Modularity maximization using completely positive programming

2017 ◽  
Vol 471 ◽  
pp. 20-32 ◽  
Author(s):  
Sakineh Yazdanparast ◽  
Timothy C. Havens
Keyword(s):  
Completely Positive ◽  
Modularity Maximization ◽  
Completely Positive Programming

scholarly journals A New Conic Approach to Semisupervised Support Vector Machines

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Ye Tian ◽  
Jian Luo ◽  
Xin Yan
Keyword(s):  
Quadratic Forms ◽  
Optimal Solution ◽  
Positive Cone ◽  
Support Vector ◽  
Completely Positive ◽  
Adaptive Scheme ◽  
Completely Positive Cone ◽  
Vector Machines ◽  
Programming Techniques ◽  
Completely Positive Programming

We propose a completely positive programming reformulation of the 2-norm soft marginS3VMmodel. Then, we construct a sequence of computable cones of nonnegative quadratic forms over a union of second-order cones to approximate the underlying completely positive cone. Anϵ-optimal solution can be found in finite iterations using semidefinite programming techniques by our method. Moreover, in order to obtain a good lower bound efficiently, an adaptive scheme is adopted in our approximation algorithm. The numerical results show that the proposed algorithm can achieve more accurate classifications than other well-known conic relaxations of semisupervised support vector machine models in the literature.

scholarly journals A Sparse Completely Positive Relaxation of the Modularity Maximization for Community Detection

2018 ◽  
Vol 40 (5) ◽  
pp. A3091-A3120 ◽  
Author(s):  
Junyu Zhang ◽  
Haoyang Liu ◽  
Zaiwen Wen ◽  
Shuzhong Zhang
Keyword(s):  
Community Detection ◽  
Completely Positive ◽  
Modularity Maximization

scholarly journals Reduction of the molecular hamiltonian matrix using quantum community detection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Susan M. Mniszewski ◽  
Pavel A. Dub ◽  
Sergei Tretiak ◽  
Petr M. Anisimov ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Community Detection ◽  
Slater Determinant ◽  
Hamiltonian Matrix ◽  
Approximate Methods ◽  
Molecular Systems ◽  
Hartree Fock ◽  
Molecular Hamiltonian ◽  
Structure Problem ◽  
Modularity Maximization ◽  
Chemical Knowledge

AbstractQuantum chemistry is interested in calculating ground and excited states of molecular systems by solving the electronic Schrödinger equation. The exact numerical solution of this equation, frequently represented as an eigenvalue problem, remains unfeasible for most molecules and requires approximate methods. In this paper we introduce the use of Quantum Community Detection performed using the D-Wave quantum annealer to reduce the molecular Hamiltonian matrix in Slater determinant basis without chemical knowledge. Given a molecule represented by a matrix of Slater determinants, the connectivity between Slater determinants (as off-diagonal elements) is viewed as a graph adjacency matrix for determining multiple communities based on modularity maximization. A gauge metric based on perturbation theory is used to determine the lowest energy cluster. This cluster or sub-matrix of Slater determinants is used to calculate approximate ground state and excited state energies within chemical accuracy. The details of this method are described along with demonstrating its performance across multiple molecules of interest and bond dissociation cases. These examples provide proof-of-principle results for approximate solution of the electronic structure problem using quantum computing. This approach is general and shows potential to reduce the computational complexity of post-Hartree–Fock methods as future advances in quantum hardware become available.

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