A Semi-supervised Learning Algorithm on Gaussian Mixture with Automatic Model Selection

In Gaussian mixture modeling, it is crucial to select the number of Gaussians for a sample set, which becomes much more difficult when the overlap in the mixture is larger. Under regularization theory, we aim to solve this problem using a semi-supervised learning algorithm through incorporating pairwise constraints into entropy regularized likelihood (ERL) learning which can make automatic model selection for Gaussian mixture. The simulation experiments further demonstrate that the presented semi-supervised learning algorithm (i.e., the constrained ERL learning algorithm) can automatically detect the number of Gaussians with a good parameter estimation, even when two or more actual Gaussians in the mixture are overlapped at a high degree. Moreover, the constrained ERL learning algorithm leads to some promising results when applied to iris data classification and image database categorization.