Innovation process for temporal independent component analysis

In temporal independent component analysis (TICA) the components are no longer random variables as required in classical independent component analysis (ICA), but stochastic processes. This paper addresses two problems of TICA when the time structure information of components is taken into account and innovation process is introduced. First it is demonstrated that the assumption that the component in ICA should be random variable can be relaxed to stochastic process as in TICA, and the classical ICA methods can also be available to TICA. Secondly, the influence of innovation process on the two crucial requirements, i.e., statistical independency and nongaussianity, is discussed. The analyses show that it has little impact on the former but can increase the nongaussianity of latent component, which leads to much faster convergence in optimal algorithms. Experimental results show that innovation process is an efficient preprocessing in TICA.