Landmarking Manifolds with Gaussian Processes

Dawen Liang, John Paisley
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:466-474, 2015.

Abstract

We present an algorithm for finding landmarks along a manifold. These landmarks provide a small set of locations spaced out along the manifold such that they capture the low-dimensional non-linear structure of the data embedded in the high-dimensional space. The approach does not select points directly from the dataset, but instead we optimize each landmark by moving along the continuous manifold space (as approximated by the data) according to the gradient of an objective function. We borrow ideas from active learning with Gaussian processes to define the objective, which has the property that a new landmark is "repelled" by those currently selected, allowing for exploration of the manifold. We derive a stochastic algorithm for learning with large datasets and show results on several datasets, including the Million Song Dataset and articles from the New York Times.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-liang15, title = {Landmarking Manifolds with Gaussian Processes}, author = {Liang, Dawen and Paisley, John}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {466--474}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/liang15.pdf}, url = {https://proceedings.mlr.press/v37/liang15.html}, abstract = {We present an algorithm for finding landmarks along a manifold. These landmarks provide a small set of locations spaced out along the manifold such that they capture the low-dimensional non-linear structure of the data embedded in the high-dimensional space. The approach does not select points directly from the dataset, but instead we optimize each landmark by moving along the continuous manifold space (as approximated by the data) according to the gradient of an objective function. We borrow ideas from active learning with Gaussian processes to define the objective, which has the property that a new landmark is "repelled" by those currently selected, allowing for exploration of the manifold. We derive a stochastic algorithm for learning with large datasets and show results on several datasets, including the Million Song Dataset and articles from the New York Times.} }
Endnote
%0 Conference Paper %T Landmarking Manifolds with Gaussian Processes %A Dawen Liang %A John Paisley %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-liang15 %I PMLR %P 466--474 %U https://proceedings.mlr.press/v37/liang15.html %V 37 %X We present an algorithm for finding landmarks along a manifold. These landmarks provide a small set of locations spaced out along the manifold such that they capture the low-dimensional non-linear structure of the data embedded in the high-dimensional space. The approach does not select points directly from the dataset, but instead we optimize each landmark by moving along the continuous manifold space (as approximated by the data) according to the gradient of an objective function. We borrow ideas from active learning with Gaussian processes to define the objective, which has the property that a new landmark is "repelled" by those currently selected, allowing for exploration of the manifold. We derive a stochastic algorithm for learning with large datasets and show results on several datasets, including the Million Song Dataset and articles from the New York Times.
RIS
TY - CPAPER TI - Landmarking Manifolds with Gaussian Processes AU - Dawen Liang AU - John Paisley BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-liang15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 466 EP - 474 L1 - http://proceedings.mlr.press/v37/liang15.pdf UR - https://proceedings.mlr.press/v37/liang15.html AB - We present an algorithm for finding landmarks along a manifold. These landmarks provide a small set of locations spaced out along the manifold such that they capture the low-dimensional non-linear structure of the data embedded in the high-dimensional space. The approach does not select points directly from the dataset, but instead we optimize each landmark by moving along the continuous manifold space (as approximated by the data) according to the gradient of an objective function. We borrow ideas from active learning with Gaussian processes to define the objective, which has the property that a new landmark is "repelled" by those currently selected, allowing for exploration of the manifold. We derive a stochastic algorithm for learning with large datasets and show results on several datasets, including the Million Song Dataset and articles from the New York Times. ER -
APA
Liang, D. & Paisley, J.. (2015). Landmarking Manifolds with Gaussian Processes. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:466-474 Available from https://proceedings.mlr.press/v37/liang15.html.

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