Tensor Representation

Tensor representation is a rapidly developing field focused on representing and analyzing multi-dimensional data using higher-order tensors, going beyond the limitations of matrix-based methods. Current research emphasizes developing efficient algorithms for tensor operations, including novel matrix-mimetic approaches and tensor factorization techniques like those used in additive models and symmetric matrix factorization, to improve accuracy, interpretability, and computational efficiency. These advancements are proving valuable across diverse applications, from multicriteria decision analysis and material modeling to image processing and machine learning, particularly in meta-learning where tensors enable the incorporation of task-specific information. The ability to effectively handle complex, high-dimensional data makes tensor representation a powerful tool with significant impact across scientific disciplines and practical applications.