Based on the basic theory of fuzzy set, this paper suggests the notion of FCM fuzzy set, which is subject to the constraint condition of fuzzy c-means clustering algorithm. The cluster fuzzy degree and the lattice degree of approaching for the FCM fuzzy set are presented, and their functions in the validation process of fuzzy clustering are deeply analyzed. A new cluster validity index is propo...

Evaluation of clustering results (or cluster validation) is an important and necessary step in cluster analysis, but it is often time-consuming and complicated work. We present a visual cluster validation tool, the Cluster Validity Analysis Platform (CVAP), to facilitate cluster validation. The CVAP provides necessary methods (e.g., many validity indices, several clustering algorithms and proce...

In this paper, a cluster validity concept from an unsupervised to a supervised manner is presented. Most cluster validity criterions were established in an unsupervised manner, although many clustering methods performed in supervised and semi-supervised environments that used context information and performance results of the model. Context-based clustering methods can divide the input spaces u...

In order to find an optimal fuzzy cluster scheme for proximity data, where just pairwise distances among objects are given, two conditions are necessary: A good cluster validity function, which can be applied to proximity data for evaluation of the goodness of cluster schemes for varying number of clusters; a good cluster algorithm that can deal with proximity data and produce an optimal soluti...

Cluster analysis is used to explore structure in unlabeled data sets in a wide range of applications. An important part of cluster analysis is validating the quality of computationally obtained clusters. A large number of different internal indices have been developed for validation in the offline setting. However, this concept has not been extended to the online setting. A key challenge is to ...