TY - GEN
T1 - Clustering Positive Definite Matrices by Learning Information Divergences
AU - Stanitsas, Panagiotis
AU - Cherian, Anoop
AU - Morellas, Vassilios
AU - Papanikolopoulos, Nikolaos
N1 - Publisher Copyright:
© 2017 IEEE.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - Data representations based on Symmetric Positive Definite (SPD) matrices are gaining popularity in visual learning applications. When comparing SPD matrices, measures based on non-linear geometries often yield beneficial results. However, a manual selection process is commonly used to identify the appropriate measure for a visual learning application. In this paper, we study the problem of clustering SPD matrices while automatically learning a suitable measure. We propose a novel formulation that jointly (i) clusters the input SPD matrices in a K-Means setup and (ii) learns a suitable non-linear measure for comparing SPD matrices. For (ii), we capitalize on the recently introduced αβ-logdet divergence, which generalizes a family of popular similarity measures on SPD matrices. Our formulation is cast in a Riemannian optimization framework and solved using a conjugate gradient scheme. We present experiments on five computer vision datasets and demonstrate state-of-the-art performance.
AB - Data representations based on Symmetric Positive Definite (SPD) matrices are gaining popularity in visual learning applications. When comparing SPD matrices, measures based on non-linear geometries often yield beneficial results. However, a manual selection process is commonly used to identify the appropriate measure for a visual learning application. In this paper, we study the problem of clustering SPD matrices while automatically learning a suitable measure. We propose a novel formulation that jointly (i) clusters the input SPD matrices in a K-Means setup and (ii) learns a suitable non-linear measure for comparing SPD matrices. For (ii), we capitalize on the recently introduced αβ-logdet divergence, which generalizes a family of popular similarity measures on SPD matrices. Our formulation is cast in a Riemannian optimization framework and solved using a conjugate gradient scheme. We present experiments on five computer vision datasets and demonstrate state-of-the-art performance.
UR - http://www.scopus.com/inward/record.url?scp=85046169233&partnerID=8YFLogxK
U2 - 10.1109/ICCVW.2017.155
DO - 10.1109/ICCVW.2017.155
M3 - Conference contribution
T3 - Proceedings - 2017 IEEE International Conference on Computer Vision Workshops, ICCVW 2017
SP - 1304
EP - 1312
BT - Proceedings - 2017 IEEE International Conference on Computer Vision Workshops, ICCVW 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 16th IEEE International Conference on Computer Vision Workshops, ICCVW 2017
Y2 - 22 October 2017 through 29 October 2017
ER -