Accelerating Matrix Computations for Mining Large Dynamic Complex Networks

Many common techniques in graph mining and machine learning are based on linear
algebra routines that are expensive on large data sets. A prime example is the computation of
many eigenpairs or even the full eigendecomposition of a graph’s Laplacian matrix. Executing such
operations on graphs with millions or billions of edges results in high running times or may even
be impractical. Moreover, library implementations of linear algebraic kernels do not take graph
changes over time into account. Since dynamic graphs such as the web graph or social interaction
networks are abundant these days, this omission leads to a waste of computing resources.

Our proposal aims at significantly faster (yet inexact) algorithms for linear algebra routines for dynamic
graph mining applications. We want to develop algorithms that monitor the graph’s and the
algorithm’s state over time with appropriate data structures; this avoids costly restarts from scratch.
Moreover, we use approximation in order to trade running time with (a still sufficient) accuracy and
exploit common structural features of complex networks. To this end, we want to combine results
and techniques from numerical linear algebra (NLA), combinatorial scientific computing and theoretical
computer science. As a significant part of the project, we demonstrate the improvement by
means of three common graph mining tasks in dynamic scenarios: clustering, similarity and representation.
Finally, the integration of our new algorithms into the open-source network analysis tool
NetworKit will help community adoption and speeds up other NLA-based graph mining routines.

Principal Investigators
Meyerhenke, Henning Prof. Dr. (Details) (Modeling and Anlysis of Complex Systems)

DFG: Sachbeihilfe

Duration of Project
Start date: 01/2020
End date: 12/2022

Research Areas
Massively Parallel and Data-Intensive Systems

Research Areas
Big Data

Last updated on 2020-08-03 at 21:23