Quantum Spectral Clustering of Mixed Graphs

Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for directed and mixed graphs utilizing various matrix representations. Despite its success in clustering tasks, classical spectral algorithms suf...

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Vydáno v:2021 58th ACM/IEEE Design Automation Conference (DAC) s. 463 - 468
Hlavní autoři: Volya, Daniel, Mishra, Prabhat
Médium: Konferenční příspěvek
Jazyk:angličtina
Vydáno: IEEE 05.12.2021
Témata:
Clustering algorithms
Computers
eigenvalue computation
eigenvector projection
Machine learning
Machine learning algorithms
Partitioning algorithms
Quantum computing
Runtime
spectral graph clustering
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Abstract Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for directed and mixed graphs utilizing various matrix representations. Despite its success in clustering tasks, classical spectral algorithms suffer from a cubic growth in runtime. In this paper, we propose a quantum spectral clustering algorithm for discovering clusters and properties of mixed graphs. Our experimental results based on numerical simulations demonstrate that our quantum spectral clustering outperforms classical spectral clustering techniques. Specifically, our approach leads to a linear growth in complexity, while state-of-the-art classical counterpart leads to cubic growth. In a case study, we apply our proposed algorithm to preform unsupervised machine learning using both real and simulated quantum computers. This work opens an avenue for efficient implementation of machine learning algorithms on directed as well as mixed graphs by making use of the inherent potential quantum speedup.
AbstractList Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for directed and mixed graphs utilizing various matrix representations. Despite its success in clustering tasks, classical spectral algorithms suffer from a cubic growth in runtime. In this paper, we propose a quantum spectral clustering algorithm for discovering clusters and properties of mixed graphs. Our experimental results based on numerical simulations demonstrate that our quantum spectral clustering outperforms classical spectral clustering techniques. Specifically, our approach leads to a linear growth in complexity, while state-of-the-art classical counterpart leads to cubic growth. In a case study, we apply our proposed algorithm to preform unsupervised machine learning using both real and simulated quantum computers. This work opens an avenue for efficient implementation of machine learning algorithms on directed as well as mixed graphs by making use of the inherent potential quantum speedup.
Author Mishra, Prabhat
Volya, Daniel
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Snippet Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for...
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StartPage 463
SubjectTerms Clustering algorithms
Computers
eigenvalue computation
eigenvector projection
Machine learning
Machine learning algorithms
Partitioning algorithms
Quantum computing
Runtime
spectral graph clustering
Title Quantum Spectral Clustering of Mixed Graphs
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