Graph Embedding via High Dimensional Model Representation for Hyperspectral Images

TL;DR

This paper introduces a nonlinear manifold learning method based on High Dimensional Model Representation (HDMR) for hyperspectral images, enabling explicit out-of-sample embedding and improving classification accuracy over traditional linear methods.

Contribution

The paper proposes a novel HDMR-based manifold learning approach that provides explicit nonlinear embedding functions for hyperspectral images, addressing the limitations of linear assumptions.

Findings

Achieves promising classification accuracy on hyperspectral datasets

Outperforms linear manifold learning methods in experiments

Enables explicit out-of-sample embedding for hyperspectral data

Abstract

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent classification, regression, or unmixing. Manifold learning methods have shown excellent performance to deal with hyperspectral image (HSI) analysis but, unless specifically designed, they cannot provide an explicit embedding map readily applicable to out-of-sample data. A common assumption to deal with the problem is that the transformation between the high-dimensional input space and the (typically low) latent space is linear. This is a particularly strong assumption, especially when dealing with hyperspectral images due to the well-known nonlinear nature of the data. To address this problem, a manifold learning method based on High Dimensional Model Representation (HDMR) is proposed, which enables to present a nonlinear embedding function to project out-of-sample samples into the latent space. The proposed method is compared to manifold learning methods along with its linear counterparts and achieves promising performance in terms of classification accuracy of a representative set of hyperspectral images.