How to determine the number of dominant eigenvalues in PCA
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
%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~% Gavin Simpson [T] +44 (0)20 7679 5522 ENSIS Research Fellow [F] +44 (0)20 7679 7565 ENSIS Ltd. & ECRC [E] gavin.simpson at ucl.ac.uk UCL Department of Geography [W] http://www.ucl.ac.uk/~ucfagls/cv/ 26 Bedford Way [W] http://www.ucl.ac.uk/~ucfagls/ London. WC1H 0AP. %~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%~%