Functional Data Clustering Via Functional Mahalanobis Distance

Abstract

As an exploratory data analysis method, functional data clustering aims to identify the underlying features of the observed data. In this context, this paper proposes a functional data clustering method based on functional Mahalanobis distance. As a distance-based non-parametric clustering model, the proposed method can effectively avoid the disadvantages of generative models and has excellent properties of decoupling and dimension standardization. Compared with other functional data clustering models, this method has lower computational complexity. In addition, the proposed method can be applied to any distance-based multivariate clustering method, thus generalizing it to the case of functional data. In practical data analysis, this paper compares the performance of this method with some other functional clustering methods, using k-means clustering as an example, and finds that it has better performance in terms of purity, adjusted Rand index, and computational speed. Finally, the idea of using Mahalanobis distance for functional data distance measurement can also be extended to construct kernel functions for measuring similarity between functional data samples, thus developing non-linear functional data analysis methods based on reproducing kernel theory.