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Similarity between maps

Two maps can be quite different even if their average quantization and/or topological errors are equal. Therefore a measure of similarity between maps would be useful. Similarity could be based on comparing the location of BMUs of input vectors tex2html_wrap_inline3158 on two different maps [49]. This is however sensitive to the size and orientation of the map.

A much better measure was proposed by Kaski and Lagus [18]. The method is an extension of the topological quantization error presented in previous section. The shortest paths between each sample vector pair tex2html_wrap_inline3158 and tex2html_wrap_inline3362 going through their BMUs i and j, respectively, are measured on both maps tex2html_wrap_inline3368 and tex2html_wrap_inline3370 :


where k' is treated in the same way as in 3.5. The dissimilarity between two maps is taken as the expectation value of the relative absolute difference of these distances:


Juha Vesanto
Tue May 27 12:40:37 EET DST 1997