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A Geometric take on Metric Learning
Søren Hauberg · Oren Freifeld · Michael J Black

Tue Dec 04 07:00 PM -- 12:00 AM (PST) @ Harrah’s Special Events Center 2nd Floor

Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.

Author Information

Søren Hauberg (Max Planck Institute)
Oren Freifeld (Brown)
Michael J Black (Max Planck Institute for Intelligent Systems)

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