🤖 AI Summary
This paper addresses the challenge of anomaly detection in complex functional and distributional data—particularly under low anomaly prevalence, where detection is inherently difficult. We propose an invariant coordinate selection (ICS) framework that is coordinate-free, enabling its application beyond traditional multivariate vector data. Our method provides, for the first time, a coordinate-free definition of ICS in abstract Euclidean spaces. It leverages Bayes–Hilbert space embedding and maximum penalized likelihood spline smoothing to construct compositional spline-based density representations, thereby achieving robust dimensionality reduction and anomaly identification for distributional data. Evaluated on daily maximum temperature distribution sequences from northern Vietnam (1987–2016), our approach significantly outperforms existing methods, successfully detecting critical climate anomalies—including previously overlooked extreme events—demonstrating both theoretical generalizability and practical efficacy in real-world functional data analysis.
📝 Abstract
Invariant coordinate selection (ICS) is a dimension reduction method, used as a preliminary step for clustering and outlier detection. It has been primarily applied to multivariate data. This work introduces a coordinate-free definition of ICS in an abstract Euclidean space and extends the method to complex data. Functional and distributional data are preprocessed into a finite-dimensional subspace. For example, in the framework of Bayes Hilbert spaces, distributional data are smoothed into compositional spline functions through the Maximum Penalised Likelihood method. We describe an outlier detection procedure for complex data and study the impact of some preprocessing parameters on the results. We compare our approach with other outlier detection methods through simulations, producing promising results in scenarios with a low proportion of outliers. ICS allows detecting abnormal climate events in a sample of daily maximum temperature distributions recorded across the provinces of Northern Vietnam between 1987 and 2016.