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Hyperspectral unmixing (HU) is regarded as an indispensable preprocessing procedure for many field of spectral data analysis because of the existence of mixed pixels. However, the unmixing algorithms are implemented under the presupposition of special mixing models. In other words, any unmixing algorithm only works on a special mixing model of the spectra. This leads to low generalization performance of most unmixing algorithms. To mitigate this problem, a robust unmixing method is proposed, which exploits dual views with adaptive weights for HU (AwDvHU). The proposed method utilizes multi-kernel learning to construct a high-dimensional space that can reflect the nonlinear interaction between spectra optimally. Then, through fusing the unmixing object of original data and the mapped high-dimensional features, the AwDvHU method takes full advantage of the complementary characteristics of features in dual views. Moreover, the AwDvHU method automatically learns the weights for dual views according to the importance of different feature spaces. Its effectiveness in unmixing is verified by experimental results both on the synthetic and real 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]

Low Rank Regularization (LRR), in essence, involves introducing a low rank or approximately low rank assumption to target we aim to learn, which has achieved great success in many data analysis tasks. Over the last decade, much progress has been made in theories and applications. Nevertheless, the intersection between these two lines is rare. In order to construct a bridge between practical applications and theoretical studies, in this paper we provide a comprehensive survey for LRR. Specifically, we first review the recent advances in two issues that all LRR models are faced with: (1) rank-norm relaxation, which seeks to find a relaxation to replace the rank minimization problem; (2) model optimization, which seeks to use an efficient optimization algorithm to solve the relaxed LRR models. For the first issue, we provide a detailed summarization for various relaxation functions and conclude that the non-convex relaxations can alleviate the punishment bias problem compared with the convex relaxations. For the second issue, we summarize the representative optimization algorithms used in previous studies, and analyze their advantages and disadvantages. As the main goal of this paper is to promote the application of non-convex relaxations, we conduct extensive experiments to compare different relaxation functions. The experimental results demonstrate that the non-convex relaxations generally provide a large advantage over the convex relaxations. Such a result is inspiring for further improving the performance of existing LRR models. [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]