By Topic

Cluster Validity for the Fuzzy c-Means Clustering Algorithrm

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
Windham, Michael P. ; Department of Mathematics, Utah State University, Logan, UT 84322.

The uniform data function is a function which assigns to the output of the fuzzy c-means (Fc-M) or fuzzy isodata algorithm a number which measures the quality or validity of the clustering produced by the algorithm. For the preselected number of cluster c, the Fc-M algorithm produces c vectors in the space in which the data lie, called cluster centers, which represent points about which the data are concentrated. It also produces for each data point c-membership values, numbers between zero and one which measure the similarity of the data points to each of the cluster centers. It is these membership values which indicate how the point is classified. They also indicate how well the point has been classified, in that values close to one indicate that the point is close to a particular center, but uniformly low memberships indicate that the point has not been classified clearly. The uniform data functional (UDF) combines the memberships in such a way as to indicate how well the data have been classified and is computed as follows. For each data point compute the ratio of its smallest membership to its largest and then compute the probability that one could obtain a smaller ratio (indicating better classification) from a clustering of a standard data set in which there is no cluster structure. These probabilities are then averaged over the data set to obtain the values of the UDF.

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:PAMI-4 ,  Issue: 4 )