# Graph Embedding via High Dimensional Model Representation for Hyperspectral Images

arXiv: https://arxiv.org/abs/2111.14680 · HTML: https://mlsanity.com/paper/2111.14680/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 77 references that are in the map.
- First posted on arXiv 29 Nov 2021.

## Builds on (most cited first, 7 of 7)

- [Advances in Hyperspectral Image Classification: Earth monitoring with statistical learning methods](https://mlsanity.com/paper/1310.5107/) (2013)
- [Joint and Progressive Subspace Analysis (JPSA) with Spatial-Spectral Manifold Alignment for Semi-Supervised Hyperspectral Dimensionality Reduction](https://mlsanity.com/paper/2009.10003/) (2020)
- [Kernel Manifold Alignment](https://mlsanity.com/paper/1504.02338/) (2015)
- [Dimensionality Reduction of Hyperspectral Imagery Based on Spatial-spectral Manifold Learning](https://mlsanity.com/paper/1812.09530/) (2018)
- [A study of the classification of low-dimensional data with supervised manifold learning](https://mlsanity.com/paper/1507.05880/) (2015)
- [Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods](https://mlsanity.com/paper/1310.5089/) (2013)
- [Efficient Nonlinear RX Anomaly Detectors](https://mlsanity.com/paper/2012.05799/) (2020)

## Built on by (most cited first, 1 of 1)

- [Large-scale unsupervised spatio-temporal semantic analysis of vast regions from satellite images sequences](https://mlsanity.com/paper/2208.13504/) (2022)

## Abstract (arXiv)

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.