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Aiming to improve the robustness and adaptiveness of the recently investigated capped norm linear discriminant analysis (CLDA), this paper proposes a regularized linear discriminant analysis based on the generalized capped l 2 , q -norm (GCLDA). Compared to CLDA, there are two improvements in GCLDA. Firstly, GCLDA uses the capped l 2 , q -norm rather than the capped l 2 , 1 -norm to measure the within-class and between-class distances for arbitrary q > 0 . By selecting an appropriate q, GCLDA is adaptive to different data, and also removes extreme outliers and suppresses the effect of noise more effectively. Secondly, by taking into account a regularization term, GCLDA not only improves its generalization ability but also avoids singularity. GCLDA is solved through a series of generalized eigenvalue problems. Experiments on an artificial dataset, some real world datasets and a high-dimensional dataset demonstrate the effectiveness of GCLDA. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, this paper introduces a capped l2,1-norm of a matrix, which employs non-squared l2-norm and "capped" operation, and further proposes a novel capped l2,1-norm linear discriminant analysis, called CLDA. Due to the use of capped l2,1-norm, CLDA can effectively remove extreme outliers and suppress the effect of noise data. In fact, CLDA can also be viewed as a weighted LDA and is solved through a series of generalized eigenvalue problems. The experimental results on an artificial data set, some UCI data sets and two image data sets demonstrate the effectiveness of CLDA. [ABSTRACT FROM AUTHOR]

Hyperspectral anomaly detection is a research hot spot in the field of remote sensing. It can distinguish abnormal targets from the scene just by utilizing the spectral differences and requiring no prior information. A series of anomaly detectors based on Reed-Xiaoli methods are very important and typical algorithms in this research area, which generally have the hypothesis about background subject to the Gaussian distribution. However, this assumption is inaccurate to describe a hyperspectral image with a complex scene in practice. Besides, due to the unavoidable existence of abnormal targets, background statistics will be affected which will reduce the detection performance. To address these problems, we propose a sparse dictionary learning method by using a capped norm to realize hyperspectral anomaly detection. Moreover, a new training data selection strategy based on clustering technique is also proposed to learn a more representative background dictionary. The main contributions are concluded in threefold: 1) neither making any assumptions on the background distribution nor computing the covariance matrix, the proposed method is more adaptive to all kinds of complex hyperspectral images in practice; 2) owing to the good qualities of the capped norm, the learned sparse background dictionary is resistant to the effect of anomalies and has stronger distinctiveness to anomalies from background; 3) without using the traditional sliding hollow window technique, the proposed method is more effective to detect different sizes of abnormal targets. The extensive experiments on four commonly used real-world hyperspectral images demonstrate the effectiveness of the proposed method and show its superiority over the benchmark methods.

As one of the most popular clustering techniques, graph clustering has attracted many researchers in the field of machine learning and data mining. Generally speaking, graph clustering partitions the data points into different categories according to their pairwise similarities. Therefore, the clustering performance is largely determined by the quality of the similarity graph. The similarity graph is usually constructed based on the data points' distances. However, the data structure may be corrupted by outliers. To deal with the outliers, we propose a capped l1 -norm sparse representation method (CSR) in this paper. The main contribution of this paper is threefold: 1) a similarity graph with clear cluster structure is learned by employing sparse representation with proper constraints; (2) the capped l1 -norm loss is utilized to remove the outliers, which ensures the graph quality; and 3) an iterative algorithm is developed to optimize the proposed non-convex problem. The extensive experiments on real-world datasets show the superiority of the proposed method over the state-of-the-art, and demonstrate its robustness to the outliers.

Photos are becoming spontaneous, objective, and universal sources of information. This paper explores evolving situation recognition using photo streams coming from disparate sources combined with the advances of deep learning. Using visual concepts in photos together with space and time information, we formulate the situation detection into a semi-supervised learning framework and propose new graph-based models to solve the problem. To extend the method for unknown situations, we introduce a soft label method that enables the traditional semi-supervised learning framework to accurately predict predefined labels as well as effectively form new clusters. To overcome the noisy data which degrades graph quality, leading to poor recognition results, we take advantage of two kinds of noise-robust norms which can eliminate the adverse effects of outliers in visual concepts and improve the accuracy of situation recognition. Finally, we demonstrate the idea and the effectiveness of the proposed models on Yahoo Flickr Creative Commons 100 Million. [ABSTRACT FROM AUTHOR]

Non-negative matrix factorization (NMF) has been widely used in machine learning and data mining fields. As an extension of NMF, non-negative matrix tri-factorization (NMTF) provides more degrees of freedom than NMF. However, standard NMTF algorithm utilizes Frobenius norm to calculate residual error, which can be dramatically affected by noise and outliers. Moreover, the hidden geometric information in feature manifold and sample manifold is rarely learned. Hence, a novel robust capped norm dual hyper-graph regularized non-negative matrix tri-factorization (RCHNMTF) is proposed. First, a robust capped norm is adopted to handle extreme outliers. Second, dual hyper-graph regularization is considered to exploit intrinsic geometric information in feature manifold and sample manifold. Third, orthogonality constraints are added to learn unique data presentation and improve clustering performance. The experiments on seven datasets testify the robustness and superiority of RCHNMTF.

Two-dimensional linear discriminant analysis (2DLDA) is an effective matrix-based supervised dimensionality reduction method that expresses 2D data directly. However, 2DLDA magnifies the influence of outliers and noise since the construction of 2DLDA is based on squared Frobenius norm. To overcome its sensitivity, this paper investigates a two-dimensional capped l 2 , 1 -norm linear discriminant analysis, called 2DCLDA. The application of capped l 2 , 1 -norm makes 2DCLDA identify outliers and suppress the effect of noise effectively. To avoid singularity and give a stable performance, a regularization term is also considered in the between-class scatter. 2DCLDA is solved through a series of generalized eigenvalue problems, with each subproblem can be deemed as a weighted 2DLDA with regularization. It is proved that the proposed iteration algorithm monotonously decreases the objective of 2DCLDA. At last, 2DCLDA with its related approaches on several face image databases is compared, and the experimental results demonstrate the superiority of 2DCLDA, especially for noise data. [ABSTRACT FROM AUTHOR]