A New Fuzzy Possibility Clustering Algorithms Based on Unsupervised Mahalanobis Distances

Abstract

The well known Fuzzy Possibility C-Mean algorithm could improve the problems of outlier and noise in fuzzy c-mean, but it was based on Euclidean distance function, which can only be used to detect spherical structural clusters. Gustafson-Kessel clustering algorithm and Gath-Geva clustering algorithm, were developed to detect non-spherical structural clusters, but both of them based on semi-supervised Mahalanobis distance, these two algorithms fail to consider the relationships between cluster centers in the objective function, needing additional prior information. The second problem is as follows, when some training cluster size is small than its dimensionality, it induces the singular problem of the inverse covariance matrix. The third important problem is how to select the better initial value to improve the cluster accuracy. In this paper, focusing attention to above three problems, First we added a regulating factor of covariance matrix, -1n| <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sub> Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> |< , to each class in objective function, second, a method to reduce the dimensions was proposed .finally, we proposed two methods to select the better initial value, and then, the improved new algorithm, "Fuzzy Possibility C-Mean based on Mahalanobis distance (FPCM-M)", is obtained. A real data set was applied to prove that the performance of the FPCM-M algorithm is better than the traditional FCM, PCM, and FPCM, and the Ratio method and Inverse method which is proposed by us is better than the Random method for selecting the initial values.