Dimension reduction using PCA in Matlab - matlab

Question

I am trying to classify vehicles in matlab. I need to reduce the dimensionality of the features to eliminate redundancy. Am using pca for this. Unfortunately, the the pca function is not returning the expected results. The output seems truncated and i don't understand why.
summary of this is as follows:
Components_matrix = [Areas_vector MajorAxisLengths_vector MinorAxisLengths_vector Perimeters_vector...
EquivDiameters_vector Extents_vector Orientations_vector Soliditys_vector]
The output is:
Components_matrix =
1.0e+03 *
1.4000 0.1042 0.0220 0.3352 0.0422 0.0003 0.0222 0.0006
2.7690 0.0998 0.0437 0.3973 0.0594 0.0005 0.0234 0.0007
1.7560 0.0853 0.0317 0.2610 0.0473 0.0005 0.0236 0.0008
1.0870 0.0920 0.0258 0.3939 0.0372 0.0003 0.0157 0.0005
0.7270 0.0583 0.0233 0.2451 0.0304 0.0004 0.0093 0.0006
1.2380 0.0624 0.0317 0.2436 0.0397 0.0004 0.0106 0.0007
Then i used the pca function as follows:
[COEFF, SCORE, LATENT] = pca(Components_matrix)
The displayed results are:
COEFF =
0.9984 -0.0533 -0.0057 -0.0177 0.0045
0.0162 0.1810 0.8788 0.0695 -0.3537
0.0099 -0.0218 -0.2809 0.8034 -0.2036
0.0514 0.9817 -0.1739 -0.0016 0.0468
0.0138 -0.0018 0.0616 0.4276 -0.3585
0.0001 -0.0008 -0.0025 0.0215 0.0210
0.0069 0.0158 0.3388 0.4070 0.8380
0.0001 -0.0011 0.0022 0.0198 0.0016
SCORE =
1.0e+03 *
-0.0946 0.0312 0.0184 -0.0014 -0.0009
1.2758 0.0179 -0.0086 -0.0008 0.0001
0.2569 -0.0642 0.0107 0.0016 0.0012
-0.4043 0.1031 -0.0043 0.0015 0.0003
-0.7721 -0.0299 -0.0079 -0.0017 0.0012
-0.2617 -0.0580 -0.0083 0.0008 -0.0020
LATENT =
1.0e+05 *
5.0614
0.0406
0.0014
0.0000
0.0000
I expected for instance COEFF and LATENT to be 8x8 and 8x1 matrices respectively. But that is not what i get. Why is this so and how can the situation be rectified. Kindly help.

Answer 1

Your usage of pca() and Matlab's output are correct. The issue is that you have more dimensions than you have samples, i.e., you only have 6 vehicles but 8 variables. If you have N samples and N or greater variables, the number of principal components there are is only N-1, because further components would not be unique. So COEFF are the eigenvectors of the covariance matrix of the input, and SCORE(:,1) is the first principal component, SCORE(:,2) is the second, etc., of which there are only N-1=5 in total, and LATENT are the eigenvalues of the covariance matrix, or the amount of variance explained by each successive principal component, of which there are, again, only N-1=5.
There is a more detailed discussion of this here.