Multiresolution Matrix Factorization

Risi Kondor, Nedelina Teneva, Vikas Garg
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):1620-1628, 2014.

Abstract

The types of large matrices that appear in modern Machine Learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecompositions. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nystrom approximations) and as a prior for matrix completion.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-kondor14, title = {Multiresolution Matrix Factorization}, author = {Kondor, Risi and Teneva, Nedelina and Garg, Vikas}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1620--1628}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/kondor14.pdf}, url = {https://proceedings.mlr.press/v32/kondor14.html}, abstract = {The types of large matrices that appear in modern Machine Learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecompositions. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nystrom approximations) and as a prior for matrix completion.} }
Endnote
%0 Conference Paper %T Multiresolution Matrix Factorization %A Risi Kondor %A Nedelina Teneva %A Vikas Garg %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-kondor14 %I PMLR %P 1620--1628 %U https://proceedings.mlr.press/v32/kondor14.html %V 32 %N 2 %X The types of large matrices that appear in modern Machine Learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecompositions. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nystrom approximations) and as a prior for matrix completion.
RIS
TY - CPAPER TI - Multiresolution Matrix Factorization AU - Risi Kondor AU - Nedelina Teneva AU - Vikas Garg BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/06/18 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-kondor14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 2 SP - 1620 EP - 1628 L1 - http://proceedings.mlr.press/v32/kondor14.pdf UR - https://proceedings.mlr.press/v32/kondor14.html AB - The types of large matrices that appear in modern Machine Learning problems often have complex hierarchical structures that go beyond what can be found by traditional linear algebra tools, such as eigendecompositions. Inspired by ideas from multiresolution analysis, this paper introduces a new notion of matrix factorization that can capture structure in matrices at multiple different scales. The resulting Multiresolution Matrix Factorizations (MMFs) not only provide a wavelet basis for sparse approximation, but can also be used for matrix compression (similar to Nystrom approximations) and as a prior for matrix completion. ER -
APA
Kondor, R., Teneva, N. & Garg, V.. (2014). Multiresolution Matrix Factorization. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(2):1620-1628 Available from https://proceedings.mlr.press/v32/kondor14.html.

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