Revisit to functional data analysis of sleeping energy expenditure.

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.