Local Coordinate Constraint Research Articles

Robust sparse concept factorization with graph regularization for subspace learning

Concept factorization (CF) is a powerful tool in subspace learning. Recently graph-based CF and local coordinate CF have been proposed to exploit the intrinsic geometrical structure of data, and have been shown quite successful in improving performance. However, these methods have limited robustness and might be sensitive to noises and disturbances in practical applications. In this paper, we propose a novel robust sparse CF framework (RSCF) for subspace learning. Specifically, we present a robust loss function to effectively eliminate the impact of the large outliers. The local coordinate constraint and the graph regularization term are incorporated into RSCF to simultaneously guarantee the sparsity of the coefficient matrix and maintain the local structure of the data. We prove that the local coordinate constraint implies the orthogonality of the coefficient matrix. By using the half-quadratic optimization technique, we transform the objective function of RSCF into a quadratic form and provide the iterative updating rules and the convergence analysis. Extensive experiments demonstrate the robustness and superiority of the proposed RSCF in comparison to state-of-the-art CF methods.

Semi-supervised graph regularized nonnegative matrix factorization with local coordinate for image representation

Nonnegative matrix factorization(NMF) is a powerful image representation algorithm in pattern recognition and data mining. However, the traditional NMF does not utilize any label information, or fail to guarantee the sparse parts-based representation. In this paper, we put forward a semi-supervised local coordinate NMF (SLNMF) algorithm, which incorporate the available label information and the local coordinate constraint into NMF. Particularly, SLNMF makes the learned coefficients sparse by adding the coordinate constraint, and enhance the discriminative ability of different classes by using the label information constraint. Furthermore, in order to extract the geometric structure of the data space, we propose a new semi-supervised graph regularized NMF with local coordinate constraint (SGLNMF) method, which incorporates the graph regularization into SLNMF to enhance the discriminative abilities of data representations. SGLNMF not only reveals the intrinsic geometrical information of the data space, but also takes into account the local coordinate constraint and the label information. Clustering experiments on several standard image datasets demonstrate the effectiveness of our proposed SLNMF and SGLNMF methods compared to the state-of-the-art methods.

Robust nonnegative matrix factorization with local coordinate constraint for image clustering

Nonnegative matrix factorization (NMF) has attracted increasing attention in data mining and machine learning. However, existing NMF methods have some limitations. For example, some NMF methods seriously suffer from noisy data contaminated by outliers, or fail to preserve the geometric information of the data and guarantee the sparse parts-based representation. To overcome these issues, in this paper, a robust and sparse NMF method, called correntropy based dual graph regularized nonnegative matrix factorization with local coordinate constraint (LCDNMF) is proposed. Specifically, LCDNMF incorporates the geometrical information of both the data manifold and the feature manifold, and the local coordinate constraint into the correntropy based objective function. The half-quadratic optimization technique is utilized to solve the nonconvex optimization problem of LCDNMF, and the multiplicative update rules are obtained. Furthermore, some properties of LCDNMF including the convergence, relation with gradient descent method, robustness, and computational complexity are analyzed. Experiments of clustering demonstrate the effectiveness and robustness of the proposed LCDNMF method in comparison to several state-of-the-art methods on six real world image datasets.

Robust Semisupervised Nonnegative Local Coordinate Factorization for Data Representation

Obtaining an optimum data representation is a challenging issue that arises in many intellectual data processing techniques such as data mining, pattern recognition, and gene clustering. Many existing methods formulate this problem as a nonnegative matrix factorization (NMF) approximation problem. The standard NMF uses the least square loss function, which is not robust to outlier points and noises and fails to utilize prior label information to enhance the discriminability of representations. In this study, we develop a novel matrix factorization method called robust semisupervised nonnegative local coordinate factorization by integrating robust NMF, a robust local coordinate constraint, and local spline regression into a unified framework. We use the l2,1 norm for the loss function of the NMF and a local coordinate constraint term to make our method insensitive to outlier points and noises. In addition, we exploit the local and global consistencies of sample labels to guarantee that data representation is compact and discriminative. An efficient multiplicative updating algorithm is deduced to solve the novel loss function, followed by a strict proof of the convergence. Several experiments conducted in this study on face and gene datasets clearly indicate that the proposed method is more effective and robust compared to the state-of-the-art methods.

Graph-regularized CF with local coordinate for image representation

Concept factorization (CF) has been a powerful data representation method, which has been widely applied in image processing and document clustering. However, traditional CF cannot guarantee the decomposition results of CF to be sparse in theory and do not consider the geometric structure of the databases. In this paper, we propose a graph-regularized CF with local coordinate (LGCF) method, which enforces the learned coefficients to be sparse by using the local coordinate constraint meanwhile preserving the intrinsic geometric structure of the data space by incorporating graph regularization. An iterative optimization method is also proposed to solve the objective function of LGCF. By comparing with the state-of-the-arts algorithms (Kmeans, NMF, CF, LCCF, LCF), experimental results on four popular databases show that the proposed LGCF method has better performance in terms of average accuracy and mutual information.

Local coordinate based graph-regularized NMF for image representation

Non-negative matrix factorization (NMF) has been a powerful data representation tool which has been widely applied in pattern recognition and computer vision due to its simplicity and effectiveness. However, existing NMF methods suffer from one or both of the following deficiencies: (1) they cannot theoretically guarantee the decomposition results to be sparse, and (2) they completely neglect geometric structure of data, especially when some examples are heavily corrupted. In this paper, we propose a local coordinate based graph regularized NMF method (LCGNMF) to simultaneously overcome both deficiencies. In particular, LCGNMF enforces the learned coefficients to be sparse by incorporating the local coordinate constraint over both factors meanwhile preserving the geometric structure of the data by incorporating graph regularization. To enhance the robustness of NMF, LCGNMF removes the effect of the outliers via the maximum correntropy criterion (MCC). LCGNMF is difficult because the MCC induced objective function is neither quadratic nor convex. We therefore developed a multiplicative update rule to solve LCGNMF and theoretically proved its convergence. Experiments of image clustering on several popular image datasets verify the effectiveness of LCGNMF compared to the representative methods in quantities.

Nonnegative Local Coordinate Factorization for Image Representation

Recently, nonnegative matrix factorization (NMF) has become increasingly popular for feature extraction in computer vision and pattern recognition. NMF seeks two nonnegative matrices whose product can best approximate the original matrix. The nonnegativity constraints lead to sparse parts-based representations that can be more robust than nonsparse global features. To obtain more accurate control over the sparseness, in this paper, we propose a novel method called nonnegative local coordinate factorization (NLCF) for feature extraction. NLCF adds a local coordinate constraint into the standard NMF objective function. Specifically, we require that the learned basis vectors be as close to the original data points as possible. In this way, each data point can be represented by a linear combination of only a few nearby basis vectors, which naturally leads to sparse representation. Extensive experimental results suggest that the proposed approach provides a better representation and achieves higher accuracy in image clustering.