Bridging the Divide: From Matrix to Tensor Algebra for Optimal Approximation and Compression

Explore the cutting-edge developments in tensor algebra and its applications in data compression and analysis through this Kirk Lecture by Professor Misha Kilmer from Tufts University. Delve into the limitations of traditional matrix-based approaches when dealing with higher-dimensional data structures and discover a novel family of tensor algebras based on a new definition of tensor-tensor products. Learn how this framework elegantly generalizes classical linear algebra algorithms to tensors, offering provable approximation properties and advantages over traditional matrix methods. Examine real-world examples demonstrating the practical benefits of this tensor-tensor product framework and gain insights into exciting open questions and future research directions in the field of tensor algebra and its applications to optimal approximation and compression.