Supervised Gaussian Process Latent Variable Model Based On Gaussian Mixture Model

In this paper, we propose a supervised Gaussian Process Latent Variable Model(GPLVM) based on Gaussian mixture model(GMM). In this model, we assume that latent variables satisfy the Gaussian mixture distribution, and the conditional distribution of latent variable given the label of the corresponding sample satisfy a Gaussian distribution. In the training process, the parameters for nonlinear dimensionality reduction are learned with the training sample and data labels. Meanwhile, the mean and variance for each class are learned. Therefore, it is tractable to evaluate the probability of a sample belongs to a particular class. The effectiveness of our model is demonstrated by comparing with some representative dimensionality reduction method. We evaluate the effectivebess of our method on UCI data set. The experiment results show that the proposed method is capable of distinguish data from different classes in low dimensional space, and it have good performance for classification.