difference between pca and pcaFromStatToolbox

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Amir
Amir 2016-2-22
评论： the cyclist 2016-2-23
It might sound stupid, but I actually am confused with the results of the pca and pcaFromStatToolbox. I noticed the different output just now and I am wondering why there are different:
[coeff1,score1]=pcaFromStatToolbox(ran)
[coeff2,score2]=pca(x)
so lets have an example:
>> pcaData=rand(4,5)
pcaData =
0.4638 0.7937 0.6250 0.1400 0.4149
0.7046 0.5080 0.3831 0.8778 0.0977
0.0153 0.8616 0.8466 0.7827 0.0962
0.5929 0.9365 0.0800 0.0978 0.8779
----
>> [n,nn]=pcaFromStatToolbox(pcaData)
n =
-0.2633 0.6508 -0.4266
-0.1495 -0.3995 0.3599
0.4276 -0.4884 -0.4736
0.6094 0.4031 0.5820
-0.5951 -0.1256 0.3542
nn =
-0.1772 -0.2040 -0.2480
0.3372 0.5222 -0.0219
0.6069 -0.3321 0.1240
-0.7668 0.0139 0.1458
------
>> [m,mm]=pca(pcaData)
netlab pca: using eig
netlab pca: sorting evec
m =
0.3671
0.1416
0.0329
0.0000
0.0000
mm =
0.2633 -0.6508 -0.4266 -0.1072 0.5601
0.1495 0.3995 0.3599 0.3753 0.7400
-0.4276 0.4884 -0.4736 -0.5079 0.3106
-0.6094 -0.4031 0.5820 -0.2916 0.2056
0.5951 0.1256 0.3542 -0.7104 0
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Amir
Amir 2016-2-23
Good call! I noticed the other pca is from a tool that was in my path
Estimation_of_Distribution_Algorithms/BNT/KPMstats/pca.m
and it says:
function [PCcoeff, PCvec] = pca(data, N)
%PCA Principal Components Analysis
%
% Description
% PCCOEFF = PCA(DATA) computes the eigenvalues of the covariance
% matrix of the dataset DATA and returns them as PCCOEFF. These
% coefficients give the variance of DATA along the corresponding
% principal components.
%
% PCCOEFF = PCA(DATA, N) returns the largest N eigenvalues.
%
% [PCCOEFF, PCVEC] = PCA(DATA) returns the principal components as well
% as the coefficients. This is considerably more computationally
% demanding than just computing the eigenvalues.
%
% See also
% EIGDEC, GTMINIT, PPCA
%
% Copyright (c) Ian T Nabney (1996-2001)
the cyclist
the cyclist 2016-2-23
编辑：the cyclist 2016-2-23
I just did a quick search KPMstats and MATLAB. I found this annotation:
"KPMstats is a directory of miscellaneous statistics functions written by Kevin Patrick Murphy and various other people (see individual file headers)."
Personally, I would need to dig in to get more confidence in Murphy et al. (who are surely fine fellows). I have a fair amount of experience with the MATLAB pca, and I am very confident in its output.

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回答（1 个）

the cyclist
the cyclist 2016-2-23
编辑：the cyclist 2016-2-23
Even without knowing the source of the other function, I can make a guess.
Notice that for the input, you have 4 observations (4 rows) of 5 variables. So, you can fully explain 100% of the variation with just 4 principal components. Furthermore, because MATLAB centers the variables, you can do it with 3 principal components.
Notice that MATLAB outputs 3 principal component coefficients, where your other software outputs 5 vectors. That other software It is clearly making a different assumption in the case where you only actually need 3 to fully span the space. My guess is that the 4th and 5th vectors (the ones that are different from MATLAB) are linear combinations of the first 3.
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the cyclist
the cyclist 2016-2-23
My speculation that the other two vector outputs are linear combinations of the other three seems not to be true. I'm not sure what's going on there.

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