Manifold Précis: An annealing technique for diverse sampling of manifolds

Nitesh Shroff, Pavan Turaga, Rama Chellappa

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

8 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 24
Subtitle of host publication25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
StatePublished - Dec 1 2011
Event25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011 - Granada, Spain
Duration: Dec 12 2011Dec 14 2011

Publication series

NameAdvances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011

Other

Other25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011
CountrySpain
CityGranada
Period12/12/1112/14/11

ASJC Scopus subject areas

  • Information Systems

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    Shroff, N., Turaga, P., & Chellappa, R. (2011). Manifold Précis: An annealing technique for diverse sampling of manifolds. In Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011 (Advances in Neural Information Processing Systems 24: 25th Annual Conference on Neural Information Processing Systems 2011, NIPS 2011).