Unsolved Subspace Mysteries

Abstract: In this talk I will introduce two new subspace models: Mixture Matrix Completion, and Subspace Splitting. Both models are motivated by metagenomics, recommender systems, and dimensionality reduction, and are tightly related to low-rank matrix completion, subspace clustering, robust matched subspace detection, and the maximum feasible subsystem problem.

I will tell you the basic theoretical requirements of both models, and some ideas of methods we’ve tried (that fail miserably), including L1 minimization, mixed integer linear programs, and heuristic greedy algorithms. Finally, I’ll tell you about open questions (pretty much all of them are), and I’ll be very interested to hear your ideas to answer them!