Projection-embedded BYY learning algorithm for Gaussian mixture-based clustering

On learning the Gaussian mixture model, existing BYY learning algorithms are featured by a gradient-based line search with an appropriate stepsize. Learning becomes either unstable if the stepsize is too large or slow and gets stuck in a local optimal solution if the stepsize is too small. An algorithm without a learning stepsize has been proposed with expectation-maximization (EM) like two alternative steps. However, its learning process may still be unstable. This paper tackles this problem of unreliability by a modified algorithm called projection-embedded Bayesian Ying-Yang learning algorithm (pBYY). Experiments have shown that pBYY outperforms learning algorithms developed from not only minimum message length with Jeffreys prior (MML-Jef) and Variational Bayesian with Dirichlet-Normal-Wishart (VB-DNW) prior but also BYY with these priors (BYY-Jef and BYY-DNW). pBYY obtains the superiority with an easy implementation, while DNW prior-based learning algorithms suffer a complicated and tedious computation load. The performance of pBYY has also been demonstrated on the Berkeley Segmentation Dataset for the topic of unsupervised image segmentation. The resulted performances of semantic image segmentation have shown that pBYY outperforms not only MML-Jef, VB-DNW, BYY-Jef, and BYY-DNW but also three leading image segmentation algorithms, namely gPb-owt-ucm, MN-Cut, and mean shift.