Minimum message length

Abstract: This paper proposes an unsupervised algorithm for learning a finite Dirichlet mixture model. An important part of the unsupervised learning problem is determining the number of clusters which best describe the data. We extend the minimum message length (MML) principle to determine the number of clusters in the case of Dirichlet mixtures. Parameter estimation is done by the expectation-maximization algorithm. The resulting method is validated for one-dimensional and multidimensional data. For the one-dimensional data, the experiments concern artificial and real SAP image histograms. The validation for multidimensional data involves synthetic data and two real applications: shadow detection in images and summarization of texture image databases for efficient retrieval. A comparison with results obtained for other selection criteria is provided

Abstract: In this work we present an unsupervised algorithm for learning finite mixture models from multivariate positive data. Indeed, this kind of data appears naturally in many applications, yet it has not been adequately addressed in the past. This mixture model is based on the inverted Dirichlet distribution, which offers a good representation and modeling of positive non-Gaussian data. The proposed approach for estimating the parameters of an inverted Dirichlet mixture is based on the maximum likelihood (ML) using Newton Raphson method. We also develop an approach, based on the minimum message length (MML) criterion, to select the optimal number of clusters to represent the data using such a mixture. Experimental results are presented using artificial histograms and real data sets. The challenging problem of software modules classification is investigated within the proposed statistical framework, also.