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# Tensor Analyzers

*Proceedings of the 30th International Conference on Machine Learning*, PMLR 28(3):163-171, 2013.

#### Abstract

Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings.