期刊
IEEE TRANSACTIONS ON IMAGE PROCESSING
卷 20, 期 6, 页码 1485-1494出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIP.2010.2103949
关键词
Correntropy; half-quadratic optimization; principal component analysis (PCA); robust
资金
- Research Foundation for the Doctoral Program of the Ministry of Education of China [20100041120009]
- Natural Science of Foundation of China [61075051, 60971095]
- NSFC-GuangDong [U0835005]
- Sun Yat-sen 985 Project [35000-3181305]
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.
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