@CONFERENCE{canal.20,
	author = {Canal, G. and Connor, M. and Jin, J. and Nadagouda, N. and O'Shaughnessy, M. and Rozell, C. and Davenport, M.},	
	title = {The {PICASSO} algorithm for {B}ayesian localization via paired comparisons in a union of subspaces model},
	booktitle = {{Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}},
	year = {2020},
	address = {Barcelona, Spain},
	month = may,
	abstract = {We develop a framework for localizing an unknown point w using paired comparisons of the form ``w is closer to point x_i than to x_j'' when the points lie in a union of known subspaces. This model, which extends a broad class of existing methods to exploit union of subspaces structure, provides a powerful framework for using the types of structure found in many practical applications. We divide the problem into two phases: (1) determining which subspace w lies in, and (2) localizing w within the identified subspace using existing techniques. We introduce two algorithms for determining the subspace in which an unknown point lies: the first admits a sample complexity guarantee demonstrating the advantage of the union of subspaces model, and the second improves performance in practice using an adaptive Bayesian strategy. We demonstrate the efficacy of our method with experiments on synthetic data and in an image search application.}
  }