Clustering of variables based on a probabilistic approach defined on the hypersphere.

• Type: Article in International Scientific Journal
• Date: 2013

Authors

Paulo Gomes (Author) Other; Adelaide Figueiredo (Author) FEP

Journal

Title: International Journal of Mathematical, Computational Science and Engineering

Vol. 7 No. 10

Pages: 564-566

Publisher: World Academy of Science Engineering and Technology

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Resumo (PT): Abstract: We consider n individuals described by p standardized variables, represented by points of the surface of the unit hypersphere Sn-1. For a previous choice of n individuals we suppose that the set of observables variables comes from a mixture of bipolar Watson distribution defined on the hypersphere. EM and Dynamic Clusters algorithms are used for identification of such mixture. We obtain estimates of parameters for each Watson component and then a partition of the set of variables into homogeneous groups of variables. Additionally we will present a factor analysis model where unobservable factors are just the maximum likelihood estimators of Watson directional parameters, exactly the first principal component of data matrix associated to each group previously identified. Such alternative model it will yield us to directly interpretable solutions (simple structure), avoiding factors rotations.

Language: English

Type (Professor's evaluation): Scientific