Generalized Multi-Linear Principal Component Analysis of Binary Tensors

Current data processing tasks often involve manipulation of multi-dimensional objects tensors. In many real world applications such as gait recognition, document analysis or graph mining (with graphs represented by adjacency tensors), the tensors can be constrained to binary values only. To the best of our knowledge at present there is no principled systematic framework for decomposition of binary tensors. To close this gap we propose a generalized multi-linear model for principal component analysis of binary tensors (GML-PCA). In the model formulation, to account for binary nature of the data, each tensor element is modeled by a Bernoulli noise distribution. To extract the dominant trends in the data, we constrain the natural parameters of the Bernoulli distributions to lie in a sub-space spanned by a reduced set of basis (principal) tensors. Bernoulli distribution is a member of exponential family with helpful analytical properties that allow us to derive a an iterative scheme for estimation of the basis tensors and other model parameters via maximum likelihood. We evaluate and compare the proposed GML-PCA technique with an existing real-valued tensor decomposition method (TensorLSI) in two scenarios: (1) in a series of controlled experiments involving synthetic data; (2) on a real world biological dataset of DNA sub-sequences from different functional regions, with sequences represented by binary tensors. The experiments suggest that the GML-PCA model is better suited for modeling binary tensors than its real-valued counterpart TensorLSI model.