Communications in Computational and Applied Mathematics, Vol. 2 No. 1 (2020) p. 1-6
CCAM Communications in Computational and Applied Mathematics
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Systematic Satisfiability Programming in Hopfield Neural Network- A Hybrid Expert System for Medical Screening
Mohd Shareduwan Mohd Kasihmuddin1, Mohd. Asyraf Mansor2,*, Siti Zulaikha Mohd Jamaludin3, Saratha Sathasivam4
1,3,4School of Mathematical Sciences, Universiti Sains Malaysia, Minden, Pulau Pinang, Malaysia
2School of Distance Education, Universiti Sains Malaysia, Minden, Pulau Pinang, Malaysia
*Corresponding Author
Received 26 January 2020; Abstract: Accurate and efficient medical diagnosis system is crucial to ensure patient with recorded Accepted 12 February 2020; system can be screened appropriately. Medical diagnosis is often challenging due to the lack of Available online 31 March patient’s information and it is always prone to inaccurate diagnosis. Medical practitioner or 2020 specialist is facing difficulties in screening the disease accurately because unnecessary attributes will lead to high operational cost. Despite of acting as a screening mechanism, expert system is required to find the relationship between the attributes that lead to a specific medical outcome. Data mining via logic mining is a new method to extract logical rule that explains the relationship of the medical attributes of a patient. In this paper, a new logic mining method namely, 2 Satisfiability based Reverse Analysis method (2SATRA) will be proposed to extract the logical rule from medical datasets. 2SATRA will capitalize the 2 Satisfiability (2SAT) as a logical rule and Hopfield Neural Network (HNN) as a learning system. The extracted logical rule from the medical dataset will be used to diagnose the final condition of the patient. The proposed 2SATRA will utilize four prominent datasets that focuses on well-known medical disease such as Hepatitis, Diabetes and Cancer. This paper utilizes Diabetic Retinopathy Debrecen, Pima Indians Diabetes, Hepatitis and Mammographic Mass datasets that were obtained from established repository. The efficiency of 2SATRA is evaluated in terms of performance error and computation time. The results obtained for all medical data sets of 2SATRA achieved acceptable accuracy.
Keywords: Hopfield Neural Network; Logic Mining; Medical Screening
1. Introduction because the main objective of ANN is to replicate the human Medical screening is a vital part of a healthy lifestyle. intelligence with astonishing computation capability. The Regular health check-up will help us detect early potential growing attention towards the ANN as a model for AI is due health problem. Most of the medical practitioner utilized to the capability of ANN in representing the model in terms of preventive health screening to analyze the condition of our mathematical equations. One of the most appreciated simple body. Patients will supply them with data (from the health ANN is Hopfield Neural Network (HNN). Popularized by screening) and the medical practitioner will classify the Hopfield, HNN [1] has been utilized to solve various both condition of the patient. Medical practitioner experienced high constrained and unconstrained optimization problem. HNN frequent of misdiagnosed due to several factors such as consists of interconnected neurons that updates missing data, unnecessary attributes and error in medical asynchronously as the dynamic of the network changes. The instruments. In that regard, the intelligent system is required quality of the solution for HNN is represented in terms of to learn the past data and utilize it to predict and classify the energy function. The main focus of the HNN model is to find current patient. Hence, a more accurate and efficient system is the solution that corresponds to the minimum Lyapunov very crucial in the field of medicine. Energy function. To serve as a useful method, the training of Artificial intelligence (AI) is a prominent field of science HNN must be conducted in an efficient and effective manner. that specializes in data modelling. The subfield of AI, Considering the network architecture, input of the neurons Artificial Neural Network (ANN) gained its popularity will be excited to generate the synaptic weight of the system [2, 3]. Fault tolerance and content addressable memory
