pcacov
Perform principal component analysis on covariance matrix
coeff = pcacov (K) performs principal component analysis
on the square covariance matrix K and returns the principal component
coefficients, also known as loadings. The columns are in order of decreasing
component variance.
[coeff, latent] = pcacov (K) also returns a vector
with the principal component variances, i.e. the eigenvalues of K.
latent has a length of size (coeff, 1).
[coeff, latent, explained] = pcacov (K) also
returns a vector with the percentage of the total variance explained by each
principal component. explained has the same size as latent.
The entries in explained range from 0 (none of the variance is
explained) to 100 (all of the variance is explained).
pcacov does not standardize K to have unit variances. In order
to perform principal component analysis on standardized variables, use the
correlation matrix R = K ./ (SD * SD'), where
SD = sqrt (diag (K)), in place of K. To perform
principal component analysis directly on the data matrix, use pca.
See also: bartlett, factoran, pcares, pca
Source Code: pcacov
x = [ 7 26 6 60;
1 29 15 52;
11 56 8 20;
11 31 8 47;
7 52 6 33;
11 55 9 22;
3 71 17 6;
1 31 22 44;
2 54 18 22;
21 47 4 26;
1 40 23 34;
11 66 9 12;
10 68 8 12
];
Kxx = cov (x);
[coeff, latent, explained] = pcacov (Kxx)
coeff =
-0.067800 -0.646018 0.567315 0.506180
-0.678516 -0.019993 -0.543969 0.493268
0.029021 0.755310 0.403553 0.515567
0.730874 -0.108480 -0.468398 0.484416
latent =
517.7969
67.4964
12.4054
0.2372
explained =
8.6597e+01
1.1288e+01
2.0747e+00
3.9662e-02
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