Functional Data Analysis as the Feature Representation for the Classification Problem in one or two dimensional spaces

In response to the challenges posed by complex neural network models and the intricacies of high-dimensional data encountered by the traditional classification methods, we introduce a novel feature representation framework that incorporates Functional Data Analysis to enhance the classification performance. Initially, we introduce the concept of functional data and the applications on one or two-dimensional spaces. We then elaborate on the method of representing features from raw data using Functional Data Analysis techniques, includes B-spline curve or surface fitting, encoding the raw data as vectors into parameter spaces, and the classification task can then be processed in the parameter spaces. Experiments including one and two-dimensional spaces real-world datasets demonstrate the advantages of our proposed method over conventional approaches. The results indicate that our feature representation method based on Functional Data Analysis reduce the time and space complexity and improve the classification accuracy.