Functional Local Mean K-Nearest Neighbor: introducing a novel metric for improved algorithm performance

Classifying high-dimensional data is problematic due to the curse of dimensionality, which complicates the analysis and accuracy of classification models. This research introduces an innovative classification approach for functional data through a novel functional metric. This metric leverages both the original curves and their derivatives to ascertain the nearest neighbors for new queries. While the classical functional K-nearest neighbor (KNN) classifier is a straightforward and effective nonparametric method for pattern classification, its performance can be compromised by the neighborhood size k and the simplistic majority voting within k-neighborhoods, particularly in scenarios characterized by small sample sizes and the presence of outliers. To address these challenges, this study proposes a locality constrained based KNN, aimed at enhancing the classification efficacy of functional data. A novel K-nearest neighbor technique, utilizing neighborhood local mean, has been developed to improve classification accuracy and decrease dependency on the neighborhood size parameter k. The performance of the proposed Functional Locality Mean KNN (FLMKNN) algorithm is rigorously evaluated against functional KNN methodology across various real functional datasets commonly referenced in scholarly research. Comprehensive experiments underscore the superior performance and robustness of our approach to classifying functional data.