TY - GEN
T1 - Manifold Précis
T2 - 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
AU - Shroff, Nitesh
AU - Turaga, Pavan
AU - Chellappa, Rama
PY - 2011/12/1
Y1 - 2011/12/1
N2 - In this paper, we consider the Précis problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and pre-filtering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also non-Euclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealing-based iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach.
AB - In this paper, we consider the Précis problem of sampling K representative yet diverse data points from a large dataset. This problem arises frequently in applications such as video and document summarization, exploratory data analysis, and pre-filtering. We formulate a general theory which encompasses not just traditional techniques devised for vector spaces, but also non-Euclidean manifolds, thereby enabling these techniques to shapes, human activities, textures and many other image and video based datasets. We propose intrinsic manifold measures for measuring the quality of a selection of points with respect to their representative power, and their diversity. We then propose efficient algorithms to optimize the cost function using a novel annealing-based iterative alternation algorithm. The proposed formulation is applicable to manifolds of known geometry as well as to manifolds whose geometry needs to be estimated from samples. Experimental results show the strength and generality of the proposed approach.
UR - http://www.scopus.com/inward/record.url?scp=84860621640&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860621640&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:84860621640
SN - 9781618395993
T3 - Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
BT - Advances in Neural Information Processing Systems 24
Y2 - 12 December 2011 through 14 December 2011
ER -