At present, nonparametric subspace classifiers, such as collaborative representation-based classification (CRC) and sparse representation-based classification (SRC), are widely used in many pattern-classification and -recognition tasks. Meanwhile, the spatial pyramid matching (SPM) scheme, which considers spatial information in representing the image, is efficient for image classification. However, for SPM, the weights to evaluate the representation of different subregions are fixed. In this paper, we first introduce the spatial pyramid matching scheme to remote-sensing (RS)-image scene-classification tasks to improve performance. Then, we propose a weighted spatial pyramid matching collaborative-representation-based classification method, combining the CRC method with the weighted spatial pyramid matching scheme. The proposed method is capable of learning the weights of different subregions in representing an image. Finally, extensive experiments on several benchmark remote-sensing-image datasets were conducted and clearly demonstrate the superior performance of our proposed algorithm when compared with state-of-the-art approaches.

Nonnegative Matrix Factorization (NMF) is a widely used technique in many applications such as face recognition, motion segmentation, etc. It approximates the nonnegative data in an original high dimensional space with a linear representation in a low dimensional space by using the product of two nonnegative matrices. In many applications data are often partially corrupted with large additive noise. When the positions of noise are known, some existing variants of NMF can be applied by treating these corrupted entries as missing values. However, the positions are often unknown in many real world applications, which prevents the usage of traditional NMF or other existing variants of NMF. This paper proposes a Robust Nonnegative Matrix Factorization (RobustNMF) algorithm that explicitly models the partial corruption as large additive noise without requiring the information of positions of noise. In practice, large additive noise can be used to model outliers. In particular, the proposed method jointly approximates the clean data matrix with the product of two nonnegative matrices and estimates the positions and values of outliers/noise. An efficient iterative optimization algorithm with a solid theoretical justification has been proposed to learn the desired matrix factorization. Experimental results demonstrate the advantages of the proposed algorithm.

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Recently, label consistent k-svd (LC-KSVD) algorithm has been successfully applied in image classification. The objective function of LC-KSVD is consisted of reconstruction error, classification error and discriminative sparse codes error with 0 -norm sparse regularization term. The 0 -norm, however, leads to NP-hard problem. Despite some methods such as orthogonal matching pursuit can help solve this problem to some extent, it is quite difficult to find the optimum sparse solution. To overcome this limitation, we propose a label embedded dictionary learning (LEDL) method to utilise the 1 -norm as the sparse regularization term so that we can avoid the hard-to-optimize problem by solving the convex optimization problem. Alternating direction method of multipliers and blockwise coordinate descent algorithm are then exploited to optimize the corresponding objective function. Extensive experimental results on six benchmark datasets illustrate that the proposed algorithm has achieved superior performance compared to some conventional classification algorithms. Figure 1:The scheme of LEDL is on the right while the LC-KSVD is on the left. The difference between the two methods is the sparse regularization term which LEDL use the 1 -norm regularization term and LC-KSVD use the 0 -norm regularization term. Compared with 0 -norm, the sparsity constraint factor of 1 -norm is unfixed so that the basis vectors can be selected freely for linear fitting. Thus, our proposed LEDL method can get smaller errors than LC-KSVD.

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