Issue No. 02 - Feb. (2015 vol. 37)
ISSN: 0162-8828
pp: 475-487
Zenglin Xu , School of Computer Science and Technology, University of Electronic Science and Technology of China, Chengdu, China
Feng Yan , , Facebook Inc., Menlo Park, CA, USA
Yuan Qi , Department of Computer Science and Department of Statistics, Purdue University, West Lafayette, USA
ABSTRACT
Tensor decomposition is a powerful computational tool for multiway data analysis. Many popular tensor decomposition approaches—such as the Tucker decomposition and CANDECOMP/PARAFAC (CP)—amount to multi-linear factorization. They are insufficient to model (i) complex interactions between data entities, (ii) various data types (e.g., missing data and binary data), and (iii) noisy observations and outliers. To address these issues, we propose tensor-variate latent nonparametric Bayesian models for multiway data analysis. We name these models InfTucker. These new models essentially conduct Tucker decomposition in an infinite feature space. Unlike classical tensor decomposition models, our new approaches handle both continuous and binary data in a probabilistic framework. Unlike previous Bayesian models on matrices and tensors, our models are based on latent Gaussian or $t$ processes with nonlinear covariance functions. Moreover, on network data, our models reduce to nonparametric stochastic blockmodels and can be used to discover latent groups and predict missing interactions. To learn the models efficiently from data, we develop a variational inference technique and explore properties of the Kronecker product for computational efficiency. Compared with a classical variational implementation, this technique reduces both time and space complexities by several orders of magnitude. On real multiway and network data, our new models achieved significantly higher prediction accuracy than state-of-art tensor decomposition methods and blockmodels.
INDEX TERMS
Tensile stress, Computational modeling, Data models, Gaussian processes, Bayes methods, Noise, Matrix decomposition,Algorithms for data and knowledge management, Machine learning,random graphs and exchangeable arrays, Multiway analysis, network modeling, Gaussian process, tensor/matrix factorization, stochastic blockmodel, nonparametric Bayes
CITATION
Zenglin Xu, Feng Yan, Yuan Qi, "Bayesian Nonparametric Models for Multiway Data Analysis", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 37, no. , pp. 475-487, Feb. 2015, doi:10.1109/TPAMI.2013.201