Dimensionality Reduction via Regression in Hyperspectral Imagery

Abstract

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).

12 pages, 6 figures, 62 references

References in corpus (4)

• Iterative Gaussianization: from ICA to Random Rotations
• Validation of nonlinear PCA
• Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis
• Principal Polynomial Analysis

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• Sequential Learning of Principal Curves: Summarizing Data Streams on the Fly
• Tight Sensitivity Bounds For Smaller Coresets
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• Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks
• A Convolutional Neural Network with Mapping Layers for Hyperspectral Image Classification