  Dimensional reduction~(DR) maps high-dimensional data into a lower dimensions
latent space with minimized defined optimization objectives. The DR method
usually falls into 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. FS and FP are traditionally
incompatible categories; thus, they have not been unified into an amicable
framework. We propose 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. In this work, we develop a unified
framework, Unified Dimensional Reduction Neural-network~(UDRN), that integrates
FS and FP in a compatible, end-to-end way. We improve the neural network
structure by implementing FS and FP tasks separately using two stacked
sub-networks. In addition, we designed data augmentation of the DR process to
improve the generalization ability of the method when dealing with extensive
feature datasets and designed loss functions that can cooperate with the data
augmentation. Extensive 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.
