Deep Two-way Matrix Reordering for Relational Data Analysis

Matrix reordering is a task to permute rows and columns of a given observed matrix so that the resulting reordered matrix shows some meaningful or interpretable structural patterns. Most of the existing matrix reordering techniques share a common process of extracting some feature representation from an observed matrix in some pre-defined way, and applying matrix reordering based on it. However, in some practical cases, we would not always have a prior knowledge about the structural pattern that an observed matrix has. In this paper, to address this problem, we propose a new matrix reordering method, Deep Two-way Matrix Reordering (DeepTMR), using a neural network model. The trained network can automatically extract nonlinear row/column features from an observed matrix, which can be used for matrix reordering. Moreover, and proposed DeepTMR provides us with the denoised mean matrix of a given observed matrix as an output of the trained network. Such a denoised mean matrix can be used for visualizing the global structure of the reordered observed matrix. We demonstrate the effectiveness of proposed DeepTMR by applying it to both synthetic and practical data sets.