Iterated relevance matrix analysis for improved classification and robustness in prototype-based learning schemes

Generalized Matrix Learning Vector Quantization (GMLVQ) is an inherently interpretable classifier, but the learned distance measure may converge into different competing solutions. Therefore, the resulting trained relevance matrix and its interpretation may differ significantly per training process, diminishing the interpretability benefit, in particular in the presence of small training sets and multiple correlated features. Iterated Relevance Matrix Analysis (IRMA) recursively applies GMLVQ while projecting out all previously found, orthogonal subspaces. Here, we propose a significant extension of the method which combines individual relevance matrices from the application of IRMA into a single, interpretable distance measure. We evaluated the robustness of the combined compared to standard GMLVQ. Moreover, we demonstrate that the associated distance measure can be exploited in the construction of a novel, improved prototype-based classifier by combining the IRMA relevance space with GLVQ (IRMA-GLVQ). Using three open source data sets, we repeatedly drew subsets for model training and evaluated the similarity in between subsets as well as model performance on a holdout test set. Performance metrics were evaluated for various subset sizes. The pairwise differences between the obtained relevance matrices were significantly smaller for IRMA than for GMLVQ for all settings and data sets, and IRMA-GLVQ performed better on holdout test sets for small and medium training set sizes. These findings indicate that IRMA-GLVQ provides a more stable solution with better classification performance for limited training set sizes compared to GMLVQ. • IRMA combines information from multiple competing solutions by recursive application of GMLVQ. • We propose a combined relevance matrix from the individual IRMA iterations. • is more robust to random sampling effects in the training set compared to standard GMVLQ. • The resulting IRMA distance metric gives higher performance on holdout test sets for small and medium sized training sets. • IRMA provides benefits for performance and stable interpretability in the presence of limited training data and correlated features.