Integrating subdivision schemes into SVM for improved signal classification

The integration of advanced signal processing techniques into machine learning models has gained increasing attention due to its potential to improve model performance, particularly for classification tasks. Support Vector Machine (SVM) is widely recognized as a powerful tool for signal classification due to its robust mathematical foundation and effectiveness in handling high-dimensional data. Subdivision schemes, originally developed in computer graphics for geometric modeling, offer a novel and parametric approach to feature preprocessing by iteratively refining input data through an efficient computational procedure. This paper studies the impact of subdivision schemes on SVM performance in terms of class separability and provides insights into the relationship between feature transformation and SVM response. Specifically, it investigates the theoretical and empirical implications of applying subdivision schemes to input features in SVM-based classification. The conditions under which these schemes preserve or enhance class separability are analyzed, focusing on the tension parameter which governs both the smoothness properties of the limit curve and the subdivision rule at each iteration. An estimation method for the tension parameter from the training data is also provided. Experimental results, performed in the context of signal classification based on the wavelet scattering transform, demonstrate that the appropriate selection of the tension parameter of the scheme can significantly enhance class separability, highlighting that subdivision schemes are a promising tool for improving classification accuracy in machine learning workflows.