Sketching for Geometric Problems (Invited Talk)

Author David P. Woodruff



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David P. Woodruff

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David P. Woodruff. Sketching for Geometric Problems (Invited Talk). In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ESA.2017.1

Abstract

In this invited talk at the European Symposium on Algorithms (ESA), 2017, I will discuss a tool called sketching, which is a form of data dimensionality reduction, and its applications to several problems in high dimensional geometry. In particular, I will show how to obtain the fastest possible algorithms for fundamental problems such as projection onto a flat, and also study generalizations of projection onto more complicated objects such as the union of flats or subspaces. Some of these problems are just least squares regression problems, with many applications in machine learning, numerical linear algebra, and optimization. I will also discuss low rank approximation, with applications to clustering. Finally I will mention a number of other applications of sketching in machine learning, numerical linear algebra, and optimization.
Keywords
  • dimensionality reduction
  • low rank approximation
  • projection
  • regression
  • sketching

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References

  1. Haim Avron, Kenneth L. Clarkson, and David P. Woodruff. Sharper bounds for regression and low-rank approximation with regularization. In RANDOM, 2017. Google Scholar
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  3. Maria-Florina Balcan, Yingyu Liang, Le Song, David Woodruff, and Bo Xie. Communication efficient distributed kernel principal component analysis. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pages 725-734. ACM, 2016. URL: https://arxiv.org/pdf/1503.06858.
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  11. Michael B. Cohen, Jelani Nelson, and David P. Woodruff. Optimal approximate matrix product in terms of stable rank. In Proceedings of the 43rd International Colloquium on Automata, Languages and Programming (ICALP), Rome, Italy, July 12-15, 2016, volume 55 of Leibniz International Proceedings in Informatics (LIPIcs), pages 11:1-11:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015. URL: https://arxiv.org/pdf/1507.02268, URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2016.11.
  12. Dan Feldman, Melanie Schmidt, and Christian Sohler. Turning big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering. In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2013, New Orleans, Louisiana, USA, January 6-8, 2013, pages 1434-1453, 2013. Google Scholar
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  21. David P. Woodruff. Sketching as a tool for numerical linear algebra. Foundations and Trends in Theoretical Computer Science, 10(1-2):1-157, 2014. Google Scholar
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