通过共同探索各种顺序的样本亲和关系来进行统一的张量集群
IEEE transactions on neural networks and learning systems
|August 14, 2024
概括
高阶亲缘关系通过克服度效应来改善对高维小样本数据的聚类. 统一张量集群 (UTC) 利用多种亲和力来增强子组的发现.
科学领域:
- 数据科学数据科学数据科学
- 机器学习 机器学习
- 计算统计学 计算统计学
背景情况:
- 传统的集群方法使用双向亲和度,由于度效应,对高维小样本 (HDLSS) 数据不够.
- 在HDLSS数据中的度效应扭曲了对式关系,导致不准确的样本分组和低于最佳的集群结果.
研究的目的:
- 提出一种使用高阶亲缘关系的新方法,以解决HDLSS数据集群中的传统方法的局限性.
- 开发一个统一的数学框架,以理解和利用不同顺序的亲和关系.
- 引入统一的张量集群 (UTC) 以提高复杂数据集的集群性能.
主要方法:
- 开发了可分解的高阶亲和关系,以建立不同亲和顺序之间的数学联系.
- 制定了一个统一的数学框架,整合了多个顺序的亲和关系.
- 拟议的统一张量集群 (UTC),一种方法,通过协同使用多个顺序的亲和关系来学习共识的低维嵌入.
主要成果:
- 证明高阶亲和关系在复杂数据中的样本关系的表征上比对对亲和关系更有效.
- 证明了不同的顺序亲和度的明智组合显著提高了聚类的有效性,特别是在高维数据.
- 在合成和现实数据集上验证了拟议的UTC方法,证实了其卓越的性能.
结论:
- 高阶亲和关系提供了一个强大的解决方案,通过减轻度效应来对HDLSS数据进行聚类.
- 拟议的统一张量集群 (UTC) 方法提供了一个有效和统一的框架,用于利用多个顺序的亲和关系.
- 这些发现突出了基于高阶亲和度的方法在机器学习和数据科学中推进聚类技术的潜力.
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