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From: HL <highlanderda@gmail.com>
Newsgroups: comp.soft-sys.matlab
Subject: Interpreting PCA results: correlation coeff close to zero. but both
 have high variances % on F2
Date: Fri, 8 Jul 2011 17:12:40 -0700 (PDT)
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Hi All,

I have trouble in interpreting PCA result.  As I know a lot of people
do PCA use matlab, I hope I can get some advice here.

Here is the correlation coefficients matrix of 6 time series
	VAR 1	VAR 2	VAR 3	VAR 4	VAR 5	VAR 6
VAR 1	1	0.86924	0.72059	0.93435	0.94902	0.60563
VAR 2	0.86924	1	0.56722	0.82527	0.86984	0.74556
VAR 3	0.72059	0.56722	1	0.81599	0.71481	0.04097
VAR 4	0.93435	0.82527	0.81599	1	0.90632	0.54128
VAR 5	0.94902	0.86984	0.71481	0.90632	1	0.68061
VAR 6	0.60563	0.74556	0.04097	0.54128	0.68061	1

note that the correlation coeff for VAR3 and VAR6 is small, almost
zero (0.04)

I can get eigen values and vectors
Eigen Vectors	F1	F2	F3	F4	F5	F6
VAR 1	-0.44868	0.044975	0.22607	0.66658	0.39593	0.38009
VAR 2	-0.42826	-0.19755	-0.86091	0.0869	0.040701	-0.16492
VAR 3	-0.34321	0.64797	-0.11832	-0.30814	-0.34259	0.48583
VAR 4	-0.44316	0.16762	0.23468	-0.49622	0.56209	-0.39782
VAR 5	-0.45069	-0.019026	0.31936	0.24333	-0.62144	-0.49912
VAR 6	-0.31301	-0.71458	0.19148	-0.38436	-0.14859	0.43002

Eigen Values	4.6795	1.022	0.13623	0.081882	0.075441	0.0049339


Square each element in the eigen vector matrix weighted by respective
eigen values, we get the The "factor loading matrix square"
	        F1	        F2	        F3	        F4	       F5	        F6
VAR 1	0.94205	0.0020673	0.0069622	0.036382	0.011826	0.0007128
VAR 2	0.85827	0.039884	0.10097	0.00061834	0.00012497	0.00013419
VAR 3	0.5512	0.4291	0.0019073	0.0077745	0.0088546	0.0011645
VAR 4	0.919	0.028715	0.0075029	0.020162	0.023835	0.00078086
VAR 5	0.95052	0.00036995	0.013894	0.0048483	0.029134	0.0012291
VAR 6	0.45847	0.52186	0.0049948	0.012097	0.0016658	0.00091238

Note that VAR3 and VAR6 each has project almost 50% of its respective
variances
on the F2 direction.  I cannot make sense of this as there correlation
coefficient is almost zero.

Thank you very much for your input and advice.

Chong