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.