A constrained EM algorithm for principal component analysis.
We propose a constrained EM algorithm for principal component analysis (PCA) using a coupled probability model derived from single-standard factor analysis models with isotropic noise structure. The single probabilistic PCA, especially for the case where there is no noise, can find only a vector set that is a linear superposition of principal components and requires postprocessing, such as diagonalization of symmetric matrices. By contrast, the proposed algorithm finds the actual principal components, which are sorted in descending order of eigenvalue size and require no additional calculation or postprocessing. The method is easily applied to kernel PCA. It is also shown that the new EM algorithm is derived from a generalized least-squares formulation.
Ahn
Jong-Hoon
JH
Department of Physics, Pohang University of Science and Technology, Pohang, Kyongbuk, Korea. junghun@postech.ac.kr
Oh
Jong-Hoon
JH
D000465:Algorithms; D025341:Principal Component Analysis / Q000379:methods*