Setting a generalized functional linear model (GFLM) for the classification of different types of cancer

Miguel Flores; Guido Saltos; Sergio Castillo Páez

Miguel Flores National Polytechnic School
Guido Saltos Escuela Politécnica del Ejército, ESPE
Sergio Castillo Páez National Polytechnic School

Keywords: Depth of functional data, DNA, functional data analysis, functional distances, statistical classification

Abstract

This work aims to classify the DNA sequences of healthy and malignant cancer respectively. For this, supervised and unsupervised classification methods from a functional context are used; i.e. each strand of DNA is an observation. The observations are discretized, for that reason different ways to represent these observations with functions are evaluated. In addition, an exploratory study is done: estimating the mean and variance of each functional type of cancer. For the unsupervised classification method, hierarchical clustering with different measures of functional distance is used. On the other hand, for the supervised classification method, a functional generalized linear model is used. For this model the first and second derivatives are used which are included as discriminating variables. It has been verified that one of the advantages of working in the functional context is to obtain a model to correctly classify cancers by 100%. For the implementation of the methods it has been used the fda.usc R package that includes all the techniques of functional data analysis used in this work. In addition, some that have been developed in recent decades. For more details of these techniques can be consulted Ramsay, J. O. and Silverman (2005) and Ferraty et al. (2006).

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Author Biographies

Miguel Flores, National Polytechnic School

Miguel Flores, is a professor at the National Polytechnic School and a researcher at the Center for Modeling Mathematics at the National Polytechnic School in Quito, Ecuador. He is a BSc. in Statistical Computing Engineer from the Polytechnic School of the Coast. In 2006 he received an in MSc. in Operations Research from the National Polytechnic School, and in 2013 received a MSc. in Technical Statistics from the University of A Coruña. He is currently a doctoral student at the University of A Coruña in the area of Statistics and Operations Research. He has over 15 years professional experience in various areas of Statistics, Computing and Optimization, multivariate data analysis, econometric, Market Research, Quality Control, definition and construction of systems indicators, development of applications and optimization modeling. ORCID ID: 0000-0002-7742-1247

Guido Saltos, Escuela Politécnica del Ejército, ESPE

Guido Saltos S. received his Engineering degree in Electronics from Escuela Politécnica del Ejército (ESPE), Quito, Ecuador in 1987. He received his M.S. degree in Applied Statistics from National Polytechnic School (EPN), Quito, Ecuador, in 2016.
He worked several years in the field of industrial automation and now he is working at Universidad de las Américas (UDLA) in Quito Ecuador. His interests are related with data depth, and non-parametric statistics.

Sergio Castillo Páez, National Polytechnic School

Sergio Castillo Páez, is a mathematical engineer graduated from the National Polytechnic School in 2002. He also studied finance in the Simon Bolivar Andean University, and is currently studying his PhD in Statistics at the University of Vigo, Spain. He is a professor at the ESPE Armed Forces University in Ecuador. His current lines of research are related to geostatistics and analysis of multivariate data.

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