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

arXiv: https://arxiv.org/abs/2207.03809 · HTML: https://mlsanity.com/paper/2207.03809/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 70 references that are in the map.
- First posted on arXiv 8 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [Quick and Robust Feature Selection: the Strength of Energy-efficient Sparse Training for Autoencoders](https://mlsanity.com/paper/2012.00560/) (2020)
- [Revisiting Dimensionality Reduction Techniques for Visual Cluster Analysis: An Empirical Study](https://mlsanity.com/paper/2110.02894/) (2021)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [Topological Data Analysis](https://mlsanity.com/paper/1609.08227/) (2016)
- [DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling](https://mlsanity.com/paper/1711.06011/) (2017)
- [DLME: Deep Local-flatness Manifold Embedding](https://mlsanity.com/paper/2207.03160/) (2022)
- [Fractal Autoencoders for Feature Selection](https://mlsanity.com/paper/2010.09430/) (2020)
- [Unsupervised Deep Manifold Attributed Graph Embedding](https://mlsanity.com/paper/2104.13048/) (2021)
- [IVFS: Simple and Efficient Feature Selection for High Dimensional Topology Preservation](https://mlsanity.com/paper/2004.01299/) (2020)

## Built on by (most cited first, 5 of 5)

- [Boosting Novel Category Discovery Over Domains with Soft Contrastive Learning and All-in-One Classifier](https://mlsanity.com/paper/2211.11262/) (2022)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [Zero-Shot Visual Deepfake Detection: Can AI Predict and Prevent Fake Content Before It's Created?](https://mlsanity.com/paper/2509.18461/) (2025)
- [Model Input-Output Configuration Search with Embedded Feature Selection for Sensor Time-series and Image Classification](https://mlsanity.com/paper/2310.17250/) (2023)

## Abstract (arXiv)

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.