EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator

Liyan Song, Haiping Lu
Proceedings of The 8th Asian Conference on Machine Learning, PMLR 63:445-460, 2016.

Abstract

Independent component analysis (ICA) is an important unsupervised learning method. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE.However, their assumption of kurtosic sources may not always be satisfied in practice. For weak-kurtosic but skewed sources, kurtosis-based methods could fail while skewness-based methods seem more promising, where skewness is another non-Gaussianity metric measuring the non-symmetry of signals. Partly due to the common assumption of signal symmetry, skewness-based ICA has not been systematically studied in spite of some existing works. In this paper, we take a systematic approach to develop EcoICA, a new skewness-based ICA method for weak-kurtosic but skewed sources. Specifically, we design a new cumulant operator, define its eigenvalues and eigenvectors, reveal their connections with the ICA model to formulate the EcoICA problem, and use Jacobi method to solve it. Experiments on both synthetic and real data show the superior performance of EcoICA over existing kurtosis-based and skewness-based methods for skewed sources. In particular, EcoICA is less sensitive to sample size, noise, and outlier than other methods. Studies on face recognition further confirm the usefulness of EcoICA in classification.

Cite this Paper

BibTeX
@InProceedings{pmlr-v63-Song94, title = {EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator}, author = {Song, Liyan and Lu, Haiping}, booktitle = {Proceedings of The 8th Asian Conference on Machine Learning}, pages = {445--460}, year = {2016}, editor = {Durrant, Robert J. and Kim, Kee-Eung}, volume = {63}, series = {Proceedings of Machine Learning Research}, address = {The University of Waikato, Hamilton, New Zealand}, month = {16--18 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v63/Song94.pdf}, url = {https://proceedings.mlr.press/v63/Song94.html}, abstract = {Independent component analysis (ICA) is an important unsupervised learning method. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE.However, their assumption of kurtosic sources may not always be satisfied in practice. For weak-kurtosic but skewed sources, kurtosis-based methods could fail while skewness-based methods seem more promising, where skewness is another non-Gaussianity metric measuring the non-symmetry of signals. Partly due to the common assumption of signal symmetry, skewness-based ICA has not been systematically studied in spite of some existing works. In this paper, we take a systematic approach to develop EcoICA, a new skewness-based ICA method for weak-kurtosic but skewed sources. Specifically, we design a new cumulant operator, define its eigenvalues and eigenvectors, reveal their connections with the ICA model to formulate the EcoICA problem, and use Jacobi method to solve it. Experiments on both synthetic and real data show the superior performance of EcoICA over existing kurtosis-based and skewness-based methods for skewed sources. In particular, EcoICA is less sensitive to sample size, noise, and outlier than other methods. Studies on face recognition further confirm the usefulness of EcoICA in classification.} }
Endnote
%0 Conference Paper %T EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator %A Liyan Song %A Haiping Lu %B Proceedings of The 8th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Robert J. Durrant %E Kee-Eung Kim %F pmlr-v63-Song94 %I PMLR %P 445--460 %U https://proceedings.mlr.press/v63/Song94.html %V 63 %X Independent component analysis (ICA) is an important unsupervised learning method. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE.However, their assumption of kurtosic sources may not always be satisfied in practice. For weak-kurtosic but skewed sources, kurtosis-based methods could fail while skewness-based methods seem more promising, where skewness is another non-Gaussianity metric measuring the non-symmetry of signals. Partly due to the common assumption of signal symmetry, skewness-based ICA has not been systematically studied in spite of some existing works. In this paper, we take a systematic approach to develop EcoICA, a new skewness-based ICA method for weak-kurtosic but skewed sources. Specifically, we design a new cumulant operator, define its eigenvalues and eigenvectors, reveal their connections with the ICA model to formulate the EcoICA problem, and use Jacobi method to solve it. Experiments on both synthetic and real data show the superior performance of EcoICA over existing kurtosis-based and skewness-based methods for skewed sources. In particular, EcoICA is less sensitive to sample size, noise, and outlier than other methods. Studies on face recognition further confirm the usefulness of EcoICA in classification.
RIS
TY - CPAPER TI - EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator AU - Liyan Song AU - Haiping Lu BT - Proceedings of The 8th Asian Conference on Machine Learning DA - 2016/11/20 ED - Robert J. Durrant ED - Kee-Eung Kim ID - pmlr-v63-Song94 PB - PMLR DP - Proceedings of Machine Learning Research VL - 63 SP - 445 EP - 460 L1 - http://proceedings.mlr.press/v63/Song94.pdf UR - https://proceedings.mlr.press/v63/Song94.html AB - Independent component analysis (ICA) is an important unsupervised learning method. Most popular ICA methods use kurtosis as a metric of non-Gaussianity to maximize, such as FastICA and JADE.However, their assumption of kurtosic sources may not always be satisfied in practice. For weak-kurtosic but skewed sources, kurtosis-based methods could fail while skewness-based methods seem more promising, where skewness is another non-Gaussianity metric measuring the non-symmetry of signals. Partly due to the common assumption of signal symmetry, skewness-based ICA has not been systematically studied in spite of some existing works. In this paper, we take a systematic approach to develop EcoICA, a new skewness-based ICA method for weak-kurtosic but skewed sources. Specifically, we design a new cumulant operator, define its eigenvalues and eigenvectors, reveal their connections with the ICA model to formulate the EcoICA problem, and use Jacobi method to solve it. Experiments on both synthetic and real data show the superior performance of EcoICA over existing kurtosis-based and skewness-based methods for skewed sources. In particular, EcoICA is less sensitive to sample size, noise, and outlier than other methods. Studies on face recognition further confirm the usefulness of EcoICA in classification. ER -
APA
Song, L. & Lu, H.. (2016). EcoICA: Skewness-based ICA via Eigenvectors of Cumulant Operator. Proceedings of The 8th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 63:445-460 Available from https://proceedings.mlr.press/v63/Song94.html.

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