Unobserved classes and extra variables in high-dimensional discriminant analysis

TL;DR

This paper introduces D-AMDA, a model-based discriminant method that detects unobserved classes and adapts to extra variables in high-dimensional classification, validated through simulations and real data.

Contribution

The paper proposes D-AMDA, a novel EM-based discriminant approach for handling unobserved classes and additional variables in high-dimensional data.

Findings

Effective detection of unobserved classes in simulations

Successful adaptation to extra variables in experiments

Robust performance in complex classification scenarios

Abstract

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.