A Tensor-Variate Gaussian Process for Classification of Multidimensional Structured Data

As tensors provide a natural and efficient representation of multidimensional structured data, in this paper, we consider probabilistic multinomial probit classification for tensor-variate inputs with Gaussian processes (GP) priors placed over the latent function. In order to take into account the underlying multimodes structure information within the model, we propose a framework of probabilistic product kernels for tensorial data based on a generative model assumption. More specifically, it can be interpreted as mapping tensors to probability density function space and measuring similarity by an information divergence. Since tensor kernels enable us to model input tensor observations, the proposed tensor-variate GP is considered as both a generative and discriminative model. Furthermore, a fully variational Bayesian treatment for multiclass GP classification with multinomial probit likelihood is employed to estimate the hyperparameters and infer the predictive distributions. Simulation results on both synthetic data and a real world application of human action recognition in videos demonstrate the effectiveness and advantages of the proposed approach for classification of multiway tensor data, especially in the case that the underlying structure information among multimodes is discriminative for the classification task.

[1]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[2]  Dominik Endres,et al.  A new metric for probability distributions , 2003, IEEE Transactions on Information Theory.

[3]  Nuno Vasconcelos,et al.  A Kullback-Leibler Divergence Based Kernel for SVM Classification in Multimedia Applications , 2003, NIPS.

[4]  Juan Carlos Niebles,et al.  Unsupervised Learning of Human Action Categories , 2006 .

[5]  Thomas B. Moeslund,et al.  A Local 3-D Motion Descriptor for Multi-View Human Action Recognition from 4-D Spatio-Temporal Interest Points , 2012, IEEE Journal of Selected Topics in Signal Processing.

[6]  Kristian Kersting,et al.  Learning Preferences with Hidden Common Cause Relations , 2009, ECML/PKDD.

[7]  Tanaya Guha,et al.  Learning Sparse Representations for Human Action Recognition , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  Frank P. Ferrie,et al.  A Note on Metric Properties for Some Divergence Measures: The Gaussian Case , 2012, ACML.

[9]  Kian Ming Adam Chai,et al.  Variational Multinomial Logit Gaussian Process , 2012, J. Mach. Learn. Res..

[10]  C. Rasmussen,et al.  Approximations for Binary Gaussian Process Classification , 2008 .

[11]  David Barber,et al.  Bayesian Classification With Gaussian Processes , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Motoaki Kawanabe,et al.  Asymptotic Properties of the Fisher Kernel , 2004, Neural Computation.

[13]  Johan A. K. Suykens,et al.  A kernel-based framework to tensorial data analysis , 2011, Neural Networks.

[14]  Changsheng Xu,et al.  Boosted Exemplar Learning for Action Recognition and Annotation , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

[15]  Tae-Kyun Kim,et al.  Canonical Correlation Analysis of Video Volume Tensors for Action Categorization and Detection , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[16]  Aki Vehtari,et al.  Nested expectation propagation for Gaussian process classification , 2013, J. Mach. Learn. Res..

[17]  Zenglin Xu,et al.  Infinite Tucker Decomposition: Nonparametric Bayesian Models for Multiway Data Analysis , 2011, ICML.

[18]  Hans De Sterck,et al.  A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition , 2011, SIAM J. Sci. Comput..

[19]  Mark Girolami,et al.  Variational Bayesian Multinomial Probit Regression with Gaussian Process Priors , 2006, Neural Computation.

[20]  Barbara Caputo,et al.  Recognizing human actions: a local SVM approach , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[21]  Peter A. Flach,et al.  Evaluation Measures for Multi-class Subgroup Discovery , 2009, ECML/PKDD.

[22]  Sheng Tang,et al.  Localized Multiple Kernel Learning for Realistic Human Action Recognition in Videos , 2011, IEEE Transactions on Circuits and Systems for Video Technology.

[23]  Mubarak Shah,et al.  Human Action Recognition in Videos Using Kinematic Features and Multiple Instance Learning , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[24]  J. Ross Beveridge,et al.  Action classification on product manifolds , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[25]  J. Bernardo,et al.  Nested Expectation Propagation for Gaussian Process Classification with a Multinomial Probit Likelihood , 2012 .

[26]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[27]  Tae-Kyun Kim,et al.  Learning Motion Categories using both Semantic and Structural Information , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Antoni B. Chan,et al.  A Family of Probabilistic Kernels Based on Information Divergence , 2004 .

[29]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorizations : An algorithmic perspective , 2014, IEEE Signal Processing Magazine.

[30]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[31]  Hyun-Chul Kim,et al.  Bayesian Gaussian Process Classification with the EM-EP Algorithm , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.