[R] How to determine the number of dominant eigenvalues in PCA

[Gavin Simpson]

Fred wrote:
> Dear All,
> 
> I want to know if there is some easy and reliable way to estimate the
> number of dominant eigenvalues when applying PCA on sample covariance
> matrix.
> 
> Assume x-axis is the number of eigenvalues (1, 2, ....,n), and y-axis
> is the corresponding eigenvalues (a1,a2,..., an) arranged in
> desceding order. So this x-y plot will be a decreasing curve. Someone
> mentioned using the elbow (knee) method to find the point that the
> maximal curvature of this curve occurs. The number at this point
> would be the number of dominant eigenvalues.
> 
> But I could not find any reference papers on this idea. Does anyone
> has tried this method or knows more details on this?
> 
> Thanks for your point.
> 
> Fred
> 

Try this reference from the field of ecology:

@Article{571,
   Author         = {D. A. Jackson},
   Title          = {Stopping rules in principal components analysis: a
                    comparison of heuristic and statistical approaches},
   Journal        = {Ecology},
   Volume         = {74},
   Number         = {8},
   Pages          = {2204--2214},
   month          = {},
   year           = 1993
}

Gav
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Gavin Simpson                     [T] +44 (0)20 7679 5522
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