Functional Subspace Clustering with Application to Time Series

Mohammad Taha Bahadori, David Kale, Yingying Fan, Yan Liu
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:228-237, 2015.

Abstract

Functional data, where samples are random functions, are increasingly common and important in a variety of applications, such as health care and traffic analysis. They are naturally high dimensional and lie along complex manifolds. These properties warrant use of the subspace assumption, but most state-of-the-art subspace learning algorithms are limited to linear or other simple settings. To address these challenges, we propose a new framework called Functional Subspace Clustering (FSC). FSC assumes that functional samples lie in deformed linear subspaces and formulates the subspace learning problem as a sparse regression over operators. The resulting problem can be efficiently solved via greedy variable selection, given access to a fast deformation oracle. We provide theoretical guarantees for FSC and show how it can be applied to time series with warped alignments. Experimental results on both synthetic data and real clinical time series show that FSC outperforms both standard time series clustering and state-of-the-art subspace clustering.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-bahadori15, title = {Functional Subspace Clustering with Application to Time Series}, author = {Bahadori, Mohammad Taha and Kale, David and Fan, Yingying and Liu, Yan}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {228--237}, 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/bahadori15.pdf}, url = {https://proceedings.mlr.press/v37/bahadori15.html}, abstract = {Functional data, where samples are random functions, are increasingly common and important in a variety of applications, such as health care and traffic analysis. They are naturally high dimensional and lie along complex manifolds. These properties warrant use of the subspace assumption, but most state-of-the-art subspace learning algorithms are limited to linear or other simple settings. To address these challenges, we propose a new framework called Functional Subspace Clustering (FSC). FSC assumes that functional samples lie in deformed linear subspaces and formulates the subspace learning problem as a sparse regression over operators. The resulting problem can be efficiently solved via greedy variable selection, given access to a fast deformation oracle. We provide theoretical guarantees for FSC and show how it can be applied to time series with warped alignments. Experimental results on both synthetic data and real clinical time series show that FSC outperforms both standard time series clustering and state-of-the-art subspace clustering.} }
Endnote
%0 Conference Paper %T Functional Subspace Clustering with Application to Time Series %A Mohammad Taha Bahadori %A David Kale %A Yingying Fan %A Yan Liu %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-bahadori15 %I PMLR %P 228--237 %U https://proceedings.mlr.press/v37/bahadori15.html %V 37 %X Functional data, where samples are random functions, are increasingly common and important in a variety of applications, such as health care and traffic analysis. They are naturally high dimensional and lie along complex manifolds. These properties warrant use of the subspace assumption, but most state-of-the-art subspace learning algorithms are limited to linear or other simple settings. To address these challenges, we propose a new framework called Functional Subspace Clustering (FSC). FSC assumes that functional samples lie in deformed linear subspaces and formulates the subspace learning problem as a sparse regression over operators. The resulting problem can be efficiently solved via greedy variable selection, given access to a fast deformation oracle. We provide theoretical guarantees for FSC and show how it can be applied to time series with warped alignments. Experimental results on both synthetic data and real clinical time series show that FSC outperforms both standard time series clustering and state-of-the-art subspace clustering.
RIS
TY - CPAPER TI - Functional Subspace Clustering with Application to Time Series AU - Mohammad Taha Bahadori AU - David Kale AU - Yingying Fan AU - Yan Liu BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-bahadori15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 228 EP - 237 L1 - http://proceedings.mlr.press/v37/bahadori15.pdf UR - https://proceedings.mlr.press/v37/bahadori15.html AB - Functional data, where samples are random functions, are increasingly common and important in a variety of applications, such as health care and traffic analysis. They are naturally high dimensional and lie along complex manifolds. These properties warrant use of the subspace assumption, but most state-of-the-art subspace learning algorithms are limited to linear or other simple settings. To address these challenges, we propose a new framework called Functional Subspace Clustering (FSC). FSC assumes that functional samples lie in deformed linear subspaces and formulates the subspace learning problem as a sparse regression over operators. The resulting problem can be efficiently solved via greedy variable selection, given access to a fast deformation oracle. We provide theoretical guarantees for FSC and show how it can be applied to time series with warped alignments. Experimental results on both synthetic data and real clinical time series show that FSC outperforms both standard time series clustering and state-of-the-art subspace clustering. ER -
APA
Bahadori, M.T., Kale, D., Fan, Y. & Liu, Y.. (2015). Functional Subspace Clustering with Application to Time Series. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:228-237 Available from https://proceedings.mlr.press/v37/bahadori15.html.

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