Analysis of Multivariate Extremes via Clustering Techniques

This study examines the integration of multivariate extreme analysis within clustering techniques, specifically focusing on spherical k-means clustering and spherical k-principal component clustering. We propose an approach to estimate linear factor models using spherical clustering methods, enhancing order selection through a novel penalized silhouette method for optimal cluster number determination. This penalized silhouette method addresses limitations in traditional order selection by incorporating a penalty term, improving the accuracy of cluster identification in high-dimensional data.

Furthermore, we demonstrate the utility of sparse spherical k-principal component clustering in identifying groups of concomitant extremes, which is crucial in contexts where extreme values play a dominant role, such as in risk management or environmental modeling. This sparse clustering approach allows for efficient dimension reduction and identifies relevant factors while preserving the interpretability of extreme groupings.

Our findings suggest that the proposed spherical clustering techniques provide robust solutions for analyzing and grouping multivariate extremes, offering an effective framework for high-dimensional data where conventional clustering methods may fall short. By enhancing the interpretability and precision of cluster detection, this research contributes valuable insights to fields requiring accurate analysis of extreme values, supporting improved data-driven decision-making.