Browsing by Author "Muzdybayeva G."

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    Numerical methods for matrix completion problem
    (Faculty of Engineering and Natural Sciences, 2024) Muzdybayeva G.
    This work addresses the significant challenge of framework completion in machi– ne learning, focusing on enhancing the accuracy and computational productivity of algorithms under conditions of large, noisy, and incomplete datasets. Central to this work are changes to two primary matrix completion techniques: Singular Value Thresholding (SVT) and Collaborative Filtering (CF). These methods were systematically progressed to handle common real-world data issues such as noise and sparsity, and were thoroughly tried over different applications, demonstrating significant execution enhancements. Through a detailed theoretical analysis, this research contributes robust frameworks for the convergence behaviors of these algorithms, giving a solid foundation for their application in practical scenarios. Improved SVT calculation, in particular, shows considerable reductions in Mean Absolute Error (MAE) and Mean Squared Error (MSE), indicating a superior performance over conventional methods. Besides, the refined CF approach presently integrates novel matrix factorization procedures, improving its utility in dynamic, personalized recommendation systems.The thesis underscores the potential of these refined algorithms in diverse fields, from advanced media to educational analytics, and sets a course for future investigate that incorporates integrating deep learning models and expanding into new data structures like tensors.