# Riemannian Nearest-Regularized Subspace Classification for Polarimetric SAR images

arXiv: https://arxiv.org/abs/2201.00337 · HTML: https://mlsanity.com/paper/2201.00337/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 19 references that are in the map.
- First posted on arXiv 2 Jan 2022.

## Builds on (most cited first, 2 of 2)

- [Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices](https://mlsanity.com/paper/1507.02772/) (2015)
- [A PolSAR Scattering Power Factorization Framework and Novel Roll-Invariant Parameters Based Unsupervised Classification Scheme Using a Geodesic Distance](https://mlsanity.com/paper/1906.11577/) (2019)

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

- [SS-MAE: Spatial-Spectral Masked Auto-Encoder for Multi-Source Remote Sensing Image Classification](https://mlsanity.com/paper/2311.04442/) (2023)
- [Riemannian Complex Matrix Convolution Network for PolSAR Image Classification](https://mlsanity.com/paper/2312.03378/) (2023)
- [Riemannian Complex Hermit Positive Definite Convolution Network for Polarimetric SAR Image Classification](https://mlsanity.com/paper/2502.08137/) (2025)
- [A Novel Riemannian Sparse Representation Learning Network for Polarimetric SAR Image Classification](https://mlsanity.com/paper/2502.15302/) (2025)

## Abstract (arXiv)

As a representation learning method, nearest regularized subspace(NRS) algorithm is an effective tool to obtain both accuracy and speed for PolSAR image classification. However, existing NRS methods use the polarimetric feature vector but the PolSAR original covariance matrix(known as Hermitian positive definite(HPD)matrix) as the input. Without considering the matrix structure, existing NRS-based methods cannot learn correlation among channels. How to utilize the original covariance matrix to NRS method is a key problem. To address this limit, a Riemannian NRS method is proposed, which consider the HPD matrices endow in the Riemannian space. Firstly, to utilize the PolSAR original data, a Riemannian NRS method(RNRS) is proposed by constructing HPD dictionary and HPD distance metric. Secondly, a new Tikhonov regularization term is designed to reduce the differences within the same class. Finally, the optimal method is developed and the first-order derivation is inferred. During the experimental test, only T matrix is used in the proposed method, while multiple of features are utilized for compared methods. Experimental results demonstrate the proposed method can outperform the state-of-art algorithms even using less features.