Boris Alexeev, Wenyan Luo, Dustin G. Mixon et al.
Things can go spectacularly wrong when clustering timeseries data that has been preprocessed with a sliding window. We highlight three surprising failures that emerge depending on how the window size compares with the timeseries length. In addition to computational examples, we present theoretical explanations for each of these failure modes.
Boris Alexeev, Rachel Ward
We show that inverse problems with a truncated quadratic regularization are NP-hard in general to solve, or even approximate up to an additive error. This stands in contrast to the case corresponding to a finite-dimensional approximation to the Mumford-Shah functional, where the operator involved is the identity and for which polynomial-time solutions are known. Consequently, we confirm the infeasibility of any natural extension of the Mumford-Shah functional to general inverse problems. A connection between truncated quadratic minimization and sparsity-constrained minimization is also discussed.