Laplacian Regularized Spatial-Aware Collaborative Graph for Discriminant Analysis of Hyperspectral Imagery

Xinwei Jiang,Xin Song,Junjun Jiang,Zhihua Cai,Yongshan Zhang,Junbin Gao

doi:10.3390/rs11010029

Abstract

Dimensionality Reduction (DR) models are of significance to extract low-dimensional features for Hyperspectral Images (HSIs) data analysis where there exist lots of noisy and redundant spectral features. Among many DR techniques, the Graph-Embedding Discriminant Analysis framework has demonstrated its effectiveness for HSI feature reduction. Based on this framework, many representation based models are developed to learn the similarity graphs, but most of these methods ignore the spatial information, resulting in unsatisfactory performance of DR models. In this paper, we firstly propose a novel supervised DR algorithm termed Spatial-aware Collaborative Graph for Discriminant Analysis (SaCGDA) by introducing a simple but efficient spatial constraint into Collaborative Graph-based Discriminate Analysis (CGDA) which is inspired by recently developed Spatial-aware Collaborative Representation (SaCR). In order to make the representation of samples on the data manifold smoother, i.e., similar pixels share similar representations, we further add the spectral Laplacian regularization and propose the Laplacian regularized SaCGDA (LapSaCGDA), where the two spectral and spatial constraints can exploit the intrinsic geometric structures embedded in HSIs efficiently. Experiments on three HSIs data sets verify that the proposed SaCGDA and LapSaCGDA outperform other state-of-the-art methods.

Highlights

As one of the most significant remote sensing techniques, Hyperspectral Images (HSIs) captured by modern remote sensors have been successfully applied in real-world tasks, such as target detection, and crop yield estimation, etc. [1,2,3]
The best regularization parameters for Laplacian regularized CGDA (LapCGDA), Sparse and Low-Rank Graph-based Discriminant Analysis (SLGDA), Spatial-aware Collaborative Graph for Discriminant Analysis (SaCGDA) and LapSaCGDA are listed in Table 1, which will be used in the following experiments
If we compare the Overall Accuracy (OA) of K-Nearest Neighbors (KNN) based on the proposed two models to OAs of Support Vector Machine (SVM) based on other Dimensionality Reduction (DR) techniques like Nonparametric Weighted Feature Extraction (NWFE), SLGDA, LapCGDA and Local Geometric Structure Fisher Analysis (LGSFA), what we can find is that the KNN classification results are better than SVM, which further proves that the proposed two algorithms are more effective to extract discriminative low-dimensional features than other contrastive approaches

Summary

Introduction

As one of the most significant remote sensing techniques, Hyperspectral Images (HSIs) captured by modern remote sensors have been successfully applied in real-world tasks, such as target detection, and crop yield estimation, etc. [1,2,3]. Reduction (DR) methods have been introduced to preprocess the HSI data so that the noisy and redundant features can be removed and the discriminative features can be extracted in low-dimensional subspace. All DR models for HSIs can be divided into two categories: bands selection and feature extraction [8,12]. The former focuses on choosing representative subset from original spectral bands with physical meanings by some criteria, while the latter tries to learn new features by transforming observed high-dimensional spectral bands/features to the low-dimensional features with discriminative and structural information. As stated in [8], discovering optimal bands from enormous numbers of possible band combinations by feature selection methods is typically suboptimal, in this paper we only focus on feature extraction based DR methods for HSIs instead of feature selection

Methods

Findings

Discussion

Conclusion