Research On Independent Component Analysis Algorithm And Its Applications To The Time Series Analysis

Assume that the observed variables(observed signals)are mixed by the hidden variables(source signals).The technique,which estimates the mixing channel from samples of the observed variables and the values of hidden variables can be estimated via the mutual independence between hidden variables,is called as independent component analysis(ICA).Wherein we have no prior knowledge about the hidden variables and mixing formation.ICA has been developed an efficient statistic and computing technologies and has been applied to image,audio and video,communication,financial analysis et al.since its concept was formally defined in 1994.Based on the time-frequency representation of the observed variables,the support set of ICA model includes the real domain and complex domain,i.e.ICA model can be analyzed in different sets.In this paper,in light of the different support set of ICA,the real-valued ICA algorithm and the performance analysis of the complex-valued ICA algorithm were analyzed.At the same time,a series of ICA algorithms with high separation effect were proposed.Further,the application of the real-valued ICA on the time series analysis was studied.The main work can be seen in the following three parts:The first part(3rd chapter)studied ICA algorithms in real domain.Firstly,a modified RLStype ICA algorithm with unknown number of sources was proposed by analyzing the convergent behavior of the RLS-type ICA algorithm at equilibrium point.Experiment results demonstrated that the proposed algorithm is better than existing learning rules in stability.Secondly,as to unknown and dynamically changing number of sources,the generalized projected orthogonal natural gradient ICA(GPONG-ICA)algorithm,which is achieved by multiplying the orthogonal projected matrix from the right of generalized orthogonal natural gradient ICA algorithm,was proposed based on the semi-parameter statistical model.Experiment results demonstrated that the proposed algorithm can track the changing number of sources and accomplish the sources estimation with unknown and dynamically changing number of sources.Comparative experiment verified the superiority of the proposed algorithm.The second part(4th and 5th chapters)derived the statistical performance of the complex ICA algorithm and proposed a complex-value ICA algorithm with stronger robustness.Research on complex ICA algorithm is not wide because of the complexity of complex-valued ICA theory.Wherein the complex-valued FastICA algorithm is the most prominent method.Therefore,it can be considered as the main element which will be analyzed in the complexvalued ICA model in this paper.Firstly,a sample derivation of the stability analysis of the nc-FastICA algorithm was given by calculating complex-valued Hessian matrix.Further,the local convergence of the complex-valued FastICA algorithm was studied:when the source signals are circular,the convergent condition of the c-FastICA algorithm is given.When the source signals are noncircular,the corresponding condition also can be given by weakening the assumption about noncircular sources as the pseudo-covariance matrix is diagonal.Secondly,the uniformity and robustness were given.Finally,we modified the complex-valued FastICA algorithm with higher robustness based on the Tukey M-estimator.Meanwhile,the stability of the c-FastICA algorithm based on the Tukey M-estimator was analyzed and its convergence was proved.Experiment verified the superiority of the proposed algorithm.The third part(6th chapter)offered applications of real-valued ICA on time seires analysis and forecasting.Firstly,the inner formation mechanism of international gold price were analyzed:it begins with 6 independent components(ICs)separated out by applying ICA to the decomposition of the gold price which decomposed by the variational mode decomposition(VMD),followed by the comparative analysis aiming at finding out the corresponding economic explanation indexes represented by the ICs.Further,we can analyze how the indexes drive the fluctuation of international gold price.Secondly,regarding international energy prices(natural gas price,crude oil price and carbon price)as the research object,a stronger ensemble forecasting model was proposed based on the aforementioned decomposition-separation strategy,i.e.separation-integration(S-I)forecasting model,the task of which is to predict the energy price accurately from the perspective of internal formation mechanism of data structure.Particularly,by selecting real-valued FastICA algorithm as separator,gated recurrent unit neural network(GRUNN)as basic predictor,support vector regression(SVR)as integrator,the forecasting approach is abbreviated to IGS.Comparative experiment results demonstrated that the proposed IGS model is superior remarkably to the existing hybrid forecasting model from the perspective of multiple performance evaluation criteria.