A Functional Data Classification Model Utilizing Functional Mahalanobis Distance and Regenerative Kernel Methods

Abstract

The classification of functional data is an important research direction in modern data mining. In this paper, we propose a similarity measurement method for functional data based on functional Mahalanobis distance and regenerative kernel theory, considering the scenario where the predictor variable is a random function and the response variable is a categorical scalar. This method is then applied to functional kernel principal component analysis. During the classification phase, classic algorithms such as support vector machines and random forests can be combined to accomplish the task of classifying functional data. In empirical analysis, compared to the regenerative kernel based on Euclidean distance and the Euclidean distance regenerative kernel based on B-spline basis functions, the proposed method achieves better classification results. Furthermore, this similarity measurement can also be utilized in other machine learning algorithms based on regenerative kernel theory, thereby developing corresponding analysis methods for functional data.