Fluid Dynamics Models for Low Rank Discriminant Analysis

Yung–Kyun Noh, Byoung–Tak Zhang, Daniel Lee
Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:565-572, 2010.

Abstract

We consider the problem of reducing the dimensionality of labeled data for classification. Unfortunately, the optimal approach of finding the low-dimensional projection with minimal Bayes classification error is intractable, so most standard algorithms optimize a tractable heuristic function in the projected subspace. Here, we investigate a physics-based model where we consider the labeled data as interacting fluid distributions. We derive the forces arising in the fluids from information theoretic potential functions, and consider appropriate low rank constraints on the resulting acceleration and velocity flow fields. We show how to apply the Gauss principle of least constraint in fluids to obtain tractable solutions for low rank projections. Our fluid dynamic approach is demonstrated to better approximate the Bayes optimal solution on Gaussian systems, including infinite dimensional Gaussian processes.

Cite this Paper

BibTeX
@InProceedings{pmlr-v9-noh10a, title = {Fluid Dynamics Models for Low Rank Discriminant Analysis}, author = {Noh, Yung–Kyun and Zhang, Byoung–Tak and Lee, Daniel}, booktitle = {Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics}, pages = {565--572}, year = {2010}, editor = {Teh, Yee Whye and Titterington, Mike}, volume = {9}, series = {Proceedings of Machine Learning Research}, address = {Chia Laguna Resort, Sardinia, Italy}, month = {13--15 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v9/noh10a/noh10a.pdf}, url = {https://proceedings.mlr.press/v9/noh10a.html}, abstract = {We consider the problem of reducing the dimensionality of labeled data for classification. Unfortunately, the optimal approach of finding the low-dimensional projection with minimal Bayes classification error is intractable, so most standard algorithms optimize a tractable heuristic function in the projected subspace. Here, we investigate a physics-based model where we consider the labeled data as interacting fluid distributions. We derive the forces arising in the fluids from information theoretic potential functions, and consider appropriate low rank constraints on the resulting acceleration and velocity flow fields. We show how to apply the Gauss principle of least constraint in fluids to obtain tractable solutions for low rank projections. Our fluid dynamic approach is demonstrated to better approximate the Bayes optimal solution on Gaussian systems, including infinite dimensional Gaussian processes.} }
Endnote
%0 Conference Paper %T Fluid Dynamics Models for Low Rank Discriminant Analysis %A Yung–Kyun Noh %A Byoung–Tak Zhang %A Daniel Lee %B Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2010 %E Yee Whye Teh %E Mike Titterington %F pmlr-v9-noh10a %I PMLR %P 565--572 %U https://proceedings.mlr.press/v9/noh10a.html %V 9 %X We consider the problem of reducing the dimensionality of labeled data for classification. Unfortunately, the optimal approach of finding the low-dimensional projection with minimal Bayes classification error is intractable, so most standard algorithms optimize a tractable heuristic function in the projected subspace. Here, we investigate a physics-based model where we consider the labeled data as interacting fluid distributions. We derive the forces arising in the fluids from information theoretic potential functions, and consider appropriate low rank constraints on the resulting acceleration and velocity flow fields. We show how to apply the Gauss principle of least constraint in fluids to obtain tractable solutions for low rank projections. Our fluid dynamic approach is demonstrated to better approximate the Bayes optimal solution on Gaussian systems, including infinite dimensional Gaussian processes.
RIS
TY - CPAPER TI - Fluid Dynamics Models for Low Rank Discriminant Analysis AU - Yung–Kyun Noh AU - Byoung–Tak Zhang AU - Daniel Lee BT - Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics DA - 2010/03/31 ED - Yee Whye Teh ED - Mike Titterington ID - pmlr-v9-noh10a PB - PMLR DP - Proceedings of Machine Learning Research VL - 9 SP - 565 EP - 572 L1 - http://proceedings.mlr.press/v9/noh10a/noh10a.pdf UR - https://proceedings.mlr.press/v9/noh10a.html AB - We consider the problem of reducing the dimensionality of labeled data for classification. Unfortunately, the optimal approach of finding the low-dimensional projection with minimal Bayes classification error is intractable, so most standard algorithms optimize a tractable heuristic function in the projected subspace. Here, we investigate a physics-based model where we consider the labeled data as interacting fluid distributions. We derive the forces arising in the fluids from information theoretic potential functions, and consider appropriate low rank constraints on the resulting acceleration and velocity flow fields. We show how to apply the Gauss principle of least constraint in fluids to obtain tractable solutions for low rank projections. Our fluid dynamic approach is demonstrated to better approximate the Bayes optimal solution on Gaussian systems, including infinite dimensional Gaussian processes. ER -
APA
Noh, Y., Zhang, B. & Lee, D.. (2010). Fluid Dynamics Models for Low Rank Discriminant Analysis. Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 9:565-572 Available from https://proceedings.mlr.press/v9/noh10a.html.

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