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2012


A Geometric Take on Metric Learning
A Geometric Take on Metric Learning

Hauberg, S., Freifeld, O., Black, M. J.

In Advances in Neural Information Processing Systems (NIPS) 25, pages: 2033-2041, (Editors: P. Bartlett and F.C.N. Pereira and C.J.C. Burges and L. Bottou and K.Q. Weinberger), MIT Press, 2012 (inproceedings)

Abstract
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.

PDF Youtube Suppl. material Poster Project Page [BibTex]

2012

PDF Youtube Suppl. material Poster Project Page [BibTex]

2005


A quantitative evaluation of video-based {3D} person tracking
A quantitative evaluation of video-based 3D person tracking

Balan, A. O., Sigal, L., Black, M. J.

In The Second Joint IEEE International Workshop on Visual Surveillance and Performance Evaluation of Tracking and Surveillance, VS-PETS, pages: 349-356, October 2005 (inproceedings)

pdf [BibTex]

2005

pdf [BibTex]


Inferring attentional state and kinematics from motor cortical firing rates
Inferring attentional state and kinematics from motor cortical firing rates

Wood, F., Prabhat, , Donoghue, J. P., Black, M. J.

In Proc. IEEE Engineering in Medicine and Biology Society, pages: 1544-1547, September 2005 (inproceedings)

pdf [BibTex]

pdf [BibTex]


Motor cortical decoding using an autoregressive moving average model
Motor cortical decoding using an autoregressive moving average model

Fisher, J., Black, M. J.

In Proc. IEEE Engineering in Medicine and Biology Society, pages: 1469-1472, September 2005 (inproceedings)

pdf [BibTex]

pdf [BibTex]


Fields of Experts: A framework for learning image priors
Fields of Experts: A framework for learning image priors

Roth, S., Black, M. J.

In IEEE Conf. on Computer Vision and Pattern Recognition, 2, pages: 860-867, June 2005 (inproceedings)

pdf [BibTex]

pdf [BibTex]


On the spatial statistics of optical flow
On the spatial statistics of optical flow

(Marr Prize, Honorable Mention)

Roth, S., Black, M. J.

In International Conf. on Computer Vision, International Conf. on Computer Vision, pages: 42-49, 2005 (inproceedings)

pdf [BibTex]

pdf [BibTex]


Modeling neural population spiking activity with {Gibbs} distributions
Modeling neural population spiking activity with Gibbs distributions

Wood, F., Roth, S., Black, M. J.

In Advances in Neural Information Processing Systems 18, pages: 1537-1544, 2005 (inproceedings)

pdf [BibTex]

pdf [BibTex]


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Energy-based models of motor cortical population activity

Wood, F., Black, M.

Program No. 689.20. 2005 Abstract Viewer/Itinerary Planner, Society for Neuroscience, Washington, DC, 2005 (conference)

abstract [BibTex]

abstract [BibTex]