Gaussian Process Latent Random Field

The Gaussian process latent variable model (GPLVM) is an unsupervised probabilistic model for nonlinear dimensionality reduction. A supervised extension, called discriminative GPLVM (DGPLVM), incorporates supervisory information into GPLVM to enhance the classification performance. However, its limitation of the latent space dimensionality to at most C − 1 (C is the number of classes) leads to unsatisfactorily performance when the intrinsic dimensionality of the application is higher than C − 1. In this paper, we propose a novel supervised extension of GPLVM, called Gaussian process latent random field (GPLRF), by enforcing the latent variables to be a Gaussian Markov random field with respect to a graph constructed from the supervisory information. In GPLRF, the dimensionality of the latent space is no longer restricted to at most C − 1. This makes GPLRF much more flexible than DGPLVM in applications. Experiments conducted on both synthetic and real-world data sets demonstrate that GPLRF performs comparably with DGPLVM and other state-ofthe-art methods on data sets with intrinsic dimensionality at most C − 1, and dramatically outperforms DG- PLVM on data sets when the intrinsic dimensionality exceeds C − 1.

Authors

• Guoqiang Zhong Ocean University of China
• Wu-Jun Li National Key Laboratory for Novel Software Technology, School of Computer Science, Nanjing University
• Dit-Yan Yeung Hong Kong University of Science and Technology
• Xinwen Hou Chinese Academy of Sciences
• Cheng-Lin Liu School of Artificial Intelligence, University of Chinese Academy of Sciences, State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS), Institution of Automation, Chinese Academy of Sciences

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