ABSTRACT

In this paper, we consider the classification problem of functional data including the sleeping energy expenditure (SEE) data, focusing on functional classification. Many existing classification rules are not effective in distinguishing the two classes of SEE data, because the trajectories of each observation have very different patterns for each class. It is often observed that some aspect of data such as the variability of paths is helpful in classification of functional data. To reflect this issue, we introduce a variable measuring the length of path in functional data and then propose a logistic model with fused lasso that considers the behavior of fluctuation of path as well as local correlations within each path. Our proposed model shows a significant improvement over some models used in the existing literature on the classification accuracy rate of functional data such as SEE data. We carry out simulation studies to show the finite sample performance and the gain that it makes in comparison with fused lasso without considering path length. With two more real datasets studied in some existing literature, we demonstrate that the new model achieves better or similar accuracy rate than the best accuracy rates reported in those studies.

摘要

在本文中，我们考虑了包括睡眠能量消耗（SEE）数据在内的功能数据的分类问题，重点是功能分类。许多现有的分类规则无法有效区分两类 SEE 数据，因为每个观察的轨迹对于每个类都有非常不同的模式。经常观察到数据的某些方面，例如路径的可变性，有助于功能数据的分类。为了反映这个问题，我们在功能数据中引入了一个测量路径长度的变量，然后提出了一个带有融合套索的逻辑模型，该模型考虑了路径波动的行为以及每条路径内的局部相关性。我们提出的模型在功能数据（例如 SEE 数据）的分类准确率方面比现有文献中使用的一些模型有显着改进。我们进行了模拟研究，以显示有限样本性能以及与融合套索相比它在不考虑路径长度的情况下获得的增益。通过在一些现有文献中研究的另外两个真实数据集，我们证明新模型比那些研究中报告的最佳准确率实现了更好或相似的准确率。