  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.
