A Novel Divide and Merge Approach for Improved Classification of Functional Data

To address the challenges posed by the complexities faced by traditional classification methods when dealing with high-dimensional functional data, we propose a divide and merge method based on B-spline for Functional Data Analysis (FDA). This method not only optimizes the classification performance for functional data, but also achieves dimension reduction and simplify the model by transitioning the learning problem from an infinite-dimensional vector space to a corresponding finite-dimensional parameter space. Unlike traditional knot placement that focus on a specific part or subset of dataset, through FDA techniques, this method first divides the input data according to categories,<br/>then determines the knot vector for each category, and dynamically merges knots to adapt to the inherent structure and trends of all kinds of labeled data. Finally, we calculate the common B-spline basis function for entire dataset by the merged knot vector, then encode the raw data into a smaller parameter space through B-spline approximation, and the classification procedure can be done through existing machine learning method, thereby enhancing the accuracy and efficiency of classification on functional data. Through four comparative experiments on real-world datasets, we demonstrate how this method significantly improves the classification accuracy over the existing functional classification methods while maintaining a moderate model complexity. Besides, our work reveals the impact of knot configuration on model interpretability and functional data analysis on dimensional reduction.