ICS for complex data with application to outlier detection for density data

TL;DR

This paper extends invariant coordinate selection (ICS) to complex data types like functional and distributional data, enabling effective outlier detection in high-dimensional and complex datasets, with applications to climate data.

Contribution

It introduces a coordinate-free ICS framework for complex data and develops an outlier detection method with preprocessing strategies, validated through simulations and climate data analysis.

Findings

ICS effectively detects outliers in complex data.

Preprocessing parameters significantly influence detection results.

Application to climate data identified abnormal temperature events.

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.