Deep Clustering and Visualization for End-to-End High-Dimensional Data Analysis.

High-dimensional data analysis for exploration and discovery includes two fundamental tasks: deep clustering and data visualization. When these two associated tasks are done separately, as is often the case thus far, disagreements can occur among the tasks in terms of geometry preservation. Namely, the clustering process is often accompanied by the corruption of the geometric structure, whereas visualization aims to preserve the data geometry for better interpretation. Therefore, how to achieve deep clustering and data visualization in an end-to-end unified framework is an important but challenging problem. In this article, we propose a novel neural network-based method, called deep clustering and visualization (DCV), to accomplish the two associated tasks end-to-end to resolve their disagreements. The DCV framework consists of two nonlinear dimensionality reduction (NLDR) transformations: 1) one from the input data space to latent feature space for clustering and 2) the other from the latent feature space to the final 2-D space for visualization. Importantly, the first NLDR transformation is mainly optimized by one Clustering Loss, allowing arbitrary corruption of the geometric structure for better clustering, while the second NLDR transformation is optimized by one Geometry-Preserving Loss to recover the corrupted geometry for better visualization. Extensive comparative results show that the DCV framework outperforms other leading clustering-visualization algorithms in terms of both quantitative evaluation metrics and qualitative visualization.