Local Metric Learning on Manifolds with Application to Query---Based Operations

Authors:
Karim Abou-Moustafa;Frank Ferrie
Affiliations:
The Artificial Perception Laboratory Centre for Intelligent Machines, McGill University, Montreal, Canada H3A 2A7;The Artificial Perception Laboratory Centre for Intelligent Machines, McGill University, Montreal, Canada H3A 2A7
Venue:
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Year:
2008

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Abstract

We first investigate the combined effect of data complexity, curse of dimensionality and the definition of the Euclidean distance on the distance measure between points. Then, based on the concepts underlying manifold learning algorithms and the minimum volume ellipsoid metric, we design an algorithm that learns a local metric on the lower dimensional manifold on which the data is lying. Experiments in the context of classification on standard benchmark data sets showed very promising results when compared to state of the art algorithms, and consistent improvements over the Euclidean distance in the context of query---based learning.