Deep Two-Way Matrix Reordering for Relational Data Analysis

TL;DR

DeepTMR is a neural network-based matrix reordering method that automatically extracts nonlinear features for better structural interpretation and provides a denoised mean matrix for visualization, applicable to synthetic and real data.

Contribution

It introduces a novel deep learning approach for matrix reordering that does not require prior structural knowledge and offers denoising capabilities.

Findings

Effective on synthetic datasets

Demonstrates utility on practical datasets

Provides clear visualization of global structure

Abstract

Matrix reordering is a task to permute the rows and columns of a given observed matrix such that the resulting reordered matrix shows meaningful or interpretable structural patterns. Most existing matrix reordering techniques share the common processes of extracting some feature representations from an observed matrix in a predefined manner, and applying matrix reordering based on it. However, in some practical cases, we do not always have prior knowledge about the structural pattern of an observed matrix. To address this problem, we propose a new matrix reordering method, called 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 then be used for matrix reordering. Moreover, the proposed DeepTMR provides the denoised mean matrix of a given observed matrix as an output of the trained network. This denoised mean matrix can be used to visualize the global structure of the reordered observed matrix. We demonstrate the effectiveness of the proposed DeepTMR by applying it to both synthetic and practical datasets.