scholarly journals Novel Hopfield Neural Network Model with Election Algorithm for Random 3 Satisfiability

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1292
Author(s):  
Muna Mohammed Bazuhair ◽  
Siti Zulaikha Mohd Jamaludin ◽  
Nur Ezlin Zamri ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Mohd. Asyraf Mansor ◽  
...  
Keyword(s):  
Neural Network ◽  
Performance Metrics ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Research Field ◽  
Learning Phase ◽  
Logical Rule ◽  
Election Algorithm ◽  
Logical Rules ◽  
Retrieval Phase

One of the influential models in the artificial neural network (ANN) research field for addressing the issue of knowledge in the non-systematic logical rule is Random k Satisfiability. In this context, knowledge structure representation is also the potential application of Random k Satisfiability. Despite many attempts to represent logical rules in a non-systematic structure, previous studies have failed to consider higher-order logical rules. As the amount of information in the logical rule increases, the proposed network is unable to proceed to the retrieval phase, where the behavior of the Random Satisfiability can be observed. This study approaches these issues by proposing higher-order Random k Satisfiability for k ≤ 3 in the Hopfield Neural Network (HNN). In this regard, introducing the 3 Satisfiability logical rule to the existing network increases the synaptic weight dimensions in Lyapunov’s energy function and local field. In this study, we proposed an Election Algorithm (EA) to optimize the learning phase of HNN to compensate for the high computational complexity during the learning phase. This research extensively evaluates the proposed model using various performance metrics. The main findings of this research indicated the compatibility and performance of Random 3 Satisfiability logical representation during the learning and retrieval phase via EA with HNN in terms of error evaluations, energy analysis, similarity indices, and variability measures. The results also emphasized that the proposed Random 3 Satisfiability representation incorporates with EA in HNN is capable to optimize the learning and retrieval phase as compared to the conventional model, which deployed Exhaustive Search (ES).

scholarly journals Optimal representation to High Order Random Boolean kSatisability via Election Algorithm as Heuristic Search Approach in Hopeld Neural Networks

2021 ◽  
pp. 201-208
Author(s):  
Hamza Abubakar ◽  
Abdu Sagir Masanawa ◽  
Surajo Yusuf ◽  
G. I. Boaku
Keyword(s):  
Neural Network ◽  
Optimization Problems ◽  
Real Life ◽  
Model Performance ◽  
Statistical Error ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Learning Phase ◽  
Life Problems ◽  
Election Algorithm

This study proposed a hybridization of higher-order Random Boolean kSatisfiability (RANkSAT) with the Hopfield neural network (HNN) as a neuro-dynamical model designed to reflect knowledge efficiently. The learning process of the Hopfield neural network (HNN) has undergone significant changes and improvements according to various types of optimization problems. However, the HNN model is associated with some limitations which include storage capacity and being easily trapped to the local minimum solution. The Election algorithm (EA) is proposed to improve the learning phase of HNN for optimal Random Boolean kSatisfiability (RANkSAT) representation in higher order. The main source of inspiration for the Election Algorithm (EA) is its ability to extend the power and rule of political parties beyond their borders when seeking endorsement. The main purpose is to utilize the optimization capacity of EA to accelerate the learning phase of HNN for optimal random k Satisfiability representation. The global minima ratio (mR) and statistical error accumulations (SEA) during the training process were used to evaluate the proposed model performance. The result of this study revealed that our proposed EA-HNN-RANkSAT outperformed ABC-HNN-RANkSAT and ES-HNN-RANkSAT models in terms of mR and SEA.This study will further be extended to accommodate a novel field of Reverse analysis (RA) which involves data mining techniques to analyse real-life problems. 

scholarly journals Random Satisfiability: A Higher-Order Logical Approach in Discrete Hopfield Neural Network

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Syed Anayet Karim ◽  
Nur Ezlin Zamri ◽  
Alyaa Alway ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Ahmad Izani Md Ismail ◽  
...  
Keyword(s):  
Neural Network ◽  
Hopfield Neural Network ◽  
Higher Order ◽  
Logical Approach

scholarly journals Logic Learning in Adaline Neural Network

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Nadia Athirah Norani ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Mohd. Asyraf Mansor ◽  
Noor Saifurina Nana Khurizan
Keyword(s):  
Neural Network ◽  
Learning Mechanism ◽  
Logical Rule ◽  
Actual Signal ◽  
Healthcare Marketing ◽  
The Mean ◽  
Processing Effort ◽  
Logical Representation ◽  
Logical Rules ◽  
Adaline Neural Network

