Co-manifold learning with missing data

Gal Mishne, Eric Chi, Ronald Coifman
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4605-4614, 2019.

Abstract

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting. Our unsupervised approach consists of three components. We first solve a family of optimization problems to estimate a complete matrix at multiple scales of smoothness. We then use this collection of smooth matrix estimates to compute pairwise distances on the rows and columns based on a new multi-scale metric that implicitly introduces a coupling between the rows and the columns. Finally, we construct row and column representations from these multi-scale metrics. We demonstrate that our approach outperforms competing methods in both data visualization and clustering.

Cite this Paper


BibTeX
@InProceedings{pmlr-v97-mishne19a, title = {Co-manifold learning with missing data}, author = {Mishne, Gal and Chi, Eric and Coifman, Ronald}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4605--4614}, year = {2019}, editor = {Kamalika Chaudhuri and Ruslan Salakhutdinov}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/mishne19a/mishne19a.pdf}, url = { http://proceedings.mlr.press/v97/mishne19a.html }, abstract = {Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting. Our unsupervised approach consists of three components. We first solve a family of optimization problems to estimate a complete matrix at multiple scales of smoothness. We then use this collection of smooth matrix estimates to compute pairwise distances on the rows and columns based on a new multi-scale metric that implicitly introduces a coupling between the rows and the columns. Finally, we construct row and column representations from these multi-scale metrics. We demonstrate that our approach outperforms competing methods in both data visualization and clustering.} }
Endnote
%0 Conference Paper %T Co-manifold learning with missing data %A Gal Mishne %A Eric Chi %A Ronald Coifman %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-mishne19a %I PMLR %P 4605--4614 %U http://proceedings.mlr.press/v97/mishne19a.html %V 97 %X Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting. Our unsupervised approach consists of three components. We first solve a family of optimization problems to estimate a complete matrix at multiple scales of smoothness. We then use this collection of smooth matrix estimates to compute pairwise distances on the rows and columns based on a new multi-scale metric that implicitly introduces a coupling between the rows and the columns. Finally, we construct row and column representations from these multi-scale metrics. We demonstrate that our approach outperforms competing methods in both data visualization and clustering.
APA
Mishne, G., Chi, E. & Coifman, R.. (2019). Co-manifold learning with missing data. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4605-4614 Available from http://proceedings.mlr.press/v97/mishne19a.html .

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