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4750 软件学报 2025 年第 36 卷第 10 期

4 结论和展望

本文利用弹球损失函数提出了新颖的超平面学习模型并用来处理集值数据. 不同于以前的模型, 提出的模型
能取得巴拿赫空间的非平行的超平面. 通过研究模型的一些性质取得了易处理的优化模型, 并利用采样策略把有
限维空间的优化问题转化成二次规划问题. 值得指出的是利用支持函数的核化取得的模型仍然是凸优化问题, 这
使得模型可直接用于不定核函数. 在一系列的数据集上做了许多实验, 从实验可知: (1) TSFM 能获取交叉类型的
集值数据的内在结构; (2) 当集值对象的事例是非高斯分布时, TSFM 比基于高斯建模的分类方法取得更好的分类
性能; (3) TSFM 能有效地抑制集值数据的离群点; (4) 当集值对象包含少量高维事例时, TSFM 比基于概率建模的
方法 (UTSVM, SMM, SOCP) 取得更好的分类性能; (5) TSFM 包含超参数, 这些超参数是数据依赖的, 即不同的数
据集对应不同的最优超参数, 通常采用交叉验证来选择最优超参数. 尽管本文利用狄拉克测度的线性组合构成的
测度空间取得了有限维空间的优化模型, 但是否存在连续测度是模型的解是值得探索的问题.

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