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Dimensional reduction~(DR) maps high-dimensional data into a lower dimensionslatent space with minimized defined optimization objectives. The DR methodusually falls into feature selection~(FS) and feature projection~(FP). FSfocuses on selecting a critical subset of dimensions but risks destroying thedata distribution (structure). On the other hand, FP combines all the inputfeatures into lower dimensions space, aiming to maintain the data structure;but lacks interpretability and sparsity. FS and FP are traditionallyincompatible categories; thus, they have not been unified into an amicableframework. We propose that the ideal DR approach combines both FS and FP into aunified end-to-end manifold learning framework, simultaneously performingfundamental feature discovery while maintaining the intrinsic relationshipsbetween data samples in the latent space. In this work, we develop a unifiedframework, Unified Dimensional Reduction Neural-network~(UDRN), that integratesFS and FP in a compatible, end-to-end way. We improve the neural networkstructure by implementing FS and FP tasks separately using two stackedsub-networks. In addition, we designed data augmentation of the DR process toimprove the generalization ability of the method when dealing with extensivefeature datasets and designed loss functions that can cooperate with the dataaugmentation. Extensive experimental results on four image and four biologicaldatasets, including very high-dimensional data, demonstrate the advantages ofDRN over existing methods~(FS, FP, and FS\&FP pipeline), especially indownstream tasks such as classification and visualization.

UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projection