# Deep Two-Way Matrix Reordering for Relational Data Analysis

arXiv: https://arxiv.org/abs/2103.14203 · HTML: https://mlsanity.com/paper/2103.14203/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 60 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 2 of 2)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Ordering: Towards the Optimal by Learning](https://mlsanity.com/paper/2001.06631/) (2020)

## Built on by (most cited first, 1 of 1)

- [AutoLL: Automatic Linear Layout of Graphs based on Deep Neural Network](https://mlsanity.com/paper/2108.02431/) (2021)

## Abstract (arXiv)

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.