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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.

The locality preserving projections (LPP) algorithm is a recently developed linear dimensionality reduction algorithm that has been frequently used in face recognition and other applications. However, the projection matrix in LPP is not orthogonal, thus creating difficulties for both reconstruction and other applications. As the orthogonality property is desirable, orthogonal LPP (OLPP) has been proposed so that an orthogonal projection matrix can be obtained based on a step by step procedure; however, this makes the algorithm computationally more expensive. Therefore, in this paper, we propose a fast and orthogonal version of LPP, called FOLPP, which simultaneously minimizes the locality and maximizes the globality under the orthogonal constraint. As a result, the computation burden of the proposed algorithm can be effectively alleviated compared with the OLPP algorithm. Experimental results on two face recognition data sets and two hyperspectral data sets are presented to demonstrate the effectiveness of the proposed algorithm.

The AdaBoost algorithm has the superiority of resisting overfitting. Understanding the mysteries of this phenomena is a very fascinating fundamental theoretical problem. Many studies are devoted to explaining it from statistical view and margin theory. In this paper, we illustrate it from feature learning viewpoint, and propose the AdaBoost+SVM algorithm, which can explain the resistant to overfitting of AdaBoost directly and easily to understand. Firstly, we adopt the AdaBoost algorithm to learn the base classifiers. Then, instead of directly weighted combination the base classifiers, we regard them as features and input them to SVM classifier. With this, the new coefficient and bias can be obtained, which can be used to construct the final classifier. We explain the rationality of this and illustrate the theorem that when the dimension of these features increases, the performance of SVM would not be worse, which can explain the resistant to overfitting of AdaBoost.