Sparse geodesic paths

Mark A. Davenport, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


In this paper we propose a new distance metric for signals that admit a sparse representation in a known basis or dictionary. The metric is derived as the length of the sparse geodesic path between two points, by which we mean the shortest path between the points that is itself sparse. We show that the distance can be computed via a simple formula and that the entire geodesic path can be easily generated. The distance provides a natural similarity measure that can be exploited as a perceptually meaningful distance metric for natural images. Furthermore, the distance has applications in supervised, semi-supervised, and unsupervised learning settings.

Original languageEnglish (US)
Title of host publicationManifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report
Number of pages8
StatePublished - 2009
Event2009 AAAI FAll Symposium - Arlington, VA, United States
Duration: Nov 5 2009Nov 7 2009

Publication series

NameAAAI Fall Symposium - Technical Report


Other2009 AAAI FAll Symposium
Country/TerritoryUnited States
CityArlington, VA

ASJC Scopus subject areas

  • Engineering(all)


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