
A robust approach for principal component analyisis
In this paper we analyze different ways of performing principal componen...
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Optimal whitening and decorrelation
Whitening, or sphering, is a common preprocessing step in statistical an...
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Robust Principal Component Analysis Based On Maximum Correntropy Power Iterations
Principal component analysis (PCA) is recognised as a quintessential dat...
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Geometric Learning and Filtering in Finance
We develop a method for incorporating relevant nonEuclidean geometric i...
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Spherical Principal Component Analysis
Principal Component Analysis (PCA) is one of the most important methods ...
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NPSA: Nonorthogonal Principal Skewness Analysis
Principal skewness analysis (PSA) has been introduced for feature extrac...
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Robust Nonlinear Component Estimation with Tikhonov Regularization
Learning reduced component representations of data using nonlinear trans...
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Improving the Accuracy of Principal Component Analysis by the Maximum Entropy Method
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The most important function is arguably the Euclidean distance between data items, This can be used, for example, to solve the approximate nearest neighbor problem. We use random variables to model the inherent uncertainty in such approximations, and apply the Maximum Entropy Method to infer the underlying probability distribution. We propose using the expected values of distances between these random variables as improved estimates of the distance. We show by analysis and experimentally that in most cases results obtained by our method are more accurate than what is obtained by the classical approach. This improves the accuracy of a classical technique that have been used with little change for over 100 years.
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