# Dimensionality Reduction via Regression in Hyperspectral Imagery

arXiv: https://arxiv.org/abs/1602.00214 · HTML: https://mlsanity.com/paper/1602.00214/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2016.

## Built on by (most cited first, 4 of 4)

- [Compressing Neural Networks: Towards Determining the Optimal Layer-wise Decomposition](https://mlsanity.com/paper/2107.11442/) (2021)
- [Deep Gaussian Processes for Biogeophysical Parameter Retrieval and Model Inversion](https://mlsanity.com/paper/2104.10638/) (2021)
- [Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks](https://mlsanity.com/paper/2111.15018/) (2021)
- [A Variational Latent-Space Framework for Uncertainty-Aware Spectral Image Emulation](https://mlsanity.com/paper/2603.21911/) (2026)

## Abstract (arXiv)

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The properties of DRR enable learning a more broader class of data manifolds than the recently proposed Non-linear Principal Components Analysis (NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance of the representation in reducing the dimensionality of remote sensing data. In particular, we tackle two common problems: processing very high dimensional spectral information such as in hyperspectral image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA).