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Nonnegative matrix factorization (NMF) is one of the most popular data representation methods in the field of computer vision and pattern recognition. High-dimension data are usually assumed to be sampled from the submanifold embedded in the original high-dimension space. To preserve the locality geometric structure of the data, k-nearest neighbor (k-NN) graph is often constructed to encode the near-neighbor layout structure. However, k-NN graph is based on Euclidean distance, which is sensitive to noise and outliers. In this article, we propose a refined-graph regularized nonnegative matrix factorization by employing a manifold regularized least-squares regression (MRLSR) method to compute the refined graph. In particular, each sample is represented by the whole dataset regularized with ℓ2-norm and Laplacian regularizer. Then a MRLSR graph is constructed based on the representative coefficients of each sample. Moreover, we present two optimization schemes to generate refined-graphs by employing a hard-thresholding technique. We further propose two refined-graph regularized nonnegative matrix factorization methods and use them to perform image clustering. Experimental results on several image datasets reveal that they outperform 11 representative methods. [ABSTRACT FROM AUTHOR]

Prior to pattern recognition, feature selection is often used to identify relevant features and discard irrelevant ones for obtaining improved analysis results. In this paper, we aim to develop an unsupervised feature ranking algorithm that evaluates features using discovered local coherent patterns, which are known as biclusters. The biclusters (viewed as submatrices) are discovered from a data matrix. These submatrices are used for scoring relevant features from two aspects, i.e., the interdependence of features and the separability of instances. The features are thereby ranked with respect to their accumulated scores from the total discovered biclusters before the pattern classification. Experimental results show that this proposed method can yield comparable or even better performance in comparison with the well-known Fisher score, Laplacian score, and variance score using three UCI data sets, well improve the results of gene expression data analysis using gene ontology annotation, and finally demonstrate its advantage of unsupervised feature ranking for high-dimensional data. [ABSTRACT FROM AUTHOR]

Abstract: For image analysis, an important extension to principal component analysis (PCA) is to treat an image as multiple samples, which helps alleviate the small sample size problem. Various schemes of transforming an image to multiple samples have been proposed. Although having been shown effective in practice, the schemes are mainly based on heuristics and experience. In this paper, we propose a probabilistic PCA model, in which we explicitly represent the transformation scheme and incorporate the scheme as a stochastic component of the model. Therefore fitting the model automatically learns the transformation. Moreover, the learned model allows us to distinguish regions that can be well described by the PCA model from those that need further treatment. Experiments on synthetic images and face data sets demonstrate the properties and utility of the proposed model. [Copyright &y& Elsevier]

Realistic action recognition has been one of the most challenging research topics in computer vision. The existing methods are commonly based on non-probabilistic classification, predicting category labels but not providing an estimation of uncertainty. In this paper, we propose a probabilistic framework using Gaussian processes (GPs), which can tackle regression problems with explicit uncertain models, for action recognition. A major challenge for GPs when applied to large-scale realistic data is that a large covariance matrix needs to be inverted during inference. Additionally, from the manifold perspective, the intrinsic structure of the data space is only constrained by a local neighborhood and data relationships with far-distance usually can be ignored. Thus, we design our GPs covariance matrix via the proposed ℓ 1 construction and a local approximation (LA) covariance weight updating method, which are demonstrated to be robust to data noise, automatically sparse and adaptive to the neighborhood. Extensive experiments on four realistic datasets, i.e., UCF YouTube, UCF Sports, Hollywood2 and HMDB51, show the competitive results of ℓ 1 -GPs compared with state-of-the-art methods on action recognition tasks. [ABSTRACT FROM AUTHOR]