Learning a set of directions

Wouter M. Koolen, Jiazhong Nie, Manfred Warmuth
; Proceedings of the 26th Annual Conference on Learning Theory, PMLR 30:851-866, 2013.

Abstract

Assume our data consists of unit vectors (directions) and we are to find a small orthogonal set of the “the most important directions” summarizing the data. We develop online algorithms for this type of problem. The techniques used are similar to Principal Component Analysis which finds the most important small rank subspace of the data.The new problem is significantly more complex since the online algorithm maintains uncertainty over the most relevant subspace as well as directional information.

Cite this Paper


BibTeX
@InProceedings{pmlr-v30-Koolen13, title = {Learning a set of directions}, author = {Wouter M. Koolen and Jiazhong Nie and Manfred Warmuth}, booktitle = {Proceedings of the 26th Annual Conference on Learning Theory}, pages = {851--866}, year = {2013}, editor = {Shai Shalev-Shwartz and Ingo Steinwart}, volume = {30}, series = {Proceedings of Machine Learning Research}, address = {Princeton, NJ, USA}, month = {12--14 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v30/Koolen13.pdf}, url = {http://proceedings.mlr.press/v30/Koolen13.html}, abstract = {Assume our data consists of unit vectors (directions) and we are to find a small orthogonal set of the “the most important directions” summarizing the data. We develop online algorithms for this type of problem. The techniques used are similar to Principal Component Analysis which finds the most important small rank subspace of the data.The new problem is significantly more complex since the online algorithm maintains uncertainty over the most relevant subspace as well as directional information.} }
Endnote
%0 Conference Paper %T Learning a set of directions %A Wouter M. Koolen %A Jiazhong Nie %A Manfred Warmuth %B Proceedings of the 26th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2013 %E Shai Shalev-Shwartz %E Ingo Steinwart %F pmlr-v30-Koolen13 %I PMLR %J Proceedings of Machine Learning Research %P 851--866 %U http://proceedings.mlr.press %V 30 %W PMLR %X Assume our data consists of unit vectors (directions) and we are to find a small orthogonal set of the “the most important directions” summarizing the data. We develop online algorithms for this type of problem. The techniques used are similar to Principal Component Analysis which finds the most important small rank subspace of the data.The new problem is significantly more complex since the online algorithm maintains uncertainty over the most relevant subspace as well as directional information.
RIS
TY - CPAPER TI - Learning a set of directions AU - Wouter M. Koolen AU - Jiazhong Nie AU - Manfred Warmuth BT - Proceedings of the 26th Annual Conference on Learning Theory PY - 2013/06/13 DA - 2013/06/13 ED - Shai Shalev-Shwartz ED - Ingo Steinwart ID - pmlr-v30-Koolen13 PB - PMLR SP - 851 DP - PMLR EP - 866 L1 - http://proceedings.mlr.press/v30/Koolen13.pdf UR - http://proceedings.mlr.press/v30/Koolen13.html AB - Assume our data consists of unit vectors (directions) and we are to find a small orthogonal set of the “the most important directions” summarizing the data. We develop online algorithms for this type of problem. The techniques used are similar to Principal Component Analysis which finds the most important small rank subspace of the data.The new problem is significantly more complex since the online algorithm maintains uncertainty over the most relevant subspace as well as directional information. ER -
APA
Koolen, W.M., Nie, J. & Warmuth, M.. (2013). Learning a set of directions. Proceedings of the 26th Annual Conference on Learning Theory, in PMLR 30:851-866

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