Variational EM Inference Algorithm for Gaussian Process Classification Model with Multiclass and Its Application to Human Action Classification

Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: Bayesian rule, Gaussian process classification model with multiclass, Gaussian process prior, human action classification, laplace approximation, variational EM algorithm.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1110275

References:

[1] C. E. Rasmussen, and C. K. I. Williams, "Gaussian Processes for Machine Learning," MIT Press, 2006.
[2] H. Nicklisch, and C. E. Rasmussen, "Approximation for Binary Gaussian process Classification," JMLR, 2008, pp. 2035-75.
[3] A. B. Chan, and D. Dong, "Generalized Gaussian process model," IEEE Conf. on Computer Vision and Pattern Recognition, Colorado Spring, 2011.
[4] A. C. Chan, "Multivariate generalized Gaussian process models," eprint arXiv: 1311.0360, 2013.
[5] H. Kim, and Z. Ghahramani, "Bayesian Gaussian Process Classification with the EM-EP algorithm," IEEE Trans. on PAMI, vol. 28, no. 12, pp 1948-1959, 2006.
[6] C. E. Rasmussen, and H. Nickisch, The GPML Toolbox version 3.4, gaussianprocess.org.
[7] L. Raskin, E. Rivlin, and M. Rudzsky, “Using Gaussian Processes for Human tracking and Action Classification”, ISVC 2007, Part 1, LNCS 4841, pp 36-45, 2007.
[8] H. Zhou, L. Wang, D. Sutter, “Human action recognition by fearture-reduced Gaussian process classification”, Pattern Recognition Letters, v0l. 30, pp 1059-1065, 2009.
[9] Q. Zhao, L. Zhang, A. Cjchocki, “A Tensor-Variate Gaussian Process for Classification of Multidinensional Structured Data”, Proceeding of the Twenty-Seventh AAAI Conference on Artificial Intelligence, pp 1041-1047, 2013.
[10] I. Laptev, M. Marszalek, C. Schmid, and B. Rozenfeld, “Learning realistic human actions from movies,” in CVPR 2008.
[11] K. Mikolajczyk and H. Uemura. “Action recognition with motion-appearance vocabulary forest,” CVPR, 2008.
[12] J. Yuan, Z. Liu, and Y. Wu, “Discriminative Subvolume Search for Efficient Action Detection,” CVPR, 2009.
[13] M. B. Kaaniche and F. Bremond, “Gesture Recognition by Learning Local Motion Signatures,” In CVPR, 2010.
[14] A. Kovashka and K. Grauman, “Learning a Hierarchy of Discriminative Space-Time Neighborhood Features for Human Action Recognition,” In CVPR, 2010.
[15] J. Yin and Y. Meng, “Human Activity Recognition in Video using a Hierarchical Probabilistic Latent Model,” In CVPR, 2010.