基于深度与融合类信息的函数型数据重构方法

A depth-based and fusion class information reconstruction method for functional data

摘要

针对部分观测函数型数据,提出一种基于深度与融合类信息的重构方法。运用基于深度的重构方法以及从K均值聚类中获取的样本曲线类间信息,在不同分类情形下对每条部分观测样本曲线进行重构。然后,利用自加权集成学习算法动态赋权,将各类别下的重构曲线融合,得到最终的重构曲线。数值模拟和实例分析表明:当样本中部分观测样本曲线占比较大时,所提方法在均方预测误差准则下优于基于深度的重构方法及正则化回归方法;而在部分观测样本曲线占比较小时,正则化回归方法表现更优。

Abstract

A depth-based and fusion class information reconstruction method is proposed for partially observed functional data. By applying the depth-based reconstruction method and the inter-class information of sample curves derived from K-means clustering, each partially observed sample curve is reconstructed under different classification scenarios. Then, with the weights dynamically assigned by the self-weighted ensemble learning algorithm, final reconstructed curves are obtained by combining the reconstructed curves of each class. Simulation studies and case analysis show that the proposed method outperforms the depth-based reconstruction method and the regularized regression method under the mean-square prediction error criterion when the proportion of partially observed sample curves in the sample is large. Conversely, the regularized regression method performs better when the proportion of partially observed sample curves is small.

关键词

部分观测函数型数据 / 函数型数据重构 / 数据深度 / 类信息

Key words

partially observed functional data / reconstruction of functional data / data depth / class information

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基金资助

贵州省教育厅自然科学研究项目(黔教技[2023]012号)

贵州省教育厅自然科学研究项目(黔教技[2023]061号)