Fast Spectral Clustering With Anchor Graph for Large Hyperspectral Images

Abstract

Hyperspectral image (HSI) clustering, which aims at dividing hyperspectral pixels into clusters, has drawn significant attention in practical applications. Recently, many graphbased clustering methods, which construct an adjacent graph to model the data relationship, have shown dominant performance. However, the high dimensionality of HSI data makes it hard to construct the pairwise adjacent graph. Besides, abundant spatial structures are often overlooked during the clustering procedure. In order to better handle the high dimensionality problem and preserve the spatial structures, this paper proposes a novel unsupervised approach called spatial-spectral clustering with anchor graph (SSCAG) for HSI data clustering. The SSCAG has the following contributions: 1) the anchor graph-based strategy is used to construct a tractable large graph for HSI data, which effectively exploits all data points and reduces the computational complexity; 2) a new similarity metric is presented to embed the spatial-spectral information into the combined adjacent graph, which can mine the intrinsic property structure of HSI data; 3) an effective neighbors assignment strategy is adopted in the optimization, which performs the singular value decomposition (SVD) on the adjacent graph to get solutions efficiently. Extensive experiments on three public HSI datasets show that the proposed SSCAG is competitive against the state-of-the-art approaches.

Anchors Bring Ease: An Embarrassingly Simple Approach to Partial Multi-View Clustering

“…Recall that Σ ∈ R N ×l is the singular value matrix of A, then ΣΣ T returns an N -by-N diagonal matrix storing all the eigen values of S = AA T . The column vectors of P are the eigen vectors of S. This has been proved in Fast Spectral Clustering (Wang, Nie, and Yu 2017). To reduce the computational complexity, we can perform SVD on A to derive the desired F rather than eigen decomposition on S. Alternatively, we can skillfully follow (Liu et al 2011) to perform eigen decomposition on a small l × l matrix 2 Some previous works ignore the smallest eigen value 0 of Laplacian matrix, since the corresponding eigen vector is 1 which is useless for the following k-means clustering.…”

Affinity Matrix Learning Via Nonnegative Matrix Factorization for Hyperspectral Imagery Clustering

“…Additionally, in order to address the issue of large HSI clustering, several methods based on anchor graph, affinity learning and matrix factorization (MF) are proposed to achieve less computational cost. The fast spectral clustering with anchor graph (FSCAG) method first constructs the anchor graph by incorporating the spatial information of HSI and then spectral analysis is efficiently achieved [36]. The scalable graph-based clustering with nonnegative relaxation (SGCNR) employs the orthonormal constraint with nonnegative relaxation to build a novel graph-based clustering model and the clustering indicators are directly obtained [37].…”

Fast Spectral Clustering for Unsupervised Hyperspectral Image Classification

“…Therefore, unsupervised HSI classification is an extremely important techniques and has attracted significant attention in recent years. Wang et al [26] illustrated that the existing algorithms can be coarsely divided into the following four categories: (1) Centroid-based clustering methods, such as k-mean [27] and fuzzy c-means [28], minimize the within cluster sample distance, but are sensitive to initialization and noise, and cannot provide a robust performance.…”

“…Another method proposed by Nie et al [43,44] constructs anchor-based affinity matrix with balanced k-means based hierarchical k-means algorithm. Wang et al [26] improved the anchor-based affinity matrix by incorporating the spatial information. Meanwhile, Nonnegative Matrix Factorization (NMF) technique [45,46] and its variants also provide an efficient solution for HSI classification.…”