A robust approach to model-based classification based on trimming and constraints

In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations, namely outliers and data with incorrect labels, can strongly undermine the classifier performance, especially if the training size is small. The present work introduces a robust modification to the Model-Based Classification framework, employing impartial trimming and constraints on the ratio between the maximum and the minimum eigenvalue of the group scatter matrices. The proposed method effectively handles noise presence in both response and exploratory variables, providing reliable classification even when dealing with contaminated datasets. A robust information criterion is proposed for model selection. Experiments on real and simulated data, artificially adulterated, are provided to underline the benefits of the proposed method

Model-Based Clustering, Classification, and Discriminant Analysis Using the Generalized Hyperbolic Distribution: MixGHD R package

The MixGHD package for R performs model-based clustering, classification, and discriminant analysis using the generalized hyperbolic distribution (GHD). This approach is suitable for data that can be considered a realization of a (multivariate) continuous random variable. The GHD has the advantage of being flexible due to skewness, concentration, and index parameters; as such, clustering methods that use this distribution are capable of estimating clusters characterized by different shapes. The package provides five different models all based on the GHD, an efficient routine for discriminant analysis, and a function to measure cluster agreement. This paper is split into three parts: the first is devoted to the formulation of each method, extending them for classification and discriminant analysis applications, the second focuses on the algorithms, and the third shows the use of the package on real datasets

Robust, fuzzy, and parsimonious clustering based on mixtures of Factor Analyzers

A clustering algorithm that combines the advantages of fuzzy clustering and robust statistical estimators is presented. It is based on mixtures of Factor Analyzers, endowed by the joint usage of trimming and the constrained estimation of scatter matrices, in a modified maximum likelihood approach. The algorithm generates a set of membership values, that are used to fuzzy partition the data set and to contribute to the robust estimates of the mixture parameters. The adoption of clusters modeled by Gaussian Factor Analysis allows for dimension reduction and for discovering local linear structures in the data. The new methodology has been shown to be resistant to different types of contamination, by applying it on artificial data. A brief discussion on the tuning parameters, such as the trimming level, the fuzzifier parameter, the number of clusters and the value of the scatter matrices constraint, has been developed, also with the help of some heuristic tools for their choice. Finally, a real data set has been analyzed, to show how intermediate membership values are estimated for observations lying at cluster overlap, while cluster cores are composed by observations that are assigned to a cluster in a crisp way.Ministerio de Economía y Competitividad grant MTM2017-86061-C2-1-P, y Consejería de Educación de la Junta de Castilla y León and FEDER grantVA005P17 y VA002G1

Robust variable selection for model-based learning in presence of adulteration

The problem of identifying the most discriminating features when performing supervised learning has been extensively investigated. In particular, several methods for variable selection in model-based classification have been proposed. Surprisingly, the impact of outliers and wrongly labeled units on the determination of relevant predictors has received far less attention, with almost no dedicated methodologies available in the literature. In the present paper, we introduce two robust variable selection approaches: one that embeds a robust classifier within a greedy-forward selection procedure and the other based on the theory of maximum likelihood estimation and irrelevance. The former recasts the feature identification as a model selection problem, while the latter regards the relevant subset as a model parameter to be estimated. The benefits of the proposed methods, in contrast with non-robust solutions, are assessed via an experiment on synthetic data. An application to a high-dimensional classification problem of contaminated spectroscopic data concludes the paper

Unobserved classes and extra variables in high-dimensional discriminant analysis

In supervised classification problems, the test set may contain data points belonging to classes not observed in the learning phase. Moreover, the same units in the test data may be measured on a set of additional variables recorded at a subsequent stage with respect to when the learning sample was collected. In this situation, the classifier built in the learning phase needs to adapt to handle potential unknown classes and the extra dimensions. We introduce a model-based discriminant approach, Dimension-Adaptive Mixture Discriminant Analysis (D-AMDA), which can detect unobserved classes and adapt to the increasing dimensionality. Model estimation is carried out via a full inductive approach based on an EM algorithm. The method is then embedded in a more general framework for adaptive variable selection and classification suitable for data of large dimensions. A simulation study and an artificial experiment related to classification of adulterated honey samples are used to validate the ability of the proposed framework to deal with complex situations.Comment: 29 pages, 29 figure