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properties contribute to the popularity of HNN in processing simulation results indicate the proposed logic mining is able and constructing the pattern of the data. In another to classify diabetic patients with high accuracy. development, the beneficial feature of HNN is implemented in The work is organized as follows. Section 2 and 3 present the field of health sciences. Chang and Chung [4] proposed the overview of 2-SAT representation and 2SAT utilization in HNN in medical image segmentation. In this paper, the image HNN respectively. In Section 4, the formation of 2SATRA segmentation produced by HNN is more continuous and used to undertake the medical data sets is presented. The smoother compared to other methods. Hsu [5] proposed fuzzy attained results and limitations encountered in this experiment HNN in clustering electroencephalogram data. The proposed are presented in Section 5. Conclusions and future work method is used to classify left and right medical imagery data directions are given in Section 6. with acceptable accuracy compared to other popular classifiers. Sammouda [6] improvised the usage of HNN in 2. 2 Satisfiability Representation performing pathological liver colour images. The proposed 2 Satisfiability or (2SAT) is variant of generalized HNN is evaluated based on 20 real pathological liver data that Satisfiability representation kSAT that consists of exactly 2 consist of various colour images and was reported to be literals per clause. 2SAT formulation can be expressed in effective in data segmentation. These applications raised an terms of 2 Conjunctive Normal Form (2CNF). 2SAT can be important question: what is the most effective method to identified based on the following criteria [10]: extract important information from the medical dataset but at 1. A set of l variables, x x,x , ...... , . the same time the extracted information is readable by the 12 l user? 2. A set of literals and each literal can be a positive or Logic programming in HNN is initially proposed by Wan negative (negation). Abdullah [7] by incorporating logical rule in Hopfield Neural 3. A set of m distinct clauses: Ci here im1,2,3,..., . Network. The proposed network obtains synaptic weight by C is connected to C by conjunction ( ). The 2 comparing the cost function with the final energy function. i i1 The quest of creating optimal HNN is continued by literals inside each Ci is connected by disjunction ( Sathasivam [8] where the proposed HNN is incorporated with ). Horn clause. The usage of Horn clause is considered effective In general, each of the variables consists of the because the proposed logical rule is always satisfiable. In information which contributes the nature of the combinatorial order to comply with real life problem, Sathasivam and problem. The state for each 2SAT variable in each C is Abdullah [9] proposed Reverse Analysis method to extract i valuable logical rule from the real-life dataset. One of the given as -1 (FALSE) and 1 (TRUE). 2SAT formulation can be limitations of the proposed Reverse Analysis is the flexibility defined explicitly as follows: of the logical rule to extract the optimal logical rule. Despite having high value of global minima ratio, the induced logical m PC2SATi (1) rule is not able to effectively generalize the real-life dataset. i1 The scope of the real-life dataset used in the proposed Reverse Analysis is also limited to small data points. In another where each clause C is given as follows: development, Kasihmuddin et al. [10, 11] proposed a new i systematic logical rule namely 2 Satisfiability (2SAT) in HNN. The proposed logical rule has been optimized by using n Cxyiii , (2) Metaheuristics Algorithm [11, 12] and the proposed method i1 managed to achieve global minimum solution. The usage