TY - GEN
T1 - Sparse geodesic paths
AU - Davenport, Mark A.
AU - Baraniuk, Richard G.
PY - 2009
Y1 - 2009
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=77954233581&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954233581&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:77954233581
SN - 9781577354383
T3 - AAAI Fall Symposium - Technical Report
SP - 2
EP - 9
BT - Manifold Learning and Its Applications - Papers from the AAAI Fall Symposium, Technical Report
T2 - 2009 AAAI FAll Symposium
Y2 - 5 November 2009 through 7 November 2009
ER -