ON THE SYMMETRICAL PROPERTY OF PROCRUSTES MEASURE OF DISTANCE

T. Bakhtiar, Siswadi Siswadi
2015 International Journal of Pure and Applied Mathematics  
Measurement the degree of difference between two matrices by using Procrustes analysis is preceded by a series of Euclidean similarity transformations namely translation, rotation, and dilation, performed in respected order, for gaining maximal matching. It is easy, by a counter example, to show that Procrustes measure does not obey the symmetrical property, something should be owned by any distance function. In this paper we analytically proved that normalization over configuration matrices as
more » ... an additional transformation results in the satisfaction of the symmetrical property by Procrustes analysis. We also proved that normalization can be undertaken prior to or after rotation to preserve symmetrical property. Moreover, we proved that Procrustes measure can be expressed in term of singular values of the matrix. We here very much exploited the characteristic of full singular value decomposition under similarity transformations. Shape is all the geometrical information that remains when location, rotational,
doi:10.12732/ijpam.v99i3.7 fatcat:qqefy3kxdjcjtjy2kt7cfyfiha