Manifold Regularized Gaussian Mixture Model for Semi-supervised Clustering

Over the last few decades, Gaussian Mixture Model (GMM) has attracted considerable interest in data mining and pattern recognition. GMM can be used to cluster a bunch of data through estimating the parameters of multiple Gaussian components using Expectation-Maximization (EM). Recently, Locally Consistent GMM (LCGMM) has been proposed to improve the clustering performance of GMM by exploiting the local manifold structure modeled by a p nearest neighbor graph. In practice, various prior knowledge may be available which can be used to guide the clustering process and improve the performance. In this paper, we introduce a semi-supervised method, called Semi-supervised LCGMM (Semi-LCGMM), where prior knowledge is provided in the form of class labels of partial data. Semi-LCGMM incorporates prior knowledge into the maximum likelihood function of LCGMM and is solved by EM. It is worth noting that in our algorithm each class has multiple Gaussian components while in the unsupervised settings each class only has one Gaussian component. Experimental results on several datasets demonstrate the effectiveness of our algorithm.