In this paper, Adaline Neural Network (ADNN) has been explored to simulate the actual signal processing between input and output. One of the drawback of the conventional ADNN is the use of the non-systematic rule that defines the learning of the network. This research incorporates logic programming that consists of various prominent logical representation. These logical rules will be a symbolic rule that defines the learning mechanism of ADNN. All the mentioned logical rule are tested with different learning rate that leads to minimization of the Mean Square Error (MSE). This paper uncovered the best logical rule that could be governed in ADNN with the lowest MSE value. The thorough comparison of the performance of the ADNN was discussed based on the performance MSE. The outcome obtained from this paper will be beneficial in various field of knowledge that requires immense data processing effort such as in engineering, healthcare, marketing, and business.

scholarly journals Modified election algorithm in hopfield neural network for optimal random k satisfiability representation

2020 ◽  
Vol 11 ◽  
pp. 16
Author(s):  
Hamza Abubakar ◽  
Shamsul Rijal Muhammad Sabri ◽  
Sagir Abdu Masanawa ◽  
Surajo Yusuf
Keyword(s):  
Neural Network ◽  
Mean Absolute Error ◽  
Search Algorithm ◽  
Optimal Solution ◽  
Information Criterion ◽  
Hopfield Neural Network ◽  
Absolute Error ◽  
Current Standard ◽  
Election Algorithm ◽  
Logical Representation

Election algorithm (EA) is a novel metaheuristics optimization model motivated by phenomena of the socio-political mechanism of presidential election conducted in many countries. The capability and robustness EA in finding an optimal solution to optimization has been proven by various researchers. In this paper, modified version of EA has been utilized in accelerating the searching capacity of Hopfield neural network (HNN) learning phase for optimal random-kSAT logical representation (HNN-R2SATEA). The utility of the proposed approach has been contrasted with the current standard exhaustive search algorithm (HNN-R2SATES) and the newly developed algorithm HNN-R2SATICA. From the analysis obtained, it has been clearly shown that the proposed hybrid computational model HNN-R2SATEA outperformed other existing model in terms of global minima ratio (Zm), mean absolute error (MAE), Bayesian information criterion (BIC) and execution time (ET). The finding portrays that the MEA algorithm surpassed the other two algorithms for optimal random-kSAT logical representation.

Studies on an Electronic Analog of a Recurrent Neural Network with Retrieval Phase Weight Adaptations

2005 ◽  
Vol 9 (2) ◽  
pp. 127-133
Author(s):  
Vishwanathan Mohan ◽  
◽  
Yashwant V. Joshi ◽  
Anand Itagi ◽  
Garipelli Gangadhar
Keyword(s):  
Neural Network ◽  
Associative Memory ◽  
Character Recognition ◽  
Storage Capacity ◽  
Hopfield Neural Network ◽  
Learning System ◽  
Adaptive Law ◽  
Stability Issues ◽  
Electronic Implementation ◽  
Retrieval Phase

It is argued that weight adaptations even during retrieval phase can greatly enhance the performance of a neurodynamic associative memory. Our simulations with an electronic implementation of an associative memory showed that extending the Hopfield dynamics with an appropriate adaptive law in retrieval phase could give rise to significant improvements in storage capacity and computational reliability. Weights, which are supposed to encode the information stored in the Hopfield neural network, are usually held constant once training/storage is complete. In our case, weights also change during retrieval, hence losing information in the process, but resulting in much better retrieval of stored patterns. We describe and characterize the functional elements comprising the network, the learning system, and include the experimental results obtained from applying the network for character recognition in various noisy conditions. Stability issues emerging as a consequence of retrieval phase weight adaptation and implications of weights being used as transitory, intermediary variables are briefly discussed.

scholarly journals Systematic Boolean Satisfiability Programming in Radial Basis Function Neural Network

Processes ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 214 ◽  
Author(s):  
Mohd. Asyraf Mansor ◽  
Siti Zulaikha Mohd Jamaludin ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Shehab Abdulhabib Alzaeemi ◽  
Md Faisal Md Basir ◽  
...  
Keyword(s):  
Neural Network ◽  
Radial Basis Function ◽  
Basis Function ◽  
Hopfield Neural Network ◽  
Boolean Satisfiability ◽  
Computational Error ◽  
Feed Forward Neural Network ◽  
Logical Rule ◽  
Final Output ◽  
Radial Basis

