Kernel Sparse Subspace Clustering with a Spatial Max Pooling Operation for Hyperspectral Remote Sensing Data Interpretation

Abstract

Hyperspectral image (HSI) clustering is generally a challenging task because of the complex spectral-spatial structure. Based on the assumption that all the pixels are sampled from the union of subspaces, recent works have introduced a robust technique-the sparse subspace clustering (SSC) algorithm and its enhanced versions (SSC models incorporating spatial information)-to cluster HSIs, achieving excellent performances. However, these methods are all based on the linear representation model, which conflicts with the well-known nonlinear structure of HSIs and limits their performance to a large degree. In this paper, to overcome these obstacles, we present a new kernel sparse subspace clustering algorithm with a spatial max pooling operation (KSSC-SMP) for hyperspectral remote sensing data interpretation. The proposed approach maps the feature points into a much higher dimensional kernel space to extend the linear sparse subspace clustering model to nonlinear manifolds, which can better fit the complex nonlinear structure of HSIs. With the help of the kernel sparse representation, a more accurate representation coefficient matrix can be obtained. A spatial max pooling operation is utilized for the representation coefficients to generate more discriminant features by integrating the spatial-contextual information, which is essential for the accurate modeling of HSIs. This paper is an extension of our previous conference paper, and a number of enhancements are put forward. The proposed algorithm was evaluated on two well-known hyperspectral data sets-the Salinas image and the University of Pavia image-and the experimental results clearly indicate that the newly developed KSSC-SMP algorithm can obtain very competitive clustering results for HSIs, outperforming the current state-of-the-art clustering methods.

Sketch-Based Subspace Clustering of Hyperspectral Images

“…The optimization problem of the SSC-TV model actually cannot be efficiently solved in practice due to its prohibitively high computational complexity. The traditional SSC-based methods [11,[20][21][22][23]41,42] also suffer from the same problem. One key obstacle is that they have to calculate and save the inverse of the entire large matrix (Y T Y + µI) ∈ R MN×MN in memory based on the ADMM algorithm, whose time complexity reaches O((MN) 3 ), which is infeasible for large-scale data sets.…”

“…As the SSC model calculates sparse coefficients individually and independently for each input data point, the clustering performance is sensitive to noise. In order to solve this problem, various extensions have been proposed with the aim to encode the spatial dependencies among the neighbouring data points in hyperspectral data, and obtain thereby more accurate similarity matrices and improved clustering results [18][19][20][21][22][23][24][25]. Guo et al [18,19] focus on the clustering of 1-D drill hole hyperspectral data and regularize the coefficients of neighbouring data points in depth to be similar by a 1 norm based smoothing regularization.…”

“…For the 2-D spatial-wise hyperspectral images, a smoothing strategy was introduced in Reference [20] by minimizing the difference between coefficients corresponding to the central pixel and to the mean of pixels in a local square window. A kernel version of SSC incorporating max pooling of the sparse coefficient matrix was presented in Reference [21]. The spectral-spatial SSC method of Reference [22] integrates an 2 spatial regularizer with the SSC model (L2-SSC), to penalize abrupt differences between the coefficients of nearby pixels.…”

Landmark-Based Large-Scale Sparse Subspace Clustering Method for Hyperspectral Images

“…In recent years, sparse subspace clustering (SSC) [1] method has achieved the state-of-the-art performance in HSI clustering [2][3][4][5][6][7]. SSC is based on a self-representation model which employs the input data as a dictionary.…”

“…To reduce the noise sensitivity, some extensions of SSC have been proposed by introducing different spatial constraints [2][3][4][5][6][7]. A smoothing strategy was introduced in [2] by minimizing the coefficient difference between the central pixel and the mean of pixels in a local square window.…”