Dimensionality Reduction via Multiple Neighborhood-Aware Nonlinear Collaborative Analysis for Hyperspectral Image Classification
Yule Duan, Chuang Chen, Maixia Fu, Yinsheng Li, Xiuwen Gong, Fulin Luo
Abstract
Local collaborative representation (CR) has drawn much attention in exploring data relationships due to considering local knowledge in the global linear combination, subsequently, local CR-based graph embedding methods have been applied to dimensionality reduction of hyperspectral image (HSI). However, HSI data with nonlinear distribution cannot be handled with pure linear combination accurately. Furthermore, the existing local knowledge in terms of binary relations between pairwise neighbors makes it hard to learn the accurate local structure among neighborhood sets through local CR-based graph embedding. To this end, this paper proposes a novel multiple neighborhood-aware nonlinear collaborative analysis (MNNCA) method. Relying on the primary and secondary neighborhoods, a dual-level neighborhood reconstruction is designed to search for optimal neighbors and mine the common attributes within the neighborhood. With the reconstruction information, a nonlinear extend multiple neighborhood-aware collaborative representation (NE-MNACR) model is built on nonlinear geodesic constraint and multi-neighborhood-aware items. It can explore the collaborative relationship among multiple neighborhood sets in the nonlinear space of HSI data. By preserving the multivariate local structure instead of pairwise local relations, a pair of collaborative structure preservation graphs are constructed to realize the final embedding of HSI data. Experimental results on serval HSI data sets demonstrate the superior performance of the proposed MNNCA method and NE-MNACR model in comparison with some state-of-the-art DR methods and local CR models.