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Nonnegative matrix factorization (NMF) and spectral clustering are two of the most widely used clustering techniques. However, NMF cannot deal with the nonlinear data, and spectral clustering relies on the postprocessing. In this article, we propose a Robust Matrix factorization with Spectral embedding (RMS) approach for data clustering, which inherits the advantages of NMF and spectral clustering, while avoiding their shortcomings. In addition, to cluster the data represented by multiple views, we present the multiview version of RMS (M-RMS), and the weights of different views are self-tuned. The main contributions of this research are threefold: 1) by integrating spectral clustering and matrix factorization, the proposed methods are able to capture the nonlinear data structure and obtain the cluster indicator directly; 2) instead of using the squared Frobenius-norm, the objectives are developed with the $\ell _{2,1}$ -norm, such that the effects of the outliers are alleviated; and 3) the proposed methods are totally parameter-free, which increases the applicability for various real-world problems. Extensive experiments on several single-view/multiview data sets demonstrate the effectiveness of our methods and verify their superior clustering performance over the state of the arts. [ABSTRACT FROM AUTHOR]

k nearest neighbor (kNN) method is a popular classification method in data mining and statistics because of its simple implementation and significant classification performance. However, it is impractical for traditional kNN methods to assign a fixed k value (even though set by experts) to all test samples. Previous solutions assign different $k$ values to different test samples by the cross validation method but are usually time-consuming. This paper proposes a kTree method to learn different optimal $k$ values for different test/new samples, by involving a training stage in the kNN classification. Specifically, in the training stage, kTree method first learns optimal $k$ values for all training samples by a new sparse reconstruction model, and then constructs a decision tree (namely, kTree) using training samples and the learned optimal $k$ values. In the test stage, the kTree fast outputs the optimal $k$ value for each test sample, and then, the kNN classification can be conducted using the learned optimal $k$ value and all training samples. As a result, the proposed kTree method has a similar running cost but higher classification accuracy, compared with traditional kNN methods, which assign a fixed k value to all test samples. Moreover, the proposed kTree method needs less running cost but achieves similar classification accuracy, compared with the newly kNN methods, which assign different k values to different test samples. This paper further proposes an improvement version of kTree method (namely, k*Tree method) to speed its test stage by extra storing the information of the training samples in the leaf nodes of kTree, such as the training samples located in the leaf nodes, their kNNs, and the nearest neighbor of these kNNs. We call the resulting decision tree as k*Tree, which enables to conduct kNN classification using a subset of the training samples in the leaf nodes rather than all training samples used in the newly kNN methods. This actually reduces running cost of test stage. Finally, the experimental results on 20 real data sets showed that our proposed methods (i.e., kTree and k*Tree) are much more efficient than the compared methods in terms of classification tasks. [ABSTRACT FROM PUBLISHER]

Regular machine learning and data mining techniques study the training data for future inferences under a major assumption that the future data are within the same feature space or have the same distribution as the training data. However, due to the limited availability of human labeled training data, training data that stay in the same feature space or have the same distribution as the future data cannot be guaranteed to be sufficient enough to avoid the over-fitting problem. In real-world applications, apart from data in the target domain, related data in a different domain can also be included to expand the availability of our prior knowledge about the target future data. Transfer learning addresses such cross-domain learning problems by extracting useful information from data in a related domain and transferring them for being used in target tasks. In recent years, with transfer learning being applied to visual categorization, some typical problems, e.g., view divergence in action recognition tasks and concept drifting in image classification tasks, can be efficiently solved. In this paper, we survey state-of-the-art transfer learning algorithms in visual categorization applications, such as object recognition, image classification, and human action recognition. [ABSTRACT FROM PUBLISHER]

Linear discriminant analysis (LDA) has been widely used as the technique of feature exaction. However, LDA may be invalid to address the data from different domains. The reasons are as follows: 1) the distribution discrepancy of data may disturb the linear transformation matrix so that it cannot extract the most discriminative feature and 2) the original design of LDA does not consider the unlabeled data so that the unlabeled data cannot take part in the training process for further improving the performance of LDA. To address these problems, in this brief, we propose a novel transferable LDA (TLDA) method to extend LDA into the scenario in which the data have different probability distributions. The whole learning process of TLDA is driven by the philosophy that the data from the same subspace have a low-rank structure. The matrix rank in TLDA is the key learning criterion to conduct local and global linear transformations for restoring the low-rank structure of data from different distributions and enlarging the distances among different subspaces. In doing so, the variations of distribution discrepancy within the same subspace can be reduced, i.e., data can be aligned well and the maximally separated structure can be achieved for the data from different subspaces. A simple projected subgradient-based method is proposed to optimize the objective of TLDA, and a strict theory proof is provided to guarantee a quick convergence. The experimental evaluation on public data sets demonstrates that our TLDA can achieve better classification performance and outperform the state-of-the-art methods. [ABSTRACT FROM AUTHOR]