This talk considers matrix completion in cases where columns are points on a nonlinear algebraic variety (in contrast to the commonplace linear subspace model). A special case arises when the columns come from a union of subspaces, a model that has numerous practical applications. We propose a new approach to …
Distributed optimization methods consist of two key aspects: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in the network requires some form of information exchange with its neighboring nodes (communication) and the computation of a (sub)-gradient (computation). The standard way …
Optimization algorithms play a fundamental role in analyzing the vast amount of data available today. Due to the need for fast optimization algorithms, there has been recent interest in understanding the mechanisms which enable optimization algorithms to converge quickly. We gain insight into these algorithms by leveraging techniques from control …
High-dimensional high-order arrays, or tensors, arise in many modern scientific applications including genomics, brain imaging, and social science. In this talk, we consider two specific problems in tensor data analysis: low-rank tensor completion and tensor SVD. We first propose a framework for low-rank tensor completion via a novel tensor measurement …