Page 230 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

FEATURE REDUCTION 219

A second drawback of PCA is that the results are not invariant to the
particular choice of the physical units of the measurements. Each elem-
ent of z is individually scaled according to its unit in which it is
expressed. Changing a unit from, for instance, m (meter) to mm (micro-
meter) may result in dramatic changes of the principal directions.
Usually this phenomenon is circumvented by scaling the vector z such
that the numerical values of the elements all have unit variance.

Example 7.1 Image compression
Since PCA aims at the reduction of a measurement vector in such a way
that it can be reconstructed accurately, the technique is suitable for
image compression. Figure 7.2 shows the original image. The image
plane is partitioned into 32 32 regions each having 8 8pixels.

original image fraction of cumulative eigenvalues reconstruction
1
0.95

0.9

0.85

0.8
0 20 40 60
D
0 eigenvector 1st eigenvector 2nd eigenvector 3rd eigenvector

4th eigenvector 5th eigenvector 6th eigenvector 7th eigenvector

Figure 7.2 Application of PCA to image compression