Comparative Analysis of Classical and Quantum Fuzzy Support Vector Machines for Binary Classification
摘要
Quantum Computing is rapidly evolving and promises significant advancements across various scientific and technological fields. In machine learning, quantum algorithms offer the potential for exponential speedup compared to classical algorithms. Among classical models, Support Vector Machines (SVM) is well-regarded for their robust classification capabilities. The Fuzzy Support Vector Machine (FSVM) extends this by addressing classification issues related to training samples, allowing different influences on the optimal hyper plane and enhancing margin separation while minimizing the impact of outliers and noise. Quantum Support Vector Machines (QSVM) represents a promising area in Quantum Machine Learning (QML). QSVMs aim to overcome the dimensional and capacity limitations of classical SVMs by utilizing quantum computing are unique properties. This includes the development of quantum feature maps and optimization techniques that can improve the performance of QSVMs, potentially allowing them to handle more complex datasets and achieve better generalization. The Quantum Fuzzy Support Vector Machine (QFSVM) combines fuzzy logic's robustness with quantum computing's power. This fusion allows QFSVM to effectively manage large and complex datasets with inherent uncertainty, making it a strong candidate for a wide range of classification problems. In this study, we perform a comparative analysis of classical and quantum-inspired models, including k-Nearest Neighbours (kNN), Linear SVM, FSVM, and QFSVM, on synthetic binary classification datasets. By evaluating performance metrics such as accuracy, precision, recall, and execution time, we have demonstrated that quantum approaches, particularly QFSVM, outperform classical methods in terms of runtime. This research highlights the potential of quantum computing to accelerate machine learning processes, leading to faster training times and improved performance.