Distance-based clustering using QUBO formulations

Matsumoto, Nasa; Hamakawa, Yohei; Tatsumura, Kosuke; Kudo, Kazue

doi:10.1038/s41598-022-06559-z

Cited by 17 publications

(18 citation statements)

References 36 publications

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“…The stochastic algorithm uses the first-optimization process that improves the network learning process. During the training, the network parameter θ should be updated as defined in (12):…”

Section: ∨ ( )mentioning

confidence: 99%

“…; ; (12) In ( 12), the gradient is denoted as ∇ θ , the learning rate is η, and k is having as 1 < k < n. The training samples are selected from the entire dataset to reduce the computation complexity, such as computation cost. The training samples are examined to get unbiased data using the stochastic process, and momentum learning is applied to improve the data analysis process.…”

Section: J X Y I I K Ii Kmentioning

confidence: 99%

“…Among the various techniques, clustering is an effective approach that analyses similar data to identify the unknown results. The clustering process [12,13] identifies the similarities between data and the similar data allocated to the same cluster.…”

Section: Introductionmentioning

confidence: 99%

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Privacy protection based distributed clustering with deep learning algorithm for distributed data mining

Mahmood¹,

Naser²,

Khalil

2022

EEJET

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Distributed Data Mining (DDM) is vital in various applications for processing large volumes of data. The datasets are saved in the local databases and operated by local communities, but it provides the solution locally and globally. However, the datasets are stored in a distributed manner which affects the scalability and reliability issues. In addition, locally stored data is influenced by security and privacy challenges. In addition, the third party may access the DDM, which causes authorization issues. Therefore, the DDM process fuses sensor data from different sources to improve knowledge discovery. During this process, the DDM faces several issues such as security concerns, privacy restrictions, technical barriers, and trust issues. To address these issues, distributed data mining (DDM) should be improved to handle homogeneous and heterogeneous data. This work uses the privacy protection-based distributed clustering (PPDC) algorithm to handle the privacy and security challenges while analyzing the distributed data. The clustering algorithm generates the semi-trusted third parties to form the cluster, which protects the data from unauthorized users. The semi-trusted party protect the locally analyzed solution by creating the random vector-based trusted process. Further, the process uses the optimized deep learning approach and clustering to improve the heterogeneous data analysis. Then the effectiveness of the introduced PPDC method is compared with existing methods, and the PPDC algorithm ensures the 0.202 error rate, 0.95 % of accuracy and manages the data security.

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Section: ∨ ( )mentioning

confidence: 99%

Section: J X Y I I K Ii Kmentioning

confidence: 99%

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Privacy protection based distributed clustering with deep learning algorithm for distributed data mining

Mahmood¹,

Naser²,

Khalil

2022

EEJET

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“…In the past decade, many optimization problems (including Karp's 21 NP-problems) have been successfully mapped onto the Ising Hamiltonian. [14][15][16][17][18][19][20] Here, mapping refers to the procedure of formulating a Hamiltonian, similar to (1), whose minimum encodes the optimal solution of the given problem; see Lucas. 14 This means that the minimum can only be achieved when an optimal spin configuration (ground state) is found, where the latter corresponds to the solution of the problem.…”

Section: Introductionmentioning

confidence: 99%

A network‐theoretical perspective on oscillator‐based Ising machines

Beattie

Ochs

2023

Circuit Theory & Apps

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Summary The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator‐based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator‐based Ising machine and address how optimization problems can be mapped onto such machines when the quadratic unconstrained binary optimization (QUBO) formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real‐time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the decision‐making question: When has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability. Our results are based on an eigenvalue analysis of the linearized system and demonstrate that all eigenvalues converge to the left complex half plane, once an optimization problem has been optimally solved. This implies that the system enters an attractor region and is hence forced to eventually converge to the optimal solution.

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“…To solve a combinatorial optimization problem, one must map the considered problem onto the Ising Hamiltonian. In the past decade, many optimization problems (including Karp's 21 NP-problems) have been successfully mapped onto the Ising Hamiltonian 14,15,16,17,18,19,20 . Here, mapping refers to the procedure of formulating a Hamiltonian, similar to (1), whose minimum encodes the optimal solution of the given problem, see 14 .…”

Section: Introductionmentioning

confidence: 99%

A Network-Theoretical Perspective on Oscillator-Based Ising Machines

Beattie

Ochs

2022

Preprint

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The standard van Neumann computer excels at many things. However, it can be very inefficient in solving optimization problems with a large solution space. For that reason, a novel analog approach, the oscillator-based Ising machine, has been proposed as a better alternative for dealing with such problems. In this work, we review the concept of oscillator-based Ising machines. In particular, we address how optimization problems can be mapped onto such machines when the QUBO formulation is given. Furthermore, we provide an ideal circuit that can be used in combination with the wave digital concept for real-time simulated annealing. The functionality of this circuit is explained on the basis of a Lyapunov stability analysis. The latter also provides an answer for the question: when has the Ising machine solved a mapped problem? At the end, we provide emulation results demonstrating the correlation between functionality and stability of the discussed machine. These results show that mapping a problem onto an Ising machine effectively maps the solution of the problem onto an equilibrium of the phase space.

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Distance-based clustering using QUBO formulations

Cited by 17 publications

References 36 publications

Privacy protection based distributed clustering with deep learning algorithm for distributed data mining

Privacy protection based distributed clustering with deep learning algorithm for distributed data mining

A network‐theoretical perspective on oscillator‐based Ising machines

A Network-Theoretical Perspective on Oscillator-Based Ising Machines

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