Shi-yun Cao, Yan-qiu Zhou, Yan-ling Wan, Tao Zhang
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引用次数: 0
摘要
在本文中,我们考虑了二元功能数据的聚类问题,其中每个随机曲面由每个受试者重复记录的一组曲线组成。针对双变量功能数据,我们提出了基于边际功能主成分分析的 k-centres 曲面聚类方法,并提出了一种新的聚类标准,即同时考虑随机曲面及其在两个方向上的偏导数函数。此外,我们还考虑了另外两种聚类方法,即基于乘积函数主成分分析或双函数主成分分析的 k 中心曲面聚类方法。仿真结果表明,所提出的方法在正确分类率和调整后兰德指数方面都有不错的表现。通过对人类死亡率数据的实证分析,进一步说明了这些方法。
In this paper, we consider the clustering of bivariate functional data where each random surface consists of a set of curves recorded repeatedly for each subject. The k-centres surface clustering method based on marginal functional principal component analysis is proposed for the bivariate functional data, and a novel clustering criterion is presented where both the random surface and its partial derivative function in two directions are considered. In addition, we also consider two other clustering methods, k-centres surface clustering methods based on product functional principal component analysis or double functional principal component analysis. Simulation results indicate that the proposed methods have a nice performance in terms of both the correct classification rate and the adjusted rand index. The approaches are further illustrated through empirical analysis of human mortality data.
期刊介绍:
Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.