A Complete Classification and Clustering Model to Account for Continuous and Categorical Data in Presence of Missing Values and Outliers

Abstract

Classification and clustering problems are closely connected with pattern recognition where many general algorithms have been developed and used in various fields. Depending on the complexity of patterns in data, classification and clustering procedures should take into consideration both continuous and categorical data which can be partially missing and erroneous due to mismeasurements and human errors. However, most algorithms cannot handle missing data and imputation methods are required to generate data to use them. Hence, the main objective of this work is to define a classification and clustering framework that handles both outliers and missing values. Here, an approach based on mixture models is preferred since mixture models provide a mathematically based, flexible and meaningful framework for the wide variety of classification and clustering requirements. More precisely, a scale mixture of Normal distributions is updated to handle outliers and missing data issues for any types of data. Then a variational Bayesian inference is used to find approximate posterior distributions of parameters and to provide a lower bound on the model log evidence used as a criterion for selecting the number of clusters. Eventually, experiments are carried out to exhibit the effectiveness of the proposed model through an application in Electronic Warfare.