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This research aims to enhance optimization processes in high-dimensional, multimodal datasets using multi-metric learning techniques.

May 27, 2026Optimization Letters0 citationsOpen Access

Algebraic formulation of simultaneous tensor-metric learning

MBMaryam BagherianIdaho State University

Key Points

This research aims to enhance optimization processes in high-dimensional, multimodal datasets using multi-metric learning techniques.
Outlined theoretical foundations of multi-distance metric learning and group theory concepts.
Presented convergence results and experimental evaluations on the LINCS dataset.
Conducted an ablation study to assess the contribution of each additional metric to performance.
Experimental evaluations showed improved optimization performance using multi-metric learning techniques.
Comparisons with two other methods indicated superior results in imputation accuracy on the LINCS dataset.

Abstract

Abstract Multi-metric learning techniques are designed to enhance optimization processes, such as imputing missing data in high-dimensional, multimodal datasets, where multiple local distance functions are defined. Here, we first outline the theoretical foundations of multi-distance metric learning and relevant concepts from group theory. Convergence results, followed by experimental evaluations on the LINCS dataset, including comparisons with two other methods are presented. Finally, an ablation study to illustrate how incorporating each additional metric contributes to improved overall performance is provided.

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