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.

翻译：矩阵重排序是通过置换给定观测矩阵的行与列，使得重排后的矩阵呈现出有意义或可解释的结构模式的任务。大多数现有矩阵重排序技术遵循共同流程：以预定义方式从观测矩阵中提取某些特征表示，并基于此进行矩阵重排序。然而，在某些实际应用中，我们并不总是对观测矩阵的结构模式具有先验知识。为解决此问题，我们提出一种新的矩阵重排序方法——深度双向矩阵重排序（DeepTMR），该方法利用神经网络模型进行学习。训练后的网络能够自动从观测矩阵中提取非线性行/列特征，这些特征随后可用于矩阵重排序。此外，所提出的DeepTMR能够通过训练网络的输出提供给定观测矩阵的去噪均值矩阵。该去噪均值矩阵可用于可视化重排后观测矩阵的全局结构。我们通过在合成数据集和实际数据集上的应用，验证了所提出DeepTMR方法的有效性。