Abstract
A robust approach for clustering functional directional data is proposed. The proposal adapts “impartial trimming” techniques to this particular framework. Impartial trimming uses the dataset itself to tell us which appears to be the most outlying curves. A feasible algorithm is proposed for its practical implementation justified by some theoretical properties. A “warping” approach is also introduced which allows including controlled time warping in that robust clustering procedure to detect typical “templates”. The proposed methodology is illustrated in a real data analysis problem where it is applied to cluster aircraft trajectories.
Highlights
Modern technologies are increasingly allowing us to measure phenomena continuously in time
A “warping” approach is introduced which allows including controlled time warping in that robust clustering procedure to detect typical “templates”
Impartial trimming has been already applied in Functional Cluster Analysis in García-Escudero and Gordaliza (2005), Cuesta-Albertos and Fraiman (2007) and, more recently, in Rivera-García et al (2019)
Summary
Modern technologies are increasingly allowing us to measure phenomena continuously in time. The term impartial means that it is the data itself the one that tell us which are the most anomalous curves This impartial trimming approach was introduced in Rousseeuw (1984), Gordaliza (1991) and Cuesta-Albertos et al (1997). Impartial trimming has been already applied in Functional Cluster Analysis in García-Escudero and Gordaliza (2005), Cuesta-Albertos and Fraiman (2007) and, more recently, in Rivera-García et