Question

Using Kurtosis To Assess Significance Of Components From Independent Component Analysis

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13.5 years ago

Eminencenoir ▴ 50

In PCA eigenvalues determine the order of components. In ICA I am using kurtosis to obtain the ordering. What are some accepted methods to assess the number, (given I have the order) of components that are significant apart from prior knowledge about the signal?

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ADD COMMENT • link updated 13.5 years ago by Craig Tracy ▴ 10 • written 13.5 years ago by Eminencenoir ▴ 50

Egon Willighagen · Answer 1 · 2011-05-11

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13.5 years ago

Genotepes ▴ 950

Check out the Tracy-Widom test of the eigenvalues. We are using it for finding out how many components are "important" in genetic structure analysis.

Christian

ADD COMMENT • link updated 13.5 years ago by Egon Willighagen 5.4k • written 13.5 years ago by Genotepes ▴ 950

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Thank You I will do so immediately

ADD REPLY • link 13.5 years ago by Eminencenoir ▴ 50

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Would You send me a link to Your paper? work so that I have some idea on how to apply it, as my problem is atypical

ADD REPLY • link 13.5 years ago by Eminencenoir ▴ 50

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Johnstone I (2001) On the distribution of the largest eigenvalue in principal components analysis. Ann Stat 29: 295–327

ADD REPLY • link 13.5 years ago by Genotepes ▴ 950

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Population Structure and Eigenanalysis, PAterson is also applying the preceding and explains.

ADD REPLY • link 13.5 years ago by Genotepes ▴ 950

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the second one is fantastic

ADD REPLY • link 13.5 years ago by Eminencenoir ▴ 50

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what if my n>m, what do I do? what distribution do I use?

ADD REPLY • link 13.5 years ago by Eminencenoir ▴ 50

score 1 · Answer 2 · 2011-05-13

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13.5 years ago

Craig Tracy ▴ 10

See also, I. Johnstone, MULTIVARIATE ANALYSIS AND JACOBI ENSEMBLES: LARGEST EIGENVALUE, TRACY–WIDOM LIMITS AND RATES OF CONVERGENCE, The Annals of Statistics 2008, Vol. 36, No. 6, 2638–2716 DOI: 10.1214/08-AOS605

ADD COMMENT • link 13.5 years ago by Craig Tracy ▴ 10

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Johnstone's 2006 ICM lecture is also a good reference:

   http://front.math.ucdavis.edu/0611.5589

ADD REPLY • link 13.5 years ago by Craig Tracy ▴ 10