Functional <i>k</i> -Nearest Neighbors algorithm based on the Fisher-Rao metric

In Functional Data Analysis (FDA), functional observations consist of two components: phase and amplitude.Therefore, it is crucial to conduct functional statistical analysis by considering not only amplitude variations but also phase variations.Among the current machine learning classification models, the functional k-Nearest Neighbors (kNN) method is a popular approach that does not account for phase variations.As a result, classification performance deteriorates when phase variations are present.In this paper, we propose an elastic functional k-nearest neighbors classification method that handles phase variations by incorporating the Fisher-Rao metric-based alignment technique.This model not only addresses several existing issues in the L 2 space but also effectively removes phase variations.We compare the classification performance using two simulated datasets and six real-world datasets to demonstrate the effectiveness of our model.