COPICA—independent component analysis via copula techniques
Independent component analysis (ICA) is a modern computational method developed in the last two decades. The main goal of ICA is to recover the original independent variables by linear transformations of the observations. In this study, a copula-based method, called COPICA, is proposed to solve the ICA problem. The proposed COPICA method is a semiparametric approach, the marginals are estimated by nonparametric empirical distributions and the joint distributions are modeled by parametric copula functions. The COPICA method utilizes the estimated copula parameter as a dependence measure to search the optimal rotation matrix that achieves the ICA goal. Both simulation and empirical studies are performed to compare the COPICA method with the state-of-art methods of ICA. The results indicate that the COPICA attains higher signal-to-noise ratio (SNR) than several other ICA methods in recovering signals. In particular, the COPICA usually leads to higher SNRs than FastICA for near-Gaussian-tailed sources and is competitive with a nonparametric ICA method for two dimensional sources. For higher dimensional ICA problem, the advantage of using the COPICA is its less storage and less computational effort.
KeywordsBlind source separation Canonical maximum likelihood method Givens rotation matrix Signal/noise ratio Simulated annealing algorithm
The authors gratefully acknowledge the National Science Council in Taiwan, National Center for Theoretical Sciences (South), Tainan, Taiwan and the Deutsche Forschungsgemeinschaft through the SFB 649 “Economic Risk”, Humboldt-Universitat zu Berlin. This work was supported in part by National Science Council under grants NSC 96-2118-M-390-002- (Chen), NSC 100-2118-M-110-001-003- (Guo) and NSC 101-2118-M-390-002- (Huang).
- Abayomi, K., Lall, U., de la Pena, V.: Copula Based Independent Component Analysis. Working paper (2008) Google Scholar
- Abayomi, K., de la Pena, V., Lall, U., Levy, M.: Quantifying sustainability: methodology for and determinants of an environmental sustainability index. In: Luo, Z.W. (ed.) Green Finance and Sustainability: Environmentally-Aware Business Models and Technologies, pp. 74–89 (2011) CrossRefGoogle Scholar
- Gretton, A., Bousquet, O., Smola, A.J., Schölkopf, B.: Measuring statistical dependence with Hilbert-Schmidt norms. In: ALT, pp. 63–78. Springer, Heidelberg (2005) Google Scholar
- Grønneberg, S., Hjort, N.L.: The Copula Information Criterion. Technical report, Department of Math., University of Oslo, Norway (2008) Google Scholar
- Kidmose, P.: Blind Separation of Heavy Tail Signals. Ph.D. Thesis, Technical University of Denmark, Lyngby (2001) Google Scholar
- Yu, L., Verducci, J.S., Blower, P.E.: The tau-path test for monotone association in an unspecified subpopulation. In: Application to Chemogenomic Data Mining Statistical Methodology, vol. 8, pp. 97–111 (2011) Google Scholar