Sketch-Based Subspace Clustering of Hyperspectral Images

Abstract

Sparse subspace clustering (SSC) techniques provide the state-of-the-art in clustering of hyperspectral images (HSIs). However, their computational complexity hinders their applicability to large-scale HSIs. In this paper, we propose a large-scale SSC-based method, which can effectively process large HSIs while also achieving improved clustering accuracy compared to the current SSC methods. We build our approach based on an emerging concept of sketched subspace clustering, which was to our knowledge not explored at all in hyperspectral imaging yet. Moreover, there are only scarce results on any large-scale SSC approaches for HSI. We show that a direct application of sketched SSC does not provide a satisfactory performance on HSIs but it does provide an excellent basis for an effective and elegant method that we build by extending this approach with a spatial prior and deriving the corresponding solver. In particular, a random matrix constructed by the Johnson-Lindenstrauss transform is first used to sketch the self-representation dictionary as a compact dictionary, which significantly reduces the number of sparse coefficients to be solved, thereby reducing the overall complexity. In order to alleviate the effect of noise and within-class spectral variations of HSIs, we employ a total variation constraint on the coefficient matrix, which accounts for the spatial dependencies among the neighbouring pixels. We derive an efficient solver for the resulting optimization problem, and we theoretically prove its convergence property under mild conditions. The experimental results on real HSIs show a notable improvement in comparison with the traditional SSC-based methods and the state-of-the-art methods for clustering of large-scale images.

Improving K-Nearest Neighbor Approaches for Density-Based Pixel Clustering in Hyperspectral Remote Sensing Images

“…The classes C8 (grapes untrained) and C15 (vineyard untrained) could not be retrieved by any method. Several published papers already show the difficulty to separate these two classes [65]. However, the class C7 (celery) was split into two clusters with visual coherence by all the density-based methods with MNN graph modification, which confirms the usefulness of this approach for detecting close clusters.…”

Affinity Matrix Learning Via Nonnegative Matrix Factorization for Hyperspectral Imagery Clustering

“…Inspired by the success of MF in hyperspectral unmixing, a robust manifold method consisting of two MF components (RMMF) for HSI clustering is proposed in [42] and the clustering indicators can be directly obtained via the second MF component. The Sketch SSC method is applied for large HSI clustering by extending integrating it with a spatial prior in [43].…”

Robust Multiview Subspace Clustering of Images via Tighter Rank Approximation

“…The most representative ones are sparse subspace clustering [10] (SSC, pursuing a sparse coefficient matrix) and low-rank subspace clustering [11] (LRR, pursuing a low-rank coefficient matrix). Thereafter, many extensions have been developed to improve these methods, such as sparse subspace clustering algorithm based on a nonconvex modeling formulation [12] and sketchbased subspace clustering [13]. FIGURE 1: The flowchart of our method.…”