This reduces the number parameters per mixture component celeux and govaert

374 Clustering

before a satisfactory clustering is produced. In any case, it is worthwhile trying several initialisations, since agreement between the resulting classifications lends more weight to the chosen solution. Celeux and Govaert (1992) describe approaches for developing the basic EM algorithm to overcome the problem of local optima.

Summary The approach detects a linear pattern in preprocessed images via model-based clustering. It employs an approximate Bayes factor which provides a criterion for assessing the evidence for the presence of a defect.

The data Two-dimensional point pattern data are generated by thresholding and clean-ing, using mathematical morphology, images of fabric. Two fabric images are used, each about 500 ð 500 pixels in size.

Results were presented for some representative examples, and contrasted with a Hough transform.

10.5.1 Clustering criteria

Let the n data samples be x1; : : : ; xn. The sample covariance matrix,O�, is given by

jD1

g n
Tr.SW/ D1 X X z jijxi � m jj2
jD1 iD1
g
D1 X Sj
jD1

where Sj DPn the minimisation of Tr.SW/ is equivalent to minimising the total within-group sum of iD1z jijxi � m jj2, the within-group sum of squares for group j. Thus,