  High dimensional data analysis for exploration and discovery includes three
fundamental tasks: dimensionality reduction, clustering, and visualization.
When the three associated tasks are done separately, as is often the case thus
far, inconsistencies can occur among the tasks in terms of data geometry and
others. This can lead to confusing or misleading data interpretation. In this
paper, we propose a novel neural network-based method, called Consistent
Representation Learning (CRL), to accomplish the three associated tasks
end-to-end and improve the consistencies. The CRL network consists of two
nonlinear dimensionality reduction (NLDR) transformations: (1) one from the
input data space to the latent feature space for clustering, and (2) the other
from the clustering space to the final 2D or 3D space for visualization.
Importantly, the two NLDR transformations are performed to best satisfy local
geometry preserving (LGP) constraints across the spaces or network layers, to
improve data consistencies along with the processing flow. Also, we propose a
novel metric, clustering-visualization inconsistency (CVI), for evaluating the
inconsistencies. Extensive comparative results show that the proposed CRL
neural network method outperforms the popular t-SNE and UMAP-based and other
contemporary clustering and visualization algorithms in terms of evaluation
metrics and visualization.
