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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]

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]