Nonlinear Spectral Clustering with C++ GraphBLAS
Additional information
Authors
Pasadakis D.,
Schenk O.,
Vlacic V. .,
Yzelman A. J.
Type
Article in conference proceedings
Year
2023
Language
English
Abstract
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear eigenvectors is associated with an increased computational cost. We present an implementation of a direct multiway spectral clustering algorithm in the p-norm, for p ∈ (1, 2], using a novel C++ GraphBLAS API. The key operations are expressed in linear algebraic terms and are executed over the resulting sparse matrices and dense vectors, parameterized in the algebra pertinent to the computation. We demonstrate the effectiveness and accuracy of our shared-memory algorithm on several artificial test cases. Our numerical examples
and comparative results against competitive methods indicate that the proposed implementation attains high quality clusters in terms of the balanced graph cut metric. The strong scaling capabilities of our algorithm are showcased on a range of datasets with up to 8 million nodes and 48 million edges.
Conference proceedings
IEEE HPEC 2023
Month
October
Publisher
IEEE
Meeting name
27th Annual IEEE High Performance Extreme Computing Conference
Meeting place
Virtual
Meeting date
25 - 29 September 2023
Keywords
Algebraic programming, C++ GraphBLAS, graph p-Laplacian, spectral clustering
