Kernel Low-Rank Entropic Component Analysis for Hyperspectral Image Classification

Abstract

Principal component analysis (PCA) and its variations are still the primary tool for feature extraction (FE) in remote sensing community. This is unfortunate, as there has been strong argument against using PCA for this purpose due to its inherent linear properties and uninformative principal components. Therefore, several critical issues still should be considered in hyperspectral image classification when using PCA, among which: 1) the large number of spectral channels and small number of training samples; 2) the nonlinearities of hyperspectral data; 3) the small-sample issue. In order to alleviate these problems, this paper employs a new information-theoretic FE method so-called kernel entropic component analysis (KECA), which can not only extract more nonlinear information, but also be adapt to limited-sample environment. A theorem of the pivoted Cholesky decomposition is also introduced to improve the efficiency of the KECA. The optimized version can more rapidly implement spectral-spatial features extraction, particularly for large-scale HSIs, while effectively maintaining the clustering performances of KECA. Experiments implemented on several real HSIs verify the effectiveness of the new method armed with a support vector machine (SVM) classifier, in comparison with other PCA-based and state-of-the-art HSI classification algorithms. The code will be also made publicly available.

KECANet: A novel convolutional kernel network for ocean SAR scene classification with limited labeled data

“…where the eigenvalues l 1 , ⋯, l N corresponding to w 1 , ⋯, w N is reserved as the entropy estimate. In another word, KECA performs feature extraction not by the eigenvectors associated with the top N c eigenvalues but by the axes contributing most to the Reńyi entropy estimate V(p) (Jenssen, 2009;Bai et al, 2020a). This can be concluded as the most distinct difference between KECA and KPCA (Jenssen, 2009).…”

“…The width coefficient, also known as the kernel width s , plays a role in kernel-based methods (Bai et al, 2019;Bai et al, 2020a). We evaluated the impact of the width of KECANet on the selected dataset.…”

“…A novel information-theoretic method, namely kernel entropy component analysis (KECA), was proposed for the nonlinear processing of image patches (Jenssen, 2009). KECA aims to seek optimal eigenvectors (defined as entropic components) in RKHS that can compress the Reńyi entropy information of the input space as much as possible instead of selecting top eigenvalues (Bai et al, 2019;Bai et al, 2020a). As compared to the principal components obtained by KPCA that solely correspond to the ranking order of eigenvalues, entropic components are strikingly different and oriented towards the maximum Reńyi entropy of the input data (Jenssen, 2009).…”

Multi-scale nonlinear edge-based three-phase model for unsupervised hyperspectral feature extraction

“…The multiple methods include the AF, 36 PCA, 37 KPCA, 38 MNF, 28 OTVCA, 23 and KLRECA. 11 The default parameters of distinct models are set to be same as the settings shown in the corresponding papers.…”

“…For the preprocessing step, most well-known methods normalize the input original hyperspectral data without additional denoising treatment. [9][10][11] However, the noisy part of the image gathered by the remote sensing technique may lower the information extraction performance due to the inhibition effect of various known and unknown factors. 12 Some projection-based band reduction techniques, for example, traditional principal component analysis (PCA), 13,14 minimum noise fraction (MNF), 15 and classic PCA with segmented-PCA joined with two-dimensional singular spectrum analysis, 16 linearly project the pretreated HSI into a linear neo-space.…”