Statistics: pcacov

### Function Reference: `pcacov`

statistics: coeff = pcacov (K)
statistics: [coeff, latent] = pcacov (K)
statistics: [coeff, latent, explained] = pcacov (K)

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`.

### References

1. Jolliffe, I. T., Principal Component Analysis, 2nd Edition, Springer, 2002

See also: bartlett, factoran, pcares, pca

Source Code: pcacov

### Example: 1

     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