RESUMEN
Dimensional reduction (DR) maps high-dimensional data into a lower dimensions latent space with minimized defined optimization objectives. The two independent branches of DR are feature selection (FS) and feature projection (FP). FS focuses on selecting a critical subset of dimensions but risks destroying the data distribution (structure). On the other hand, FP combines all the input features into lower dimensions space, aiming to maintain the data structure, but lacks interpretability and sparsity. Moreover, FS and FP are traditionally incompatible categories and have not been unified into an amicable framework. Therefore, we consider that the ideal DR approach combines both FS and FP into a unified end-to-end manifold learning framework, simultaneously performing fundamental feature discovery while maintaining the intrinsic relationships between data samples in the latent space. This paper proposes a unified framework named Unified Dimensional Reduction Network (UDRN) to integrate FS and FP in an end-to-end way. Furthermore, a novel network framework is designed to implement FS and FP tasks separately using a stacked feature selection network and feature projection network. In addition, a stronger manifold assumption and a novel loss function are proposed. Furthermore, the loss function can leverage the priors of data augmentation to enhance the generalization ability of the proposed UDRN. Finally, comprehensive experimental results on four image and four biological datasets, including very high-dimensional data, demonstrate the advantages of DRN over existing methods (FS, FP, and FS&FP pipeline), especially in downstream tasks such as classification and visualization.
