Feature selection is critical in machine learning to reduce dimensionality
and improve model accuracy and efficiency. The exponential growth in feature
space dimensionality for modern datasets directly results in ambiguous samples
and redundant features, which can severely degrade classification accuracy.
Quantum machine learning offers potential advantages for addressing this
challenge. In this paper, we propose a novel method, quantum support vector
machine feature selection (QSVMF), integrating quantum support vector machines
with multi-objective genetic algorithm. QSVMF optimizes multiple simultaneous
objectives: maximizing classification accuracy, minimizing selected features
and quantum circuit costs, and reducing feature covariance. We apply QSVMF for
feature selection on a breast cancer dataset, comparing the performance of
QSVMF against classical approaches with the selected features. Experimental
results show that QSVMF achieves superior performance. Furthermore, The Pareto
front solutions of QSVMF enable analysis of accuracy versus feature set size
trade-offs, identifying extremely sparse yet accurate feature subsets. We
contextualize the biological relevance of the selected features in terms of
known breast cancer biomarkers. This work highlights the potential of
quantum-based feature selection to enhance machine learning efficiency and
performance on complex real-world data.

本研究提出了一种新颖的方法，量子支持向量机特征选择（QSVMF），将量子支持向量机与多目标遗传算法相结合。QSVMF 通过优化多个同时目标来实现：最大化分类准确性，最小化选定特征和量子电路成本，并减少特征协方差。我们将 QSVMF 应用于一个乳腺癌数据集进行特征选择，将 QSVMF 与传统方法在选定特征上的性能进行对比。实验结果表明，QSVMF 取得了卓越的性能。此外，QSVMF 的帕累托前缘解能够分析准确性与特征集大小的权衡，识别出极度稀疏但准确的特征子集。我们从已知的乳腺癌生物标志物的角度解释了所选特征的生物学相关性。本研究强调了量子特征选择在提高机器学习效率和性能方面的潜力，尤其是在处理复杂的真实世界数据时。