A New Separation Index and Classification Techniques Based on Shannon Entropy

Methodology And Computing In Applied Probability, vol. 25

Abstract

Abstract The purpose is to use Shannon entropy measures to develop classification techniques and an index which estimates the separation of the groups in a finite mixture model. These measures can be applied to machine learning techniques such as discriminant analysis, cluster analysis, exploratory data analysis, etc. If we know the number of groups and we have training samples from each group (supervised learning) the index is used to measure the separation of the groups. Here some entropy measures are used to classify new individuals in one of these groups. If we are not sure about the number of groups (unsupervised learning), the index can be used to determine the optimal number of groups from an entropy (information/uncertainty) criterion. It can also be used to determine the best variables in order to separate the groups. In all the cases we assume that we have absolutely continuous random variables and we use the Shannon entropy based on the probability density function. Theoretical, parametric and non-parametric techniques are proposed to get approximations of these entropy measures in practice. An application to gene selection in a colon cancer discrimination study with a lot of variables is provided as well.

Authors 3

1. Jorge Navarro corresponding

   Universidad de Murcia

   Affiliation as printed

   Department Statistics and Operational Research, Universidad de Murcia, Facultad de Matemáticas, Murcia, 30100, Spain

2. Francesco Buono Aachen

   RWTH Aachen University · University of Naples Federico II

   Affiliation as printed

   RWTH Aachen University, Pontdriesch 14-16, Aachen, 52062, Germany

   Università di Napoli Federico II, Via Cintia, Napoli, I-80126, Italy

3. Jorge M. Arevalillo

   Universidad Nacional de Educación a Distancia · Universidad Carlos III de Madrid

   Affiliation as printed

   Department of Statistics and Operational Research, University Nacional Educación a Distancia (UNED), Juan del Rosal 10, Madrid, 28040, Spain

   UC3M-Santander Big Data Institute, Madrid Street 135, Getafe, 28903, Madrid, Spain