Unsupervised logic mining with a binary clonal selection algorithm in multi-unit discrete Hopfield neural networks via weighted systematic 2 satisfiability

Nurul Atiqah Romli; Nur Fariha Syaqina Zulkepli; Mohd Shareduwan Mohd Kasihmuddin; Nur Ezlin Zamri; Nur 'Afifah Rusdi; Gaeithry Manoharam; Mohd. Asyraf Mansor; Siti Zulaikha Mohd Jamaludin; Amierah Abdul Malik; Nurul Atiqah Romli; Nur Fariha Syaqina Zulkepli; Mohd Shareduwan Mohd Kasihmuddin; Nur Ezlin Zamri; Nur 'Afifah Rusdi; Gaeithry Manoharam; Mohd. Asyraf Mansor; Siti Zulaikha Mohd Jamaludin; Amierah Abdul Malik

doi:10.3934/math.20241087

AIMS Mathematics

2024, Volume 9, Issue 8: 22321-22365. doi: 10.3934/math.20241087

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Research article

Unsupervised logic mining with a binary clonal selection algorithm in multi-unit discrete Hopfield neural networks via weighted systematic 2 satisfiability

1.
School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia
2.
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia
3.
Institute of Engineering Mathematics, Universiti Malaysia Perlis, Kampus Pauh Putra, 02600 Arau, Perlis, Malaysia
4.
School of Distance Education, Universiti Sains Malaysia, 11800 USM, Penang, Malaysia

Received: 04 March 2024 Revised: 24 April 2024 Accepted: 16 May 2024 Published: 17 July 2024
MSC : 68N17, 68R07, 68T27

Evaluating behavioral patterns through logic mining within a given dataset has become a primary focus in current research. Unfortunately, there are several weaknesses in the research regarding the logic mining models, including an uncertainty of the attribute selected in the model, random distribution of negative literals in a logical structure, non-optimal computation of the best logic, and the generation of overfitting solutions. Motivated by these limitations, a novel logic mining model incorporating the mechanism to control the negative literal in the systematic Satisfiability, namely Weighted Systematic 2 Satisfiability in Discrete Hopfield Neural Network, is proposed as a logical structure to represent the behavior of the dataset. For the proposed logic mining models, we used ratio of r to control the distribution of the negative literals in the logical structures to prevent overfitting solutions and optimize synaptic weight values. A new computational approach of the best logic by considering both true and false classification values of the learning system was applied in this work to preserve the significant behavior of the dataset. Additionally, unsupervised learning techniques such as Topological Data Analysis were proposed to ensure the reliability of the selected attributes in the model. The comparative experiments of the logic mining models by utilizing 20 repository real-life datasets were conducted from repositories to assess their efficiency. Following the results, the proposed logic mining model dominated in all the metrics for the average rank. The average ranks for each metric were Accuracy (7.95), Sensitivity (7.55), Specificity (7.93), Negative Predictive Value (7.50), and Mathews Correlation Coefficient (7.85). Numerical results and in-depth analysis demonstrated that the proposed logic mining model consistently produced optimal induced logic that best represented the real-life dataset for all the performance metrics used in this study.
- discrete Hopfield neural network,
- improved logic mining,
- binary clonal selection algorithm,
- weighted systematic 2 satisfiability,
- topological data analysis
Citation: Nurul Atiqah Romli, Nur Fariha Syaqina Zulkepli, Mohd Shareduwan Mohd Kasihmuddin, Nur Ezlin Zamri, Nur 'Afifah Rusdi, Gaeithry Manoharam, Mohd. Asyraf Mansor, Siti Zulaikha Mohd Jamaludin, Amierah Abdul Malik. Unsupervised logic mining with a binary clonal selection algorithm in multi-unit discrete Hopfield neural networks via weighted systematic 2 satisfiability[J]. AIMS Mathematics, 2024, 9(8): 22321-22365. doi: 10.3934/math.20241087

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Abstract

Evaluating behavioral patterns through logic mining within a given dataset has become a primary focus in current research. Unfortunately, there are several weaknesses in the research regarding the logic mining models, including an uncertainty of the attribute selected in the model, random distribution of negative literals in a logical structure, non-optimal computation of the best logic, and the generation of overfitting solutions. Motivated by these limitations, a novel logic mining model incorporating the mechanism to control the negative literal in the systematic Satisfiability, namely Weighted Systematic 2 Satisfiability in Discrete Hopfield Neural Network, is proposed as a logical structure to represent the behavior of the dataset. For the proposed logic mining models, we used ratio of r to control the distribution of the negative literals in the logical structures to prevent overfitting solutions and optimize synaptic weight values. A new computational approach of the best logic by considering both true and false classification values of the learning system was applied in this work to preserve the significant behavior of the dataset. Additionally, unsupervised learning techniques such as Topological Data Analysis were proposed to ensure the reliability of the selected attributes in the model. The comparative experiments of the logic mining models by utilizing 20 repository real-life datasets were conducted from repositories to assess their efficiency. Following the results, the proposed logic mining model dominated in all the metrics for the average rank. The average ranks for each metric were Accuracy (7.95), Sensitivity (7.55), Specificity (7.93), Negative Predictive Value (7.50), and Mathews Correlation Coefficient (7.85). Numerical results and in-depth analysis demonstrated that the proposed logic mining model consistently produced optimal induced logic that best represented the real-life dataset for all the performance metrics used in this study.

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