A Validity Measure for Fuzzy Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new cluster validity index for the fuzzy c-mean
Pattern Recognition Letters
A new cluster validity measure and its application to image compression
Pattern Analysis & Applications
A fast kernel-based nonlinear discriminant analysis for multi-class problems
Pattern Recognition
On fuzzy cluster validity indices
Fuzzy Sets and Systems
Agglomerative Fuzzy K-Means Clustering Algorithm with Selection of Number of Clusters
IEEE Transactions on Knowledge and Data Engineering
Mercer kernel-based clustering in feature space
IEEE Transactions on Neural Networks
Survey of clustering algorithms
IEEE Transactions on Neural Networks
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Many validity index algorithms have been proposed to determine the number of clusters. These methods usually employ the Euclidean distance as the measurement. However, it is difficult for the Euclidean distance metric to evaluate the compactness of data when non-linear relationship exists between different components of data. Moreover, most current algorithms can not estimate well the scope of the number of clusters. To address these problems, in this paper, we adopt the kernel-induced distance to measure the relationship among data points. We first estimate the upper bound of the number of clusters to effectively reduce iteration time of validity index algorithm. Then, to determine the number of clusters, we design a kernelized validity index algorithm to automatically determine the optimal number of clusters. Experiments show that the proposed approach can obtain promising results.