A Projected Clustering Algorithm and Its Biomedical Application - Clustering Challenges in Biological Network - page 200

factors for the 20 dimensions are random numbers uniformly distributed between
1 and 20.

Table 9.1. Dimensions of the Input Clusters

Input Dimensions Points

A 0, 2, 3, 10, 16, 17, 18 16768

B 9, 10, 12, 16, 17, 18, 19 23859

C 1, 3, 9, 12, 13, 14, 16 25678

D 1, 5, 9, 10, 12, 13, 14 23093

E 3, 6, 9, 10, 11, 12, 14 5602

Outlier 5000

Table 9.2 shows a typical result of the dimensions of the output clusters found
by PROCLUS and IPROCLUS. We can find a good correspondence between the
sets of dimensions of the output clusters found by IPROCLUS and their corre-
sponding input clusters.

Table 9.2. Dimensions of the Output Clusters for IPROCLUS and PROCLUS

IPROCLUS

Dimensions Points

1 1, 5, 9, 10, 12, 13, 14 23304

2 0, 2, 3, 10, 14, 16, 18 2802

3 9, 10, 12, 16, 17, 18, 19 25034

4 1, 3, 9, 12, 13, 14, 16 25982

5 0, 2, 3, 10, 16, 17, 18 15991

Outliers 6887

PROCLUS Dimensions Points

1 0, 2, 3, 4, 9, 12, 16, 17, 18 17660

2 3, 9, 12, 16, 17, 18 24971

3 3, 4, 9, 12, 16, 189 11844

4 1, 3, 9, 12, 13, 14, 16 19130

5 0, 3, 4, 8, 9, 12, 18 8236

Outliers 18159

Table 9.3 gives the confusion matrix for the output clusters in Table 9.2. Con-
fusion matrix is definedinthesamewayasinPROCLUSpaper. Entry( i , j ) is
equal to the number of data points assigned to output cluster i , which were gener-
ated as part of input cluster j . IPROCLUS discovers output clusters in which the
majority of points come from one input cluster. In other words, it recognizes the
natural clustering of the points. More specifically, we calculate the accuracy from
the confusion matrix. In order to define the accuracy, for each output cluster i ,we
identify the input cluster j with which it shares the largest number of points. We
say that output cluster i corresponds to input cluster j . All points in their common
intersection are clustered correctly. All the other points in output cluster i are clus-