An unified EM algorithm for PCA and KPCA

作者：Wang Haixian^*; Hu Zilan

来源：Neurocomputing, 2007, 71(1-3): 459-462.

DOI：10.1016/j.neucom.2007.06.008

• probabilistic principal component analysis (PPCA)
• kernel principal component analysis (KPCA)
• constrained expectation-maximization (EM) algorithm
• nonlinear feature extraction

In this note, from another point of view and in a more general situation, we formulate an EM algorithm for finding the leading eigen system of any positive semi-definite matrix in a very simple derivation. The proposed EM approach can directly compute not only the eigen-system of sample covariance matrix in data space but also that of kernel matrix. Thus, the proposed algorithm provides an unified framework for EM-based principal component analysis (PCA) and kernel PCA (KPCA). Particularly, when it is applied to KPCA, it is a dual form of the commonly used constrained EM algorithm for performing KPCA. And thus it is a beneficial complementarity or dual description of the constrained EM method.

• 出版日期2007-12
• 单位东南大学