Radial Basis Function Neural Network (RBFNN) is a class of Artificial Neural Network (ANN) that contains hidden layer processing units (neurons) with nonlinear, radially symmetric activation functions. Consequently, RBFNN has extensively suffered from significant computational error and difficulties in approximating the optimal hidden neuron, especially when dealing with Boolean Satisfiability logical rule. In this paper, we present a comprehensive investigation of the potential effect of systematic Satisfiability programming as a logical rule, namely 2 Satisfiability (2SAT) to optimize the output weights and parameters in RBFNN. The 2SAT logical rule has extensively applied in various disciplines, ranging from industrial automation to the complex management system. The core impetus of this study is to investigate the effectiveness of 2SAT logical rule in reducing the computational burden for RBFNN by obtaining the parameters in RBFNN. The comparison is made between RBFNN and the existing method, based on the Hopfield Neural Network (HNN) in searching for the optimal neuron state by utilizing different numbers of neurons. The comparison was made with the HNN as a benchmark to validate the final output of our proposed RBFNN with 2SAT logical rule. Note that the final output in HNN is represented in terms of the quality of the final states produced at the end of the simulation. The simulation dynamic was carried out by using the simulated data, randomly generated by the program. In terms of 2SAT logical rule, simulation revealed that RBFNN has two advantages over HNN model: RBFNN can obtain the correct final neuron state with the lowest error and does not require any approximation for the number of hidden layers. Furthermore, this study provides a new paradigm in the field feed-forward neural network by implementing a more systematic propositional logic rule.

2 satisfiability logical rule by using ant colony optimization in Hopfield Neural Network

2019 ◽  
Author(s):  
Liew Ching Kho ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Mohd. Asyraf Mansor ◽  
Saratha Sathasivam
Keyword(s):  
Neural Network ◽  
Ant Colony Optimization ◽  
Hopfield Neural Network ◽  
Ant Colony ◽  
Logical Rule

scholarly journals Election Algorithm for Random k Satisfiability in the Hopfield Neural Network

Processes ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 568 ◽  
Author(s):  
Saratha Sathasivam ◽  
Mohd. Asyraf Mansor ◽  
Mohd Shareduwan Mohd Kasihmuddin ◽  
Hamza Abubakar
Keyword(s):  
Neural Network ◽  
Learning Algorithm ◽  
Mean Absolute Error ◽  
Global Solutions ◽  
Hopfield Neural Network ◽  
Absolute Error ◽  
Learning Processes ◽  
Logic Function ◽  
Election Algorithm ◽  
Logical Representation

Election Algorithm (EA) is a novel variant of the socio-political metaheuristic algorithm, inspired by the presidential election model conducted globally. In this research, we will investigate the effect of Bipolar EA in enhancing the learning processes of a Hopfield Neural Network (HNN) to generate global solutions for Random k Satisfiability (RANkSAT) logical representation. Specifically, this paper utilizes a bipolar EA incorporated with the HNN in optimizing RANkSAT representation. The main goal of the learning processes in our study is to ensure the cost function of RANkSAT converges to zero, indicating the logic function is satisfied. The effective learning phase will affect the final states of RANkSAT and determine whether the final energy is a global minimum or local minimum. The comparison will be made by adopting the same network and logical rule with the conventional learning algorithm, namely, exhaustive search (ES) and genetic algorithm (GA), respectively. Performance evaluation analysis is conducted on our proposed hybrid model and the existing models based on the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Sum of Squared Error (SSE), and Mean Absolute Error (MAPE). The result demonstrates the capability of EA in terms of accuracy and effectiveness as the learning algorithm in HNN for RANkSAT with a different number of neurons compared to ES and GA.

scholarly journals Modified Election Algorithm in Accelerating the Performance of Hopfield Neural Network for Random kSatisfiability

2020 ◽  
Author(s):  
Hamza Abubakar ◽  
Saratha Sathasivam ◽  
Mohd. Asyraf Mansor ◽  
Mohd Shareduwan Mohd Kasihmuddin
Keyword(s):  
Neural Network ◽  
Bayesian Information Criterion ◽  
Mean Absolute Error ◽  
Logic Program ◽  
Information Criterion ◽  
Hopfield Neural Network ◽  
Absolute Error ◽  
Global Minima ◽  
Expected Outcome ◽  
Election Algorithm

Election Algorithm (EA) is a powerful metaheuristics model motivated by phenomena of the socio-political mechanism of the presidential election conducted in many countries. EA is selected as a topic of discussion due to its capability and robustness to carry out complex problems in the random-2SAT logic program. This paper utilizes a hybridized EA assimilated with the Hopfield neural network (HNN) in carrying out random logic program (HNN-R2SATEA). The efficiency of the proposed method was compared with the existing traditional exhaustive search (HNN-R2SATES) model and the recently introduced HNN-R2SATICA model. From the result obtained, clearly proven that based on our proposed hybrid model outperformed other existing model based on the Global Minima Ratio (ZM), Mean Absolute Error (MAE), Bayesian Information Criterion (BIC) and Execution Time (ET). The expected outcome portrays that the EA algorithm outperformed the other two algorithms in doing random-kSAT logic program. The results proved the robustness, effectiveness, and compatibility of the HNN-R2SATEA model.

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