计算机科学 ›› 2025, Vol. 52 ›› Issue (11): 71-81.doi: 10.11896/jsjkx.240900160
易丽莎, 彭宁宁
YI Lisha, PENG Ningning
摘要： 为了解决持续同调从数据中提取的拓扑特征输出形式与机器学习算法的常用输入形式不匹配这一难题,提出了一个新的算法框架——基于持续同调的空间金字塔词袋模型(PHSBoW算法)。该算法将持续同调输出的持续性图(PD图)转换为固定长度的向量,同时最大限度地保留PD图中所包含的拓扑特征。为提高算法准确率、降低运行时间,在PHSBoW算法的基础上,通过权重优化、聚类模型替代以及词袋模型扩展等改进,进一步发展了PHSsBoW,PHSwBoW,PHSVLAD 3种算法。通过在不同类型和规模的9个数据集上进行实验,将以上4种算法与支持向量机相结合,对数据进行分类。实验结果表明,与传统核函数算法(SWK,PSSK,PWGK)及向量化算法(PBoW,PI,PL)相比,该方法的分类准确率平均提高了3.29个百分点~17.98个百分点,运行时间相较于核函数算法显著降低。这表明,所提出的算法有效解决了持续同调在机器学习中难以结合的问题,同时显著提高了分类准确率和算法运行速度。
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