Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound
FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm whi...
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| Veröffentlicht in: | IEEE transactions on neural networks Jg. 17; H. 5; S. 1265 - 1277 |
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01.09.2006
Institute of Electrical and Electronics Engineers |
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| Abstract | FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramer-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha>2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo on separating sources with distribution GG(alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals |
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| AbstractList | FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha > 2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo et al. on separating sources with distribution GG (alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals.FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha > 2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo et al. on separating sources with distribution GG (alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals. FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramer-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha>2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo on separating sources with distribution GG(alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals FastICA is one of the most popular algorithms for independent component analysis (ICA), demixing a set of statistically independent sources that have been mixed linearly. A key question is how accurate the method is for finite data samples. We propose an improved version of the FastICA algorithm which is asymptotically efficient, i.e., its accuracy given by the residual error variance attains the Cramér-Rao lower bound (CRB). The error is thus as small as possible. This result is rigorously proven under the assumption that the probability distribution of the independent signal components belongs to the class of generalized Gaussian (GG) distributions with parameter alpha, denoted GG(alpha) for alpha > 2. We name the algorithm efficient FastICA (EFICA). Computational complexity of a Matlab implementation of the algorithm is shown to be only slightly (about three times) higher than that of the standard symmetric FastICA. Simulations corroborate these claims and show superior performance of the algorithm compared with algorithm JADE of Cardoso and Souloumiac and nonparametric ICA of Boscolo et al. on separating sources with distribution GG (alpha) with arbitrary alpha, as well as on sources with bimodal distribution, and a good performance in separating linearly mixed speech signals. |
| Author | Koldovsky, Z. Oja, E. Tichavsky, P. |
| Author_xml | – sequence: 1 givenname: Z. surname: Koldovsky fullname: Koldovsky, Z. organization: Fac. of Nucl. Sci. & Phys. Eng., Czech Tech. Univ., Prague – sequence: 2 givenname: P. surname: Tichavsky fullname: Tichavsky, P. – sequence: 3 givenname: E. surname: Oja fullname: Oja, E. |
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| Cites_doi | 10.1109/TNN.2003.820667 10.1109/78.752592 10.1109/SSP.2003.1289540 10.1109/SSP.2005.1628757 10.1016/0165-1684(94)90029-9 10.1109/TSP.2006.870561 10.1109/MWSCAS.2002.1186887 10.1049/ip-f-2.1993.0054 10.1109/TNN.2003.813843 10.1109/72.761722 10.1109/5.720250 10.1162/neco.1997.9.7.1483 10.1002/0471221317 10.1109/18.312156 10.1109/78.757233 10.1002/0470845899 10.1109/TSP.2004.834398 10.1109/78.599941 10.1002/9780470316436 10.1007/978-3-540-30110-3_22 10.1109/ICASSP.2006.1661415 10.1109/78.650095 |
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| Keywords | Source separation Cramér-Rao lower bound (CRB) independent component analysis (ICA) Independent component analysis Error bound Blind deconvolution Neural network Computational complexity Algorithm FastICA blind source separation Algorithm analysis Blind separation |
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| References | porat (ref16) 1994 koldovsk (ref14) 0 cardoso (ref18) 1994 ref15 koldovsk (ref9) 2005; iii ref11 ref10 ref2 ref1 ref17 ref19 learned-miller (ref12) 2004; 4 ref24 ref23 ref26 ref25 ref20 ref22 ref21 (ref13) 0 ref28 ref27 ref8 ref7 ref3 ref6 ref5 rao (ref4) 1973 |
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| SubjectTerms | Algorithm FastICA Algorithms Applied sciences Artificial Intelligence Asymptotic properties Automation blind deconvolution blind source separation Computational complexity Computational modeling Computer science; control theory; systems Computer Simulation Computing Methodologies Connectionism. Neural networks CramÉr-Rao lower bound (CRB) Data Interpretation, Statistical Deconvolution Errors Exact sciences and technology Independent component analysis independent component analysis (ICA) Information theory Lower bounds Matlab Models, Statistical Neural networks Pattern Recognition, Automated - methods Principal Component Analysis Probability distribution Signal processing Signal processing algorithms Signal Processing, Computer-Assisted Speech |
| Title | Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound |
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