A note on the determination of configuration and weights for a class of individual scaling models |
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| Authors: | Vina Vani M. Raghavachari |
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| Affiliation: | (1) M. G. Science Institute, Ahmedabad, India;(2) I. I. M. Ahmedabad and University of Pennsylvania, USA;(3) Department of Statistics, Wharton School, University of Pennsylvania, 19104 Philadelphia, PA |
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| Abstract: | Consider the typical problem in individual scaling, namely finding a common configuration and weights for each individual from the given interpoint distances or scalar products. Within the STRAIN framework it is shown that the problem of determining weights for a given configuration can be posed as a standard quadratic programming problem. A set of necessary conditions for an optimal configuration to satisfy are given. A closed form expression for the configuration is obtained for the one dimensional case and an approach is given for the two dimensional case. |
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| Keywords: | individual scaling configuration weights quadratic programming STRAIN eigenvector eigenvalue |
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