A Probabilistic Distance Clustering Algorithm Using Gaussian and Studentt Multivariate Density Distributions A new dissimilarity measure for cluster analysis is presented and used in the context of probabilistic distance (PD) clustering. The basic assumption of PDclustering is that for each unit, the product between the probability of the unit belonging to a cluster and the distance between the unit and the cluster is constant. This constant is a measure of the classifiability of the point, and the sum of the constant over units is called joint distance function (JDF). The parameters that minimize the JDF maximize the classifiability of the units. The new dissimilarity measure is based on the use of symmetric density functions and allows the method to find clusters characterized by different variances and correlation among variables. The multivariate Gaussian and the multivariate Studentt distributions have been used, outperforming classical PD clustering, and its variation PD clustering adjusted for cluster size, on simulated and real datasets.

Automatic Clustering by Detecting Significant Density Dips in Multiple Dimensions Clustering algorithms are used to find groups of similar items in a dataset. Automatic clustering algorithms achieve this task without requiring users to input critical parameters. A recent automatic clustering methodology uses Hartiganu0027s dip test to detect significant peaks in the distribution of a dataset. This test can detect peaks in the distribution of a onedimensional variable. To perform clustering in multiple dimensions, algorithms of this methodology rely on onedimensional transformations of the dataset, which limits their effectiveness. In this paper, we present MDip, an automatic clustering algorithm that works directly on multidimensional space. MDip also assumes that clusters correspond to different peaks in the distribution of the dataset. It separates clusters at the dips that form between neighboring peaks. Dips are detected directly in multidimensional space, using a graphbased method. Their statistical significance is evaluated through appropriate simulations. Our experimental evaluation indicates that MDip achieves significantly better results than existing algorithms based on Hartiganu0027s dip, as well as other stateoftheart automatic clustering algorithms.