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 = {Risi Kondor and Nedelina Teneva and Vikas Garg}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {1620--1628}, year = {2014}, editor = {Eric P. Xing and Tony Jebara}, 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 = {http://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 %J Proceedings of Machine Learning Research %P 1620--1628 %U http://proceedings.mlr.press %V 32 %N 2 %W PMLR %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 PY - 2014/01/27 DA - 2014/01/27 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-kondor14 PB - PMLR SP - 1620 DP - PMLR EP - 1628 L1 - http://proceedings.mlr.press/v32/kondor14.pdf UR - http://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 PMLR 32(2):1620-1628

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