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Robust Principal Component Analysis Based on Maximum Correntropy Criterion
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DOI：10.1109/TIP.2010.2103949.png)
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Abstract
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Principal component analysis (PCA) minimizes the mean square error (MSE) and is sensitive to outliers. In this paper, we present a new rotational-invariant PCA based on maximum correntropy criterion (MCC). A half-quadratic optimization algorithm is adopted to compute the correntropy objective. At each iteration, the complex optimization problem is reduced to a quadratic problem that can be efficiently solved by a standard optimization method. The proposed method exhibits the following benefits: 1) it is robust to outliers through the mechanism of MCC which can be more theoretically solid than a heuristic rule based on MSE; 2) it requires no assumption about the zero-mean of data for processing and can estimate data mean during optimization; and 3) its optimal solution consists of principal eigenvectors of a robust covariance matrix corresponding to the largest eigen-values. In addition, kernel techniques are further introduced in the proposed method to deal with nonlinearly distributed data. Numerical results demonstrate that the proposed method can outperform robust rotational-invariant PCAs based on norm when outliers occur.
Keywords:
Correntropy
half-quadratic optimization
principal component analysis (PCA)
robust
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