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

Camille Mondon (), Thi Huong Trinh, Anne Ruiz-Gazen () and Christine Thomas-Agnan
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Camille Mondon: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Thi Huong Trinh: Thuongmai University - Partenaires INRAE
Anne Ruiz-Gazen: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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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.

Keywords: Outlier detection; Temperature distribution; Bayes spaces; Distributional data; Extreme weather; Functional data; Invariant coordinate selection (search for similar items in EconPapers)
Date: 2025-05-23
Note: View the original document on HAL open archive server: https://hal.science/hal-05081264v1
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Working Paper: ICS for complex data with application to outlier detection for density data (2025)
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