Lengths of principal components to determinate SOM grid

by MomoMI   Last Updated May 06, 2017 13:19 PM

"Most applications of the SOM are based on regular arrays of nodes. Sometimes one uses rectangular arrays of nodes for simplicity. However, the hexagonal arrays are visually much more illustrative and accurate, and are recommended. Whatever regular architectures are used, it is advisable to select the lengths of the horizontal and vertical dimensions of the array to correspond to the lengths of the two largest principal components (i.e., those with the highest eigenvalues of the input correlation matrix), because then the SOM complies better with the low-order signal statistics.The oblong regular array shave the advantage over the square ones of guaranteeing faster and safer convergence in learning"

This is taken from the article "Essentials of the self-organizing map" written by Teuvo Kohonen itself. What does he mean by lenghts of the two largest principal components and what is the rationale of choosing the dimensions of the grid in this way?



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