of 2SAT in HNN has been extended to several applications such as Pattern Satisfiability [13] and Very Large-Scale Integration One of the example of P2SAT instance based on Equations (1) (VLSI) [14]. The recent works demonstrated the practical and (2) is: usage of 2SAT in Mutation HNN [10] and Radial Basis Function Neural Network [15]. Pxxxx21234SAT (3) Unfortunately, the usage of 2SAT in Reverse Analysis method is still poorly understood. In this case, there is no recent innovation to extract important logical rule in the One possible variable assignation that would satisfy medical datasets. Hence, the contributions of this paper are: Equation (3) is xxxxx12345,,,,1,1,1,1 . In this case, (1) This paper explores the representation of the dataset by both clauses C1 and C2 are satisfied CC121,1 that lead using 2SAT logical rule. (2) A novel logic mining method via 2 Satisfiability Reverse Analysis method is proposed by to P2SAT 1 . On the other hand, Equation (3) shows logical implementing 2SAT as a systematic logical rule in HNN. The inconsistencies P2SAT 1 if one of the clauses does not functionality of the proposed methods is divided into 2 parts. satisfied C 1. Note that, the state of variable in each C The first part discusses the implementation of 2SAT in HNN. i i The later part will explain the implementation of HNN in 2 exhibits useful logical informations that contribute the Satisfiability Based Reverse Analysis method. (3) Logic outcome of the P2SAT . In this case, we choose k 2 Mining will be used to extract the logical relationship that because we only consider two-dimensional relationship explains the behaviour of the medical datasets. The induced between two medical attributes. We believe that, k 2 will logical rule will be utilized to screen the potential patients. result in higher dimensional interpretation that will lead to Therefore, the proposed model can be utilized in finding higher complexity (at least in the perspective of the search important information based on logical extraction for various space) of the logic mining. medical datasets. The developed logic mining method is evaluated using a widely adopted performance evaluation. The
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3. P2SAT in Hopfield Neural Network 2 2 condition or no self-connection, W ( ) = W ( ) = 0 and Hopfield neural network (HNN) is a recurrent neural ii jj network that consists only input and output layer with no 22 WWij ji . By utilizing theorem [1], the Lyapunov Energy hidden layer [1]. Each neuron is updated asynchronously in order to establish convergence during the final neuron state function is given as: [1]. Note that, the state of the neuron is given by S 1, 1 i NNN where i =1,2,3,...,N . The bipolar pattern, in the input 1 21 HWSPiji SWS iji (9) 2SAT 2 layer represents the information of a given constrained iij1,1, jij i1 optimization problem. In this paper, the information of P2SAT will be representing the logical rule of HNN. Each variable in In this case, all possible permutation of i and j will be P2SAT is represented in terms of neuron that is connected by considered in the calculation for H . According to [17], P2SAT synaptic weight. Hence, P2SAT is embedded in HNN by H always decreases monotonically because the final state P2S A T calculating the synaptic weight that minimizes the cost of the neuron will always converge to a stable state. The usage function. The cost function Q2SAT for P2SAT in HNN is of Hyperbolic Activation Function (HTAF) in Equation (8) given as follows: will reduce the unnecessary neuron oscilations. The governed HNN by using P2SAT is abbreviated as HNN-2SAT. The NCNV energy function of Equation (9) differs from other works such QR (4) Pij2SAT as [18] because this work utilizes k 3 that constitute to ij11 higher order of . In another perspective such as [1], the Lyapunov function is intelligently used to define the where NC and NV represents the number of clause and continuous space which we believe, is not approriate for our variables in a particular P2S A T . Rij is defined as follows: proposed 2SAT.
