EM Clustering Example.
Prof. Ruiz

1. Generate two sets X and Y of 100 random numbers, where each set following a normal distribution. In this example:
   • the normal distribution for X has mean 90 and standard deviation 10.
   • the normal distribution for Y has mean 60 and standard deviation 10.
   Below is the Matlab program two_random_normal_sets.m that I used to achieve this.

   X = random('Normal',90,10,1,100);
   Y = random('Normal',60,10,1,100);
   D(1:100,1) = X;
   D(1:100,2) = 1;
   D(101:200,1) = Y;
   D(101:200,2) = 2;
   

   D contains now 200 data instances, whose first column is a randomly generated number, and its second column tells if the number came from X or from Y. See D contents.

2. Translate D to an arff file: em_dataset_example.arff.

3. I include below the clustering results in Weka: (note that the parameters I used for EM were: weka.clusterers.EM -I 100 -N 2 -M 8.0 -S 100)

   === Run information ===
   
   Scheme:       weka.clusterers.EM -I 100 -N 2 -M 8.0 -S 100
   Relation:     em_example
   Instances:    200
   Attributes:   2
                 A
   Ignored:
                 class
   Test mode:    Classes to clusters evaluation on training data
   === Model and evaluation on training set ===
   
   
   EM
   ==
   
   Number of clusters: 2
   
   
               Cluster
   Attribute         0       1
                (0.49)  (0.51)
   ============================
   A
     mean       89.7246  60.419
     std. dev.   9.0504  8.8655
   
   Clustered Instances
   
   0      100 ( 50%)
   1      100 ( 50%)
   
   
   Log likelihood: -4.1775
   
   
   Class attribute: class
   Classes to Clusters:
   
     0  1  <-- assigned to cluster
    94  6 | 1
     6 94 | 2
   
   Cluster 0 <-- 1
   Cluster 1 <-- 2
   
   Incorrectly clustered instances :	12.0	  6      %
   

4. We can also use Matlab to cluster D. see em_clustering_D_matlab.m. Here is the summary result of the clustering reported by Matlab:

   obj = 
   
   Gaussian mixture distribution with 2 components in 1 dimensions
   Component 1:
   Mixing proportion: 0.482694
   Mean:    91.0523
   
   Component 2:
   Mixing proportion: 0.517306
   Mean:    60.0800