TY - GEN
T1 - Statistical analysis of sample-size effects in ICA
AU - Herrmann, J. Michael
AU - Theis, Fabian J.
PY - 2007
Y1 - 2007
N2 - Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourth-order moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increase with the deviation from Gaussianity. Secondly, errors in kurtosis-based ICA algorithms increase when approaching the Gaussian case. These considerations allow us to derive a strict lower bound for the sample size to achieve a given separation quality, which we study analytically for a specific family of distributions and a particular algorithm (fastICA). We further provide results from simulations that support the relevance of the analytical results.
AB - Independent component analysis (ICA) solves the blind source separation problem by evaluating higher-order statistics, e.g. by estimating fourth-order moments. While estimation errors of the kurtosis can be shown to asymptotically decay with sample size according to a square-root law, they are subject to two further effects for finite samples. Firstly, errors in the estimation of kurtosis increase with the deviation from Gaussianity. Secondly, errors in kurtosis-based ICA algorithms increase when approaching the Gaussian case. These considerations allow us to derive a strict lower bound for the sample size to achieve a given separation quality, which we study analytically for a specific family of distributions and a particular algorithm (fastICA). We further provide results from simulations that support the relevance of the analytical results.
UR - https://www.scopus.com/pages/publications/38449091933
U2 - 10.1007/978-3-540-77226-2_43
DO - 10.1007/978-3-540-77226-2_43
M3 - Conference contribution
AN - SCOPUS:38449091933
SN - 9783540772255
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 416
EP - 425
BT - Intelligent Data Engineering and Automated Learning - IDEAL 2007 - 8th International Conference, Proceedings
PB - Springer Verlag
T2 - 8th International Conference on Intelligent Data Engineering and Automated Learning, IDEAL 2007
Y2 - 16 December 2007 through 19 December 2007
ER -