Johns Hopkins Algorithms and Complexity
https://www.cs.jhu.edu/~mdinitz/theory
America/New_York
America/New_York
America/New_York
20221106T020000
-0400
-0500
EST
20230312T020000
-0500
-0400
EDT
ai1ec-317@www.cs.jhu.edu/~mdinitz/theory
20230201T082414Z
Speaker: Aditya Krishnan
Affiliation: Johns Hopkins University
Title: Schatten Norms in Matrix Streams: The Role of Sparsity
Abstract:
Spectral functions of large matrices contain important structural information about the underlying data, and are thus becoming increasingly important to efficiently compute. Many times, large matrices representing real-world data are sparse or doubly sparse (i.e., sparse in both rows and columns), and are accessed as a stream of updates, typically organized in row-order. In this setting, where space (memory) is the limiting resource, all known algorithms require space that is polynomial in the dimension of the matrix, even for sparse matrices. We address this challenge by providing the first algorithms whose space requirement is independent of the matrix dimension, assuming the matrix is doubly-sparse and presented in row-order.
In addition, we prove that multiple passes are unavoidable in this setting and show extensions of our primary technique, including a trade-off between space requirements and number of passes. Our algorithms approximate the Schatten p-norms, which we use in turn to approximate other spectral functions, such as logarithm of the determinant, trace of matrix inverse, and Estrada index.
Joint work with Vladimir Braverman, Robert Krauthgamer and Roi Sinoff.
20200311T120000
20200311T130000
0
[Theory Seminar] Aditya Krishnan
free