4. 2 Satisfiability Reverse Analysis Method 1 1,SifAA The robustness of the network in discovering the 2 Rij (5) relationship of the dataset with the given set of attributes is 1 1,Otherwise SA vital. One of the recent data extractions that incorporates logic 2 programming, neural network and data mining is called logic mining. The attributes of the data set can behave according to SA is the neuron state, where SA 1, 1 . The synaptic bipolar representation { 1, 1} and can be represented in terms of state for all variable in P2S A T clause. In such case, weight, Wij for P2SAT in HNN is obtained by comparing Equation (4) and (5) with Lyapunov energy function. In this 2SATRA reveals the level of connectedness between 2 attributes in the data set by obtaining the optimal synaptic W 1 case, ij and Wi will be represented in terms of weight weight. Hence WA method [7] will be employed by 2SATRA matrix. The updating rule of HNN is given as follows: during the learning phase in order to establish the correct synaptic weight between two attributes. For example, consider both attributes A and B where SA { 1, 1} and SB { 1, 1} , N the possible 2SAT clause with its corresponding synaptic 21 htWStWij iji (6) weight are summarized in Table 1. j The attribute of the datasets will formulate the clause of
the P2SAT . According to Table 1, if the SA 1 , SB = 1 , where i and j are running over all neurons N . W (2) and i ij PSSlearn AB will be chosen to be embedded into W (1) are the second and first order connection, respectively. i i HNN-2SAT. The synaptic weight for Plearn for this case is Hence, the updating rule remains 112 WW,0.25,0.25,0.25 W . We recommended SSSABA S B S t +1 = sgnéh t ù (7) i ( ) ë i ( )û
Table 1 – Synaptic weight for P2SAT according to [7] where the final neuron state is based on the following: k ( ) SSAB SSAB SSAB SSAB Wi sinhhi 1, (1) sgn ht cosh h (8) W 0.25 -0.25 0.25 -0.25 1 i S A 1 ,Otherwise (1) W 0.25 0.25 0.25 -0.25 SB It is worth mentioning that 0 which was coined by [16]. (2) The synaptic weight of the HNN followed the zero diagonal W -0.25 0.25 -0.25 -0.25 SASB
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WA method [7] in finding synaptic weight of the proposed Table 2 – Detail of the medical datasets 2SATRA because the final neuron state by using this method is always coverge to global minimum solution. In WA Datasets DRD PID HD MMD method, the synaptic weight is obtained by comparing the Equation (4) with Equation (9). Other method such as Hebb Instances 1151 768 155 960 rule [19] prone to possible oscillation as the number of clauses increased. The algorithm (2SATRA) that extract important Attributes 6 out 20 6 out 8 6 out 19 6 out 6 logical rule and behaviour of the dataset is sketched in the Missing No No Yes Yes following Algorithm 1: Value
Algorithm 1: The implementation of 2SATRA 691 461 93 576 460 307 62 384 1. Convert all the input datasets into bipolar representations which consist of P i and P i learn test Table 3 – The Parameter Settings for HNN-2SAT with the corresponding outcome. Dataset Parameters i 2. Assign neuron to each variable in and Ptest . Neuron Combination 100 Number of learning ( ) 100 3. Assign two neurons ( Si and Sk ) that represents No_ Neuron String 100 each Ci , where i =1,2,3,..,n. Selection_Rate 0.1 CPU time 24 Hours 4. Identify the P formula that lead to P i = 1. 2SAT learn Hyperbolic Activation Activation Function Function [16] 5. Calculate the max én Pi = 1 ù. Obtain P that êë ( learn )úû best Clausal Noise CN 1 1 0CN corresponds to the input datasets. 6. Embed the into HNN-2SAT. The synaptic Processing Unit (CPU) time for each simulation is 1 day. The weight of the will be derived by using Table 1. performance of the 2SATRA in processing all the proposed 7. By using Equation (5), obtain the final state of the datasets will be evaluated based on Root Mean Squared Error neuron. (RMSE), Mean Absolute Error (MAE) and CPU time.
