to each outcome
variable. The hidden units combine inputs, and apply a function to predict outputs. Hidden layers are often
nonlinear.
Decision trees provide a completely different approach to the problem of classification. The decision tree develops a
series of if…then rules. Each rule assigns an observation to one segment of the tree, at which point there is another
if…then rule applied. The initial segment, containing the entire dataset, is the root node for the decision tree. The
final nodes are called leaves. Intermediate nodes (a node plus all its successors) forms a branch of the tree. The
final leaf containing an observation is its predictive value. Unlike neural networks and regression, decision trees will
not work with interval data. It will work with nominal outcomes that have more than two possible results. Decision
trees will also work with ordinal outcome variables.
The Assessment Node is used to compare outcome methods (Table10).
Table 10. Comparison of Methods
Tool
Target Event
Neural Network
Undergraduate
Tree
Undergraduate
Regression
Undergraduate
Misclass
Rate
0.381578947
4
0.342105263
2
0.197368421
1
Valid:
Misclass
Rate
0.333333333
3
0.315789473
7
0.473684210
5
Test:
Misclass
Rate
0.245614035
1
0.280701754
4
0.438596491
2
Interestingly, logistic regression has the lowest misclassification rate on the initial training set but the highest
misclassification rate on the testing set. The results suggest that logistic regression tends to inflate results. Similarly,
the receiver operating curve is given in Figure 7 for three models. Note also that the data sample is partitioned into
three sets instead of two. Predictive modeling in Enterprise Miner is iterative. The initial result is compared to the
validation set and adjustments are made to the model. Once all adjustments are completed, the final testing is used
to validate the results.
8
Figure 7. ROC Curves
According to this measure, logistic regression gives the optimal outcome. However, the misclassification rate on the
testing sample indicates that the decision tree gives a better overall result.
DATA VISUALIZATION
With large datasets, data visualization becomes an important part of exploring in data mining. Version 4.3 of
Enterprise Miner included a node for SAS/Insight, and included all graphics within Insight. Version 5.1 removed the
SAS/Insight Node, adding a Stat/
Explore Node. However, neither yet provides the point-and-click graphics that are readily available in SAS Enterprise
Guide.
There is, however, one set of graphics available in SAS/Stat that are not available in any other component of SAS.
That procedure, PROC KDE, allows the investigator to overlay smoothed histograms to examine data. It is available
for interval data only. In addition to questions concerning preferences for mathematics, students were asked to
estimate the number of hours per week they expected to study for their mathematics courses. In Enterprise Miner, it
is possible to use histograms to examine the data. Figure 8 was provided in Enterprise Miner using the StatExplore
Node. Figure 9 shows the corresponding smoothed histogram as provided by SAS/Stat.
Figure 8. Bar Chart of Hours Studied by Student Type
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Comparing one to the other is difficult because grouped histograms are side-by-side. PROC KDE allows an overlay
comparison:
Proc sort data=sasuser.studentsurvey;
By student_type;
Proc KDE data=sasuser.studentsurvey;
Univar hours/gridl=0 gridu=25 out=sasuser.kdesurvey;
By student_type;
Run;
Proc GPlot is used to graph the results as given in Figure 9. Although Proc KDE has added graphics in version 9, the
overlay still must be done with GPlot.
Figure 9. Smoothed, Over-layed Histogram by Student Type
With the overlay, it is clear that almost all undergraduate students spend 10 hours or less in study compared to
graduate students who are divided between 0-10 hours and 10-18 hours per week. In a similar comparison given in
Figure 10, students who enjoy pure mathematics spend about the same amount of time in study as do the students
who do not enjoy pure mathematics.
Figure 10. Smoothed Histogram for Those Students Who Favor Pure Mathematics
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However, with the exception of a small group of students at the 15 hour mark who do not like pure mathematics,
students who enjoy applied mathematics are more likely to study more than 7 hours per week.
Figure 11. Smoothed Histogram for Those Students Who Favor Applied Mathematics
The comparison is not as clear in the histogram provided in Enterprise Miner.
Figure 12. Histogram in Enterprise Miner for Those Students Who Favor Applied Mathematics
CONCLUSION
There are many similar procedures in SAS/Stat and Enterprise Miner that can be used for similar needs. However,
generally the process is different since data are routinely partitioned to validate models, and to optimize the choice of
model. Although SAS/Stat contains many similar models, it does not have the partitioning process readily available,
although it can be coded into the process. There are some exploratory techniques built into SAS/Stat, such as
PROC KDE, that can complement Enterprise Miner. In addition, partitioning and imputation steps can be performed
in Enterprise Miner, and the data analyzed using SAS/Stat techniques.
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CONTACT INFORMATION
Patricia Cerrito
Department of Mathematics
University of Louisville
Louisville, KY 40292
502-852-6826
502-852-7132 (fax)
[email protected]
SAS and all other SAS Institute Inc. product or service names are registered trademarks or trademarks of SAS
Institute Inc. in the USA and other countries. ® indicates USA registration.
Other brand and product names are trademarks of their respective companies.
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