TY - JOUR
T1 - Jensen-Bregman LogDet divergence with application to efficient similarity search for covariance matrices
AU - Cherian, Anoop
AU - Sra, Suvrit
AU - Banerjee, Arindam
AU - Papanikolopoulos, Nikolaos
PY - 2013
Y1 - 2013
N2 - Covariance matrices have found success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. This is because they provide an easy platform for fusing multiple features compactly. An important task in all of these applications is to compare two covariance matrices using a (dis)similarity function, for which the common choice is the Riemannian metric on the manifold inhabited by these matrices. As this Riemannian manifold is not flat, the dissimilarities should take into account the curvature of the manifold. As a result, such distance computations tend to slow down, especially when the matrix dimensions are large or gradients are required. Further, suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics. To alleviate these difficulties, this paper proposes a novel dissimilarity measure for covariances, the Jensen-Bregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding (compared to standard measures). Utilizing the fact that the square root of JBLD is a metric, we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure. To this end, we propose a K-Means clustering algorithm on JBLD. We demonstrate the superior performance of JBLD on covariance datasets from several computer vision applications.
AB - Covariance matrices have found success in several computer vision applications, including activity recognition, visual surveillance, and diffusion tensor imaging. This is because they provide an easy platform for fusing multiple features compactly. An important task in all of these applications is to compare two covariance matrices using a (dis)similarity function, for which the common choice is the Riemannian metric on the manifold inhabited by these matrices. As this Riemannian manifold is not flat, the dissimilarities should take into account the curvature of the manifold. As a result, such distance computations tend to slow down, especially when the matrix dimensions are large or gradients are required. Further, suitability of the metric to enable efficient nearest neighbor retrieval is an important requirement in the contemporary times of big data analytics. To alleviate these difficulties, this paper proposes a novel dissimilarity measure for covariances, the Jensen-Bregman LogDet Divergence (JBLD). This divergence enjoys several desirable theoretical properties and at the same time is computationally less demanding (compared to standard measures). Utilizing the fact that the square root of JBLD is a metric, we address the problem of efficient nearest neighbor retrieval on large covariance datasets via a metric tree data structure. To this end, we propose a K-Means clustering algorithm on JBLD. We demonstrate the superior performance of JBLD on covariance datasets from several computer vision applications.
KW - Bregman divergence
KW - LogDet divergence
KW - Region covariance descriptors
KW - activity recognition
KW - image search
KW - nearest neighbor search
KW - video surveillance
UR - http://www.scopus.com/inward/record.url?scp=84880825073&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84880825073&partnerID=8YFLogxK
U2 - 10.1109/TPAMI.2012.259
DO - 10.1109/TPAMI.2012.259
M3 - Article
C2 - 23868777
AN - SCOPUS:84880825073
SN - 0162-8828
VL - 35
SP - 2161
EP - 2174
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
JF - IEEE Transactions on Pattern Analysis and Machine Intelligence
IS - 9
M1 - 6378374
ER -