8. Obtain the induced logic B B B B . P1 ,P2 ,P3 ,...., Pn 5. Result and Discussion B Bi 9. Verify whether the outcome of Pi is PPi test . The main purpose of this work was to extract the induced i B P2S A T from the dataset via 2SATRA. Presently, information The induced logic Pi obtained from 2SATRA will be used as a model to classify the outcome of the dataset. Thus, from the datasets is extracted and the connection between the B dataset and the outcome will be obtained. The main problem Pi 1 indicate the outcome of the dataset is expected to be with this paradigm is the ability to generalize the information -1 and the reverse case is applied as well. into more readable rule. In this case, 2SATRA is reported to i decipher the medical dataset into simple P2SAT that can be 4.1 Experimental Setup used to do classification. The choice of Pi as logical rule The simulation was designed to evaluate the capability of 2SAT 2SATRA in extracting several established medical datasets. is due to the systematic logical rule of k 2 compared to The medical dataset chosen were Diabetic Retinopathy other work such as [9] and [18]. Worth mentioning that, the i Debrecen (DRD) [20], Pima Indians Diabetes (PID) [21], global minima ratio for each P2S A T is approximately 1 due to Hepatitis (HD) [22] and Mammographic Mass datasets minimization of energy during retrieval phase of HNN-2SAT (MMD) [23]. All the datasets were retrieved from UCI [12]. In this experiment, the value of Lyapunov Energy is not machine learning repository and the detail of each dataset were evaluated due to the scalar property of HP . Hence, we summarized in Table 2. In DRD and PID, the PB is used to 2SAT i i only examine the effect of hti towards P2S A T . Hyperbolic clasify the diabetic and non diabetic patient. In HD, the is Activation Function (HTAF) is chosen in this simulation expected to classify the likelihood for the hepatitis patient to because HTAF can provide a non-linear property of the B live or die. In MMD, Pi is expected to classify the severity . Other activation functions such as traditional of the Mammographic image based on the given attributes. McCulloch Pitts [8] and Bipolar Activation Function is prone The proposed 2SATRA will be executed in Microsoft Visual to neuron oscilation which may lead to suboptimal Pi . Basic C++ 2013 for Windows 10. Note that, the 2SATRA 2SAT consist of HNN-2SAT which requires certain specification in Table 4 to Table 6 demonstrate the performance error of order to function optimally. The details of the parameters 2SATRA and CPU time in all proposed medical datasets. Note involved in HNN-2SAT are shown in Table 3. In order to that, the value of error in Table 4 and 5 signify the number of iteration required to arrive to final Pi . The result allow the increase the number of during retrieval phase, Clausal 2SAT following general conculsion to be drawn on the induced noise (CN) is added to each attribute during the simulation. In i this case, CN is added to increase the accuracy of the network P2SAT : by exploring various search space. The threshold Computer 4 Published by FAZ Publishing http://www.fazpublishing.com/ccam
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Table 4 – RMSE for all medical dataset required to extend the decision into more than 2 classifications. NC DRD PID HD MMD 2 3.464 0.793294 3.179 5.5549 6. Conclusion 4 6.573 10.606501 11.2990 11.471 Motivated by considerations in the foundation of logical 6 17.693 17.418961 17.582 17.78 rule and neural network, we investigated the usage 2SATRA 8 23.914 23.956505 22.942 23.95 in extracting the classification model in the proposed medical 10 29.975 23.956831 28.168 29.91 dataset. The performance of 2SATRA in extracting important logical rule that corresponds to the behaviour of four Table 5 – MAE for all medical dataset established medical datasets. The result obtained shows that the induced i from 2SATRA classify the datasets with NC DRD PID HD MMD P2SAT 2 2.0 4.254996 2.0 5.1429 acceptable accuracy. Certainly, the simulation reported here should be extended in accelerating the capability of 2SATRA. 4 6.00 9.507923 10.6401 10.97 The usage of Metaheuristics algorithm such Genetic 6 17.39 16.913445 16.37 17.51 Algorithm (GA) and Artificial Bee Colony (ABC) is expected 8 23.83 23.913540 23.803 23.49 to reduce the learning error of 2SATRA. Moreover, this paper 10 29.95 23.913769 28.192 29.93 can be further extended by utilizing variety of datasets such as finance, human resources and game strategy. Table 6 – CPU Time for all medical dataset Acknowledgement NC DRD PID HD MMD 2 15.97 10.975 0.27 0.3477 This research was funded by Fundamental Research 4 50.586 45.914 0.58 0.591 Grant Scheme (FRGS), Ministry of Education Malaysia, grant 6 61.63 78.091 1.02 2.367 number 203/PMATHS/6711804. We would like to thank the anonymous reviewers for the insightful and constructive 8 200.76 124.3 1.72 4.101 suggestions. We also thank Alyaa Alway and Ezlin Zamri for 10 321.98 412.8 3.07 7.764 their critical inputs during the review process.
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