Publication Type

Conference Proceeding Article

Publication Date

12-2009

Abstract

Learning distance functions with side information plays a key role in many machine learning and data mining applications. Conventional approaches often assume a Mahalanobis distance function. These approaches are limited in two aspects: (i) they are computationally expensive (even infeasible) for high dimensional data because the size of the metric is in the square of dimensionality; (ii) they assume a fixed metric for the entire input space and therefore are unable to handle heterogeneous data. In this paper, we propose a novel scheme that learns nonlinear Bregman distance functions from side information using a nonparametric approach that is similar to support vector machines. The proposed scheme avoids the assumption of fixed metric by implicitly deriving a local distance from the Hessian matrix of a convex function that is used to generate the Bregman distance function. We also present an efficient learning algorithm for the proposed scheme for distance function learning. The extensive experiments with semi-supervised clustering show the proposed technique (i) outperforms the state-of-the-art approaches for distance function learning, and (ii) is computationally efficient for high dimensional data.

Discipline

Computer Sciences | Databases and Information Systems

Research Areas

Data Management and Analytics

Publication

Advances in Neural Information Processing Systems: 23rd Annual Conference on Neural Information Processing Systems 2009, December 7-10, 2009, Vancouver, BC, Canada

Volume

22

ISBN

9781615679119

Publisher

Neural Information Processing Systems

City or Country

La Jolla, CA

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://papers.nips.cc/paper/3678-learning-bregman-distance-functions-and-its-application-for-semi-supervised-clustering

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