The minimum volume ellipsoid metric

Authors:
Karim T. Abou-Moustafa;Frank P. Ferrie
Affiliations:
The Artificial Perception Laboratory, Centre for Intelligent Machines, McGill University, Montreal, QC, Canada;The Artificial Perception Laboratory, Centre for Intelligent Machines, McGill University, Montreal, QC, Canada
Venue:
Proceedings of the 29th DAGM conference on Pattern recognition
Year:
2007

Citing 6
Cited 1

Locally Weighted Learning

Artificial Intelligence Review - Special issue on lazy learning
A fast algorithm for the minimum covariance determinant estimator

Technometrics
Convex Optimization

Convex Optimization
Learning a Mahalanobis Metric from Equivalence Constraints

The Journal of Machine Learning Research
Computation of Minimum-Volume Covering Ellipsoids

Operations Research
The minimum volume covering ellipsoid estimation in kernel-defined feature spaces

ECML'06 Proceedings of the 17th European conference on Machine Learning

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

SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose an unsupervised "local learning" algorithm for learning a metric in the input space. Geometrically, for a given query point, the algorithm finds the minimum volume ellipsoid (MVE) covering its neighborhood which characterizes the correlations and variances of its neighborhood variables. Algebraically, the algorithm maximizes the determinant of the local covariance matrix which amounts to a convex optimization problem. The final matrix parameterizes a Mahalanobis metric yielding the MVE metric (MVEM). The proposed metric was tested in a supervised learning task and showed promising and competitive results when compared with state of the art metrics in the literature.