Pusat Pengajian Sains Matematik - Tesis

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Multi-objective Binary Clonal Selection Algorithm In The Retrieval Phase Of Discrete Hopfield Neural Network With Weighted Systematic Satisfiability
(2024-09)
Romli, Nurul Atiqah
The stability of the Discrete Hopfield Neural Network is dependent on the ability of the network to govern the neuron connections that caused several issues to arise, such as random distribution of positive and negative literals and overfitting final neuron states. Therefore, this thesis proposes a new systematic Satisfiability logical rule namely Weighted Systematic 2 Satisfiability that uses a weighted feature to control the distribution of the negative literals. The proposed logic embedded into Discrete Hopfield Neural Network and considered the optimization of multi-objective function in the retrieval phase to locate superior final neuron states. A Binary Clonal Selection Algorithm is being proposed to ensure optimal generation of the superior final neuron states. The proposed algorithm in the retrieval phase showed optimal performance as compared to the baseline algorithms. The newly proposed logical rule and the algorithm will be the components in the logic mining model namely Weighted Systematic 2 Satisfiability Modified Reverse Analysis. The proposed logic mining model is able to retrieve best induced logic that represents the optimal patterns of the dataset. Based on the findings, the proposed logic mining model outperformed other baseline logic mining models for all the performance metrics used in the repository dataset. The proposed logic mining model was tested on a real-life dataset from the Alzheimer’s Disease Neuroimaging Initiative, and it showed superior performance.
Evaluating A New Adaptive Group Lasso Imputation Technique For Handling Missing Values In Compositional Data
(2024-08)
Tian, Ying
Pie chart is a widely used statistical chart to represent the proportions of various components in a certain entity. The shares of data in a pie chart, also known as compositional data, consist of non-negative values, containing only relative information. However, in many real-life domains, a substantial amount of missing values is often collected. The complexity of compositional data with missing values renders traditional estimation methods inadequate. In this thesis, a compositional data imputation method designed based on LASSO is proposed combining group LASSO and adaptive LASSO analysis methods. The estimation effects of highdimensional and low-dimensional compositional data with missing values are compared through simulation studies and case analyses under different missing rates, dimensions, and correlation coefficients. Considering the impact of outliers on the accuracy of estimation, both simulation and case analysis are conducted to compare the proposed algorithm against four existing methods. The experimental results demonstrate that the proposed adaptive group LASSO method produces a better imputation performance, MSE, MADE, RMSE and NRMSE increased by up to 26.6% at selected missing rates. Future work analyses the effect of imputation under continuous missing rates, MAR missing mechanism and more model evaluation criteria.
An Integrated Fuzzy Model For Pattern Recognition
(2016-02)
Sagir, Abdu Masanawa
Medical diagnosis is a process of investigating which medical condition, disease or disorder describes signs and symptoms of a patient. Medical diagnosis helps to obtain different features representing the different variation of the disease. The decision about presence or absence of diseases of patients is a challenging task because many signs and symptoms are non-specific; and many tests might be required. To recognise an accurate diagnosis of symptom analysis, the physician may need efficient diagnosis system that can predict and classify patient condition. This thesis describes a methodology for developing an integrated fuzzy model by utilising the application of adaptive neuro fuzzy inference system (ANFIS) that can be used by physicians to accelerate diagnosis process. Feature selection approach was used to identify and remove unneeded, irrelevant and redundant attributes from the data that do not contribute to the accuracy of a predictive model. The proposed method used Hold-out validation technique, which divides the training and test data sets into twothirds to one-third, respectively. The proposed method uses grid partition technique to cope with seven input attributes and Gaussian membership functions than conventional method built-in Matlab, which uses small number of input attributes usually less than five. For robustness, twelve benchmarked datasets obtained from University of California at Irvine’s (UCI) machine learning repository were used in this research.
Approximation Methods For Solving Hiv Infection Models In Fuzzy Environment
(2024-05)
Almismaery, Hafed H Saleh
Fuzzy differential equations (FDEs) have a wide range of applications in physics, applied sciences, and engineering and has become undeniably an essential tool for modelling a wide range of real-life phenomena and even more so, those involved with uncertainties such as HIV infection models. Nevertheless, the majority of mathematical representations for fuzzy HIV infection, as depicted in nonlinear models, suffer from a deficiency in analytical solutions whereby these solutions are frequently elusive. Consequently, the prevalent approach to address fuzzy HIV models involves employing approximation methods, typically through numerical techniques. Such numerical methods yield solutions in numeric values. However, it's important to note that these approximate numerical methods face limitations in directly resolving fuzzy HIV infection models and necessitate the use of discretization or linearization. In contrast, approximate analytical methods prove versatile, as they not only apply to fuzzy HIV models without requiring linearization or discretization but also furnish continuous solutions. Therefore, in this thesis, the approximate analytical methods fuzzy homotopy perturbation method (FHPM), fuzzy variational iteration method (FVIM), and their modified versions are considered for solving several linear and nonlinear fuzzy HIV infection models under the concept of Hukuhara differentiability approach to provide approximate analytical solutions in the form of convergence series solution. The existence and uniqueness of the solution for linear and nonlinear fuzzy HIV infection models in this work have also been investigated.
Flood Prediction Based On Deep Learning Networks With Variational Mode Decomposition
(2024-09)
Ni, Chenmin
Climate change increases the frequency of extreme weather events, causing river overflow floods that threaten human safety and ecosystems. Traditional flood prediction models face challenges due to fluctuations in water levels from topography and rainfall, leading to less accurate forecasts. This thesis aims to enhance flood prediction accuracy by developing and evaluating three new machine learning models that incorporate data decomposition, feature selection, and parameter optimization. The first two models use water level data for each hour. The first model utilizes hydrological data by integrating the Variational Mode Decomposition (VMD) method to reduce disturbances, along with Directional Bidirectional Long Short-Term Memory (BiLSTM) optimized with attention for forecasting purposes. The second model enhances prediction effectiveness by incorporating meteorological data specifically rainfall, humidity, and wind speed. This model emphasizes the benefits of VMD component classification and feature selection by considering water level changes to categorize Intrinsic Mode Functions (IMFs) obtained from the VMD method and using feature selection through the Pearson correlation method. The third model uses an optimized Gated Recurrent Unit - Temporal Convolutional Network (GRU-TCN) to forecast daily data at point estimates and confidence intervals. This model improves Kernel Density Estimate (KDE) predictions to assess forecast uncertainty more accurately and enhance model reliability. These three proposed models can overcome the weaknesses of traditional methods by utilizing real data from the Yangtze River station.

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