2006 Fiscal Year Final Research Report Summary
Theory and applications of independent component analysis
| Project/Area Number |
16500184
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
MINAMI Mihoko The Institute of Statistical Mathematics, associate professor, 数理・推論研究系, 助教授 (70277268)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Independent Component Analysis / Blind source separation / beta-divergence / robustness / outliers / non-negative matrix factorization / Tweedie models |
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| Research Abstract |
The independent component analysis aims to recover independent source signals from observed signals assuming observed signals are linear mixtures of original independent signals. When linear mixtures are instantaneous, it is often called as blind source separation. Minami has proposed a robust blind source separation method based on beta-divergence (minimum beta-divergence method) which can recover independent source signals even when data contain outliers or spike noises. This method is more robust to outliers with a larger value of beta, but then it loses efficiency with too large value of beta. Minami has also proposed an adaptive selection procedure of beta so that the minimum beta-divergence estimator is robust to outliers and yet does not lose efficiency so much. Simulation results showed that the procedure works well for various kinds of situations.
Robustness of the minimum beta-divergence estimator to outliers can be also utilized in the mixture ICA situation. Suppose there are
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several independent component structures in an entire space. The minimum beta-divergence estimator finds an independent component structure considering data points that belong to other independent structures as outliers. All independent component structures can be found sequentially by changing the initial values appropriately. The minimum beta-divergence estimator is also used for pre-whitening procedure that is required for many independent component estimation methods. These researches were jointly conducted with Professor Shinto Eguchi of the Institute of Statistical Mathematics and the Graduate University for Advanced Studies and his Ph.D. student, Md. Nurul Hague Mollah.
Non-negative matrix factorization (NMF) is a method to factorize a matrix with non-negative elements into the product of two matrices with non-negative elements with lower ranks. NMF has attracted a great deal of attention in theories and applications and many methods based on various types of divergences have been proposed. Minami gave an interpretation for these methods from statistical points of view and proposed a new method that allows errors with a very non-normal distribution. This method was applied for feature extraction for multivariate bycatch data by purse-seine tuna fisheries. Less
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Research Products
(4 results)
