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Register a new userRobust Principal Component Analysis Based On Maximum Correntropy Power Iterations
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Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian samples and/or outliers often makes it unreliable in practice. To this end, a robust formulation of PCA is derived based on the maximum correntropy criterion (MCC) so as to maximise the expected likelihood of Gaussian distributed reconstruction errors. In this way, the proposed solution reduces to a generalised power iteration, whereby: (i) robust estimates of the principal components are obtained even in the presence of outliers; (ii) the number of principal components need not be specified in advance; and (iii) the entire set of principal components can be obtained, unlike existing approaches. The advantages of the proposed maximum correntropy power iteration (MCPI) are demonstrated through an intuitive numerical example.
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Infrared target tracking plays an important role in both civil and military fields. The main challenges in designing a robust and high-precision tracker for infrared sequences include overlap, occlusion and appearance change. To this end, this paper proposes an infrared target tracker based on proximal robust principal component analysis method. Firstly, the observation matrix is decomposed into a sparse occlusion matrix and a low-rank target matrix, and the constraint optimization is carried out with an approaching proximal norm which is better than L1-norm. To solve this convex optimization problem, Alternating Direction Method of Multipliers (ADMM) is employed to estimate the variables alternately. Finally, the framework of particle filter with model update strategy is exploited to locate the target. Through a series of experiments on real infrared target sequences, the effectiveness and robustness of our algorithm are proved.
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use the data-centering method and reestimate the covariance matrix using robust statistic techniques such as median, robust scaling which is a booster to data-centering and Huber M-estimator which measures the presentation of outliers and reweight them with small values. The results on several real world data sets show that our proposed method handles outliers and gains better results than the original PCA and provides the same accuracy with lower computation cost than the Kernel PCA using the polynomial kernel in classification tasks.
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