Using Kurtosis To Assess Significance Of Components From Independent Component Analysis

Question

[Eminencenoir]

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?

Answer 1

[Genotepes]

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

[Eminencenoir]

Thank You I will do so immediately

[Eminencenoir]

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

[Genotepes]

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

[Genotepes]

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

[Eminencenoir]

the second one is fantastic

[Eminencenoir]

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

Answer 2

[Craig Tracy]

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

[Craig Tracy]

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

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