关键词: 快速独立成分分析（FastICA）, 收敛性, 不动点, 依概率一致收敛, 一致性

Abstract: Fast Independent Component Analysis（FastICA） is the most widely used method to solve blind source separation problems. Since only limited data samples can be obtained in practice, the FastICA algorithm usually used is based on sample. However, the common convergence analysis of the FastICA algorithm is with respect to the ensemble FastICA algorithm. Therefore, it is of great significance to explore convergence and consistency of the FastICA algorithm based on sample. Firstly, the relevant convergence properties of the ensemble FastICA algorithm are proved in a more concise way, including the relationship between the local maximum of the contrast function and the fixed point of the FastICA iterative function. Secondly, the Dirac function is introduced to construct the probability density function of observed signals. The convergence condition of the FastICA algorithm based on sample is given by the law of large numbers. Finally, based on the M-estimator consistency theorem, it is proved that the FastICA estimator is a consistent estimator. The results of the simulation experiments verify the consistency of the FastICA estimator.

Key words: Fast Independent Component Analysis（FastICA）, convergence, fixed point, consistent converge in probability, consistency