Dynamic statistical classification

Pulido-Cejudo, Javier; Cuevas-Covarrubias, Carlos; Pulido-Cejudo, Javier; Cuevas-Covarrubias, Carlos

doi:10.15517/rmta.v24i1.27774

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Revista de Matemática Teoría y Aplicaciones

Print version ISSN 1409-2433

Rev. Mat vol.24 n.1 San José Jan./Jun. 2017

http://dx.doi.org/10.15517/rmta.v24i1.27774

Artículo

Dynamic statistical classification

Clasificación estadística dinámica

Javier Pulido-Cejudo¹

Carlos Cuevas-Covarrubias¹

^¹CIEMA, Universidad Anáhuac, México D.F., México. E-Mail: javierpulidocejudo@gmail.com, ccuevas@anahuac.mx

Abstract

We consider the statistical supervised classification problem from a dynamical systems approach. We assume that two classes exist and that, for each one, a multivariate normal distribution determines the probability to be in a certain region in the n dimensional real vector space. These density functions are the potentials of corresponding gradient vector fields for each class; we construct a “classifying vector field” as a suitable weighted mean of them. From data known in the literature, we estimate the population parameters, and the classes are successfully distinguished; we compute and present confusion matrices. A one and two-dimensional analysis is given.

Keywords: supervised statistical classification; multivariate normal distribution; vector fields; attractors; bifurcation; dynamical systems

Resumen

Consideramos el problema de la clasificación estadística supervisada desde la perspectiva de los sistemas dinámicos. Suponemos la existencia de dos clases cuyas poblaciones se distribuyen como normales en un espacio real de dimensión n. Estas funciones de densidad son los potenciales de los correspondientes campos gradientes de cada clase; construímos el “campo vectorial clasificante” como un campo promedio con pesos apropiados. A partir de datos bien conocidos en la literatura, estimamos los parámetros poblacionales y las clases son clasificadas exitosamente. Un análisis en dimensiones uno y dos es presentado.

Palabras clave: Clasificación estadística supervisada; distribución normal multivariada; campos vectoriales; atractores; bifurcación; sistemas dinámicos

Mathematics Subject Classification: 37B25, 62G32.

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References

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Received: March 03, 2016; Revised: August 25, 2016; Accepted: October 07, 2016

This is an open-access article distributed under the terms of the Creative Commons Attribution License