A unified learning algorithm to extract principal and minor components

作者：Peng, Dezhong^*; Yi, Zhang; Xiang, Yong

来源：Digital Signal Processing, 2009, 19(4): 640-649.

DOI：10.1016/j.dsp.2009.03.004

• Principal component analysis (PCA)
• Minor component analysis (MCA)
• Deterministic discrete time (DDT) system
• Eigenvalue
• Eigenvector

Recently, many unified learning algorithms have been developed to solve the task of principal component analysis (PCA) and minor component analysis (MCA). These unified algorithms can be used to extract principal component and if altered simply by the sign, it can also serve as a minor component extractor. This is of practical significance in the implementations of algorithms. Convergence of the existing unified algorithms is guaranteed only under the condition that the learning rates of algorithms approach zero, which is impractical in many practical applications. In this paper, we propose a unified PCA & MCA algorithm with a constant learning rate, and derive the sufficient conditions to guarantee convergence via analyzing the discrete-time dynamics of the proposed algorithm. The achieved theoretical results lay a solid foundation for the applications of our proposed algorithm.

• 出版日期2009-7
• 单位迪肯大学; 四川大学