EM Clustering Algorithm Modification Using Multivariate Hierarchical Histogram in The Case of Undefined Cluster Number

摘要

In the scope of image processing expectation maximization (EM) algorithm takes conspicuous place among the other clustering techniques. EM algorithm is suitable for multidimensional data but it requires a number of clusters to be defined a priori that might be a problem for particular applications. The main aim of this paper is to provide time effective EM clustering modification in the case of the unknown number of clusters and multidimensional input. Our work is based on statistical histogram based expectation maximization algorithm (SHEM) proposed by Yang and Huang with the predefined number of clusters. This method utilizes the histogram to provide EM iterations. However, the estimation of the histogram becomes time consuming task with the increase of input data dimension. Our algorithm extends the use of SHEM algorithm by means of a hierarchical histogram data structure, which allows us to reduce the computational load in the multidimensional case as well as to provide an initialization in the case of the unknown number of clusters. The paper includes several experimental results demonstrating the advantages and the disadvantages of the proposed solution.