In this paper, we propose the variational EM inference

\r\nalgorithm for the multi-class Gaussian process classification model

\r\nthat can be used in the field of human behavior recognition. This

\r\nalgorithm can drive simultaneously both a posterior distribution of a

\r\nlatent function and estimators of hyper-parameters in a Gaussian

\r\nprocess classification model with multiclass. Our algorithm is based

\r\non the Laplace approximation (LA) technique and variational EM

\r\nframework. This is performed in two steps: called expectation and

\r\nmaximization steps. First, in the expectation step, using the Bayesian

\r\nformula and LA technique, we derive approximately the posterior

\r\ndistribution of the latent function indicating the possibility that each

\r\nobservation belongs to a certain class in the Gaussian process

\r\nclassification model. Second, in the maximization step, using a derived

\r\nposterior distribution of latent function, we compute the maximum

\r\nlikelihood estimator for hyper-parameters of a covariance matrix

\r\nnecessary to define prior distribution for latent function. These two

\r\nsteps iteratively repeat until a convergence condition satisfies.

\r\nMoreover, we apply the proposed algorithm with human action

\r\nclassification problem using a public database, namely, the KTH

\r\nhuman action data set. Experimental results reveal that the proposed

\r\nalgorithm shows good performance on this data set.<\/p>\r\n","references":"[1] C. E. Rasmussen, and C. K. I. Williams, \"Gaussian Processes for\r\nMachine Learning,\" MIT Press, 2006.\r\n[2] H. Nicklisch, and C. E. Rasmussen, \"Approximation for Binary Gaussian\r\nprocess Classification,\" JMLR, 2008, pp. 2035-75.\r\n[3] A. B. Chan, and D. Dong, \"Generalized Gaussian process model,\" IEEE\r\nConf. on Computer Vision and Pattern Recognition, Colorado Spring,\r\n2011. [4] A. C. Chan, \"Multivariate generalized Gaussian process models,\" eprint\r\narXiv: 1311.0360, 2013.\r\n[5] H. Kim, and Z. Ghahramani, \"Bayesian Gaussian Process Classification\r\nwith the EM-EP algorithm,\" IEEE Trans. on PAMI, vol. 28, no. 12, pp\r\n1948-1959, 2006.\r\n[6] C. E. Rasmussen, and H. Nickisch, The GPML Toolbox version 3.4,\r\ngaussianprocess.org.\r\n[7] L. Raskin, E. Rivlin, and M. Rudzsky, \u201cUsing Gaussian Processes for\r\nHuman tracking and Action Classification\u201d, ISVC 2007, Part 1, LNCS\r\n4841, pp 36-45, 2007.\r\n[8] H. Zhou, L. Wang, D. Sutter, \u201cHuman action recognition by\r\nfearture-reduced Gaussian process classification\u201d, Pattern Recognition\r\nLetters, v0l. 30, pp 1059-1065, 2009.\r\n[9] Q. Zhao, L. Zhang, A. Cjchocki, \u201cA Tensor-Variate Gaussian Process for\r\nClassification of Multidinensional Structured Data\u201d, Proceeding of the\r\nTwenty-Seventh AAAI Conference on Artificial Intelligence, pp\r\n1041-1047, 2013.\r\n[10] I. Laptev, M. Marszalek, C. Schmid, and B. Rozenfeld, \u201cLearning\r\nrealistic human actions from movies,\u201d in CVPR 2008.\r\n[11] K. Mikolajczyk and H. Uemura. \u201cAction recognition with\r\nmotion-appearance vocabulary forest,\u201d CVPR, 2008.\r\n[12] J. Yuan, Z. Liu, and Y. Wu, \u201cDiscriminative Subvolume Search for\r\nEfficient Action Detection,\u201d CVPR, 2009.\r\n[13] M. B. Kaaniche and F. Bremond, \u201cGesture Recognition by Learning\r\nLocal Motion Signatures,\u201d In CVPR, 2010.\r\n[14] A. Kovashka and K. Grauman, \u201cLearning a Hierarchy of Discriminative\r\nSpace-Time Neighborhood Features for Human Action Recognition,\u201d In\r\nCVPR, 2010.\r\n[15] J. Yin and Y. Meng, \u201cHuman Activity Recognition in Video using a\r\nHierarchical Probabilistic Latent Model,\u201d In CVPR, 2010.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 104, 2015"}