Multilinear Decomposition and Topographic Mapping of Binary Tensors

Abstract

Current methods capable of processing tensor objects in their natural higher-order structure have been introduced for real-valued tensors. Such techniques, however, are not suitable for processing binary tensors which arise in many real world problems, such as gait recognition, document analysis, or graph mining. To account for binary nature of the data, we propose a novel generalized multi-linear model for principal component analysis of binary tensors (GML-PCA). We compare the performance of GML-PCA with an existing model for real-valued tensor decomposition (TensorLSI) in two experiments. In the first experiment, synthetic binary tensors were compressed and consequently reconstructed, yielding the reconstruction error in terms of AUC. In the second experiment, we compare the ability to reveal biologically meaningful dominant trends in a real world large-scale dataset of DNA sequences represented through binary tensors. Both experiments show that our GML-PCA model is better suited for modeling binary tensors than the TensorLSI.