A Functional Data Classification Framework Based on Functional Sufficient Dimension Reduction and Model Averaging

Abstract

With the ever-evolving advancements in data collection and storage technologies, high-frequency data recorded in patterns that change over time have become increasingly common. In many application scenarios for this type of data, functional data classification has emerged as a prominent issue in the field of statistics. In light of this, this paper proposes a functional data classification model based on the functional sufficient dimensionality reduction method and the idea of model averaging. The proposed method utilizes techniques such as Functional Slice Inverse Regression (FSIR) and Functional Average Variance Estimation (FSAVE) to project an infinite-dimensional random function onto a function space spanned by a finite wiki function, ensuring that the original data's effective information for categorical variables is not lost. Additionally, the Bagging algorithm effectively addresses the overfitting and underfitting problems that arise in single predictive models, while employing model averaging instead of model selection to adaptively select the sufficient dimensionality reduction sub-directions. Notably, in the prediction stage, the number and types of base models are flexible. Empirical analysis demonstrates that the proposed method outperforms some comparative methods in terms of prediction accuracy and robustness.