A Comparative Study on Lagrange Ying-Yang Alternation Method in Gaussian Mixture-Based Clustering

Gaussian Mixture Model (GMM) has been applied to clustering with wide applications in image segmentation, object detection and so on. Many algorithms were proposed to learn GMM with appropriate number of Gaussian components automatically determined. Lagrange Ying-Yang alternation method (LYYA) is one of them and it has advantages of no priors as well as the posterior probability bounded by traditional probability space. This paper aims to investigate the performance of LYYA, in comparisons with other methods including Bayesian Ying-Yang (BYY) learning, Rival penalized competitive learning (RPCL), hard-cut Expectation Maximization (EM) method, and classic EM with Bayesian Information Criterion (BIC). Systematic simulations show that LYYA is generally more robust than others on the data generated by varying sample size, data dimensionality and real components number. Unsupervised image segmentation results on Berkeley datasets also confirm LYYA advantages when comparing to the Mean shift and Multiscale graph decomposition algorithms.