Clustering with density based initialization and Bhattacharyya based merging

Abstract

Centroid based clustering approaches, such as k-means, are relatively fast but inaccurate for arbitrary shape clusters. Fuzzy c-means with Mahalanobis distance can accurately identify clusters if data set can be modelled by a mixture of Gaussian distributions. However, they require number of clusters apriori and a bad initialization can cause poor results. Density based clustering methods, such as DBSCAN, overcome these disadvantages. However, they may perform poorly when the dataset is imbalanced. This paper proposes a clustering method, named clustering with density initialization and Bhattacharyya based merging based on the fuzzy clustering. The initialization is carried out by density estimation with adaptive bandwidth using k-Nearest Orthant-Neighbor algorithm to avoid the effects of imbalanced clusters. The local peaks of the point clouds constructed by the k-Nearest Orthant-Neighbor algorithm are used as initial cluster centers for the fuzzy clustering. We use Bhattacharyya measure and Jensen inequality to find overlapped Gaussians and merge them to form a single cluster. We carried out experiments on a variety of datasets and show that the proposed algorithm has remarkable advantages especially for imbalanced and arbitrarily shaped data sets.