Example of "Principal Component Analysis" for weights computation

Small PCA Example

The folowing figure shows the PCA for 6 segmentations over the same audio file. In the first image, each point corresponds to (lengths values of) a segmentation on a projectional space detailed by the second image.

Lengths obtained for 6 segmentation projected by PCA Dimentions of the PCA projection

Possible Weights computations

The distances to the center in this 2-dimensional projection are:
d1=1.335866, d2=1.049168, d3=1.532614, d4=2.392316, d5=1.375279, and d6=2.269634.

In this example, weights are computed for two simple f functions, the first line for a linear correlation to the distance to center, and the second line for a large amplification.

f λ1 λ2 λ3 λ4 λ5 λ6
1/di 0.19 0.24 0.17 0.1 0.19 0.11
e-(di)2 0.222 0.44 0.126 0.004 0.2 0.008