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Control and Optimization in Applied Mathematics - Volume:6 Issue: 1, Winter-Spring 2021

Control and Optimization in Applied Mathematics
Volume:6 Issue: 1, Winter-Spring 2021

  • تاریخ انتشار: 1401/02/14
  • تعداد عناوین: 6
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  • Ali Shojaeifard, Hamid Reza Yazdani *, Mohsen Shahrezaee Pages 1-10
    In this paper‎, ‎we are going to analyze big data (embedded in the digital images) with new methods of tensor completion (TC)‎. ‎The determination of tensor ranks and the type of decomposition are significant and essential matters‎. ‎For defeating these problems‎, ‎Bayesian CP-Factorization (BCPF) is applied to the tensor completion problem‎. ‎The textit{BCPF} can optimize the type of ranks and decomposition for achieving the best results‎. ‎In this paper‎, ‎the hybrid method is proposed by integrating BCPF and general TC‎. ‎The tensor completion problem was briefly introduced‎. ‎Then‎, ‎based on our implementations‎, ‎and related sources‎, ‎the proposed tensor-based completion methods emphasize their strengths and weaknesses‎. ‎Theoretical‎, ‎practical‎, ‎and applied theories have been discussed and two of them for analyzing big data have been selected‎, ‎and applied to several examples of selected images‎. ‎The results are extracted and compared to determine the method's efficiency and importance compared to each other‎. ‎Finally‎, ‎the future ways and the field of future activity are also presented.
    Keywords: Image Recovery‎, ‎Matrix Completion‎, ‎Optimization Problems‎, ‎Tensor Completion‎, ‎Variational Bayesian inference
  • Mostafa Boroumandzadeh, Elham Parvinnia *, Reza Boostani, Sepideh Sefidbakht Pages 11-29
    Medical decision support systems (MDSS) are designed to assist physicians in making accurate decisions‎. ‎The required data by MDSS are collected from various resources such as physical examinations and electronic health records (EHR)‎. ‎In this paper‎, ‎an MDSS framework has been proposed to diagnose and classify breast cancer patients (DSS-BC)‎. ‎Medical texts reports (MTR) were embedded‎, ‎and essential feature vectors combined with EHR were extracted using principal component analysis (PCA)‎. ‎A new method based on a fuzzy min-max neural network with hyper box variable expansion coefficient (FMNN-HVEC) was used to determine the molecular subtypes‎, ‎and the feature vectors were clustered using deep clustering‎. ‎Also‎, ‎a new decision fusion algorithm called weighted Yager was proposed based on the F1-Score for each class‎. ‎This algorithm proposed a mathematical decision fusion technique to determine the Breast Imaging-Reporting and Data System (BI-RADS) and molecular subtypes values with the accuracy of 95.12% and 89.56%‎, ‎respectively.
    Keywords: Decision support system‎, ‎Text mining‎, ‎Breast cancer‎, ‎BI-RADS‎, ‎Decision fusion
  • Leader Navaei *, Reza Akbari Pages 31-41
    In this paper, the problem of identification of distributions for two‎ ‎independent objects via simple homogeneous stationary Markov chains with a finite number of states is studied‎. ‎This problem is introduced by Ahlswede and Haroutunian on the identification of hypotheses under reliability requirements‎. ‎The problem of identification of distributions for one object via Markov chains was studied by Haroutunian and Navaei in 2009.
    Keywords: Identification‎, ‎Error probability‎, ‎Two independent objects‎, ‎Markov chain
  • Ali Badie *, Mohammad Amin Moragheb, Ali Noshad Pages 43-59
    This research explores the prominent signals and presents an effective approach to identify emotional experiences and mental states based on EEG signals‎. ‎First‎, ‎PCA is used to reduce the data's dimensionality from 2K and 1K down to 10 and 15 while improving the performance‎. ‎Then‎, ‎regarding the insufficient high-quality training data for building EEG-based recognition methods‎, ‎a multi-generator conditional GAN is presented for the generation of high-quality artificial data that covers a more complete distribution of actual data by utilizing different generators‎. ‎Finally‎, ‎to perform classification‎, ‎a new hybrid LSTM-SVM model is introduced‎. ‎The proposed hybrid network attained overall accuracy of 99.43% in EEG emotion state classification and showed an outstanding performance in identifying the mental states with accuracy of 99.27%‎. ‎The introduced approach successfully combines two prominent targets of machine learning‎: ‎high accuracy and small feature size‎, ‎and demonstrates a great potential to be utilized in future classification tasks.
    Keywords: EEG‎, ‎GANs‎, ‎LSTM Networks‎, ‎Biomedical signal processing‎, ‎Deep learning
  • Mohammad Dehghandar *, Ghasem Ahmadi, Heydar Aghebatbeen Monfared Pages 61-80

    The purpose of this study was to provide a fuzzy system for predicting and diagnosing metabolic syndrome (MetS) in preschoolers‎, ‎children‎, ‎and adolescents‎. ‎In this study‎, ‎previous research on the factors affecting metabolic syndrome‎, ‎especially in children‎, ‎and adolescents‎, ‎has been considered‎. ‎After integrating the initial variables‎, ‎a fuzzy system has been designed with 8 data on age‎, ‎waist size‎, ‎systole blood pressure‎, ‎diastole blood pressure‎, ‎body mass index (BMI)‎, ‎waist-to-height ratio‎, ‎nutrition‎, ‎and abdominal obesity‎. ‎Ultimately‎, ‎the system gives us an output that diagnoses the health status of a child or adolescent with MetS or predicts the possibility of a person contracting the disease in the future‎. ‎The system is designed based on the data of 1300 persons participating in the fifth study of the program for monitoring and prevention of non-communicable diseases of children‎, ‎and Adolescents in Tehran and Isfahan provinces that 1050 data were used as training data and 250 data as test data that used to test the rules and output of the system‎. ‎After reviewing the rules and eliminating similar or contradictory rules using their degree calculation‎, ‎finally‎, ‎the system was designed with 45 rules‎, ‎a multiplication inference engine‎, ‎a single fuzzifier‎, ‎and a centroid defuzzifier‎. ‎Then the system was evaluated using the confusion matrix accuracy‎, ‎sensitivity‎, ‎and specificity‎. ‎Our analysis shows that this method‎, ‎with an error rate of less than 4 percent more accurate than other methods‎, ‎can predict and diagnose MetS in children.

    Keywords: Metabolic syndrome‎, ‎Children, adolescents‎, ‎Fuzzy expert system‎, ‎Lookup table‎, ‎Accuracy
  • Siyamak Firouzian *, Shaban Sedghi, Nabi Shobe Pages 81-89
    In this paper‎, ‎we introduce some new concepts of fuzzy graphs with the notion of degree of an edge in fuzzy line graphs and congraphs‎. ‎Also‎, ‎some properties and some‎ ‎lemmas of edge fuzzy line graphs and congraphs are studied‎. ‎Finally‎, ‎we state and prove some results‎ ‎related to these concepts.
    Keywords: Fuzzy graph‎, ‎Fuzzy line graph‎, ‎Fully connected graph‎, ‎Common neighborhood graph‎, ‎Congraph