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Preserving projection-based methods are good for finding the manifold structure embedded in data. As they use the Euclidean distance as a metric, which is sensitive to noise and outliers in data, nuclear norm-based 2D locality preserving projection (NN-2DLPP) is thus proposed to improve the robustness of 2DLPP. However, NN-2DLPP does not consider the discriminant ability of data. In order to improve the discriminant ability of preserving projection methods, in this paper, we use preserving projection learning with structurally incoherence of data and propose structurally incoherent low-rank 2DLPP (SILR-2DLPP) for image classification. This approach provides a discriminative representation of preserving projection learning by recovering the distinct different classes of the data. SILR-2DLPP searches the optimal subspace and low-rank representation simultaneously. We further extend SILR-2DLPP to a kernel case and propose kernel SILR-2DLPP (KSILR-2DLPP) to obtain a nonlinear representation. The theoretical analysis including the convergence and computational complexity of SILR-2DLPP are presented. To verify the performance of SILR-2DLPP and KSILR-2DLPP, six well-known image databases were used in the experiments. The experimental results show that the proposed methods are superior to the previous preserving projection methods for image classification. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF), known as a famous matrix factorization technique, has been widely used in pattern recognition and computer vision. NMF represents the input data matrix as a product of two nonnegative factors. As NMF is based on the Euclidean distance, which is sensitive to noise or errors in the data, some robust NMF methods are proposed. Mainly focusing on parts-based representation, these robust NMF methods often neglect global representation of data. In fact, the global geometry information of data is more robust than the local information about the noisy data in terms of image classification. In order to effectively improve the robustness of NMF and learn part-based and global representation of the data, a novel method low-rank nonnegative factorization (LRNF) is proposed in this paper. First, we assume that the data are grossly corrupted, and the $L_{1} $ norm is used as a sparse constraint on the assumed noise matrix. Then, LRNF learns a low-rank matrix with the global representation ability. Finally, we make a nonnegative factorization of the learned low-rank matrix. We can obtain a base matrix, which preserves locality and globality properties of the data in the meantime. Extensive experiments have been conducted on nine real-world image databases to verify the performance of the proposed LRNF method by comparing with the state-of-the-art algorithms on robust dimensionality reduction. [ABSTRACT FROM AUTHOR]

This paper addresses two fundamental problems: 1) learning discriminative model parameters and 2) avoiding over-fitting, which often occurs in regression-based classification tasks. We formulate these two problems in terms of relaxing both the strict binary label matrix and graph regularization term into more flexible forms so that the margins between different classes are enlarged as much as possible and the problem of over-fitting is avoided to some extent. This task is accomplished by the proposed double relaxed regression (DRR) method. The convex problem of DRR is solved efficiently with an iterative procedure. Extensive experiments on synthetic and real world image data sets demonstrate the effectiveness of the proposed method in terms of both classification accuracy and running time. [ABSTRACT FROM AUTHOR]

2-D linear discriminant analysis (2DLDA) has been widely used in pattern recognition and image classification. 2DLDA selects discriminative features from the up and left corner of images. However, 2DLDA uses the Frobenius norm (F-norm), which is sensitive to noise or outliers in data, as a metric. In this paper, we propose a novel framework, called horizontal and vertical nuclear norm-based 2DLDA (HVNN-2DLDA) for image representation. In the proposed framework, HVNN-2DLDA methods (i.e., HNN-2DLDA and VNN-2DLDA) are proposed, and both use the nuclear norm as a criterion. The nuclear norm can provide more structure and global information for the reconstruction of noisy images. HNN-2DLDA and VNN-2DLDA represent images in the row and column directions, respectively. In addition, by combining the row and column directions, we propose a bilateral nuclear norm-based 2DLDA method called BNN-2DLDA. The advantage of BNN-2DLDA over HNN-2DLDA and VNN-2DLDA is that an image sample can be represented by both the row and the column directions instead of only the row or column direction. HVNN-2DLDA learns a set of local optimal projection vectors by maximizing the ratio of the nuclear norm of the between-class scatter matrix and the nuclear norm of the within-class scatter matrix. To verify the robustness and recognition performance in image classification of HVNN-2DLDA, six public image databases are used for experiments. The experimental results demonstrate the effectiveness and the feasibility of the proposed framework. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF), which aims at obtaining the nonnegative low-dimensional representation of data, has received wide attention. To obtain more effective nonnegative discriminant bases from the original NMF, in this paper, a novel method called nonnegative discriminant matrix factorization (NDMF) is proposed for image classification. NDMF integrates the nonnegative constraint, orthogonality, and discriminant information in the objective function. NDMF considers the incoherent information of both factors in standard NMF and is proposed to enhance the discriminant ability of the learned base matrix. NDMF projects the low-dimensional representation of the subspace of the base matrix to regularize the NMF for discriminant subspace learning. Based on the Euclidean distance metric and the generalized Kullback–Leibler (KL) divergence, two kinds of iterative algorithms are presented to solve the optimization problem. The between- and within-class scatter matrices are divided into positive and negative parts for the update rules and the proofs of the convergence are also presented. Extensive experimental results demonstrate the effectiveness of the proposed method in comparison with the state-of-the-art discriminant NMF algorithms. [ABSTRACT FROM PUBLISHER]