Algebraic formulation of simultaneous tensor-metric learning

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.