Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Tuesday, May 02, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Kenneth Clarkson (IBM Research Almaden)

Low-rank PSD Approximation in Input-Sparsity Time

A number of matrices that arise in machine learning and data analysis are symmetric positive semidefinite (PSD), including covariance matrices, kernel matrices, Laplacian matrices, random dot product graph models, and others. A common task related to such matrices is to approximate them with a low-rank matrix, for efficiency or statistical inference; spectral clustering, kernel PCA, manifold learning, and Gaussian process regression can all involve this task. Given a square n by n matrix A, target rank k, and error parameter epsilon, we show how to find a PSD matrix B of rank k, such that the Frobenius norm of A-B is within (1+epsilon) of best possible; our algorithm needs O(nnz(A) + n*poly(k/epsilon)) time to do this, where nnz(A) is the number of nonzero entries of A. We also show how to find such a rank-k matrix PSD B of the form CUC^T, where the O(k/eps) columns of C are a subset of those of A, with a similar runtime. Joint work with David Woodruff.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login