The Factorial Minimum Spanning Tree as a Reference for a Synthetic Index of Complex Phenomena |
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Authors: | Sergio Scippacercola |
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Affiliation: | (1) Research and Development Division, Bloomberg LP, New York, NY 10022, USA;(2) Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, Gainesville, FL 32611, USA |
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Abstract: | This paper is aimed at combining both the properties of factorial subspaces and those of the Minimum Spanning Tree Algorithm (MST) to obtain a reference structure (the Maximum Path) in which the statistical units are in reduced subordering. The coordinates (factor scores) of the statistical units in a multi-factorial subspace through Principal Component Analysis are the basis for the Minimum Spanning Tree. In the MST, we single out a path of maximum length. On the Maximum Path each graduation obtained for the unit can be used as a Synthetic Index of the phenomenon analyzed. Two distinct strategies lead to the choice of the subspace in which we have the best representation of the units in the Maximum Path. The validity of the method is confirmed by results achieved in various applications to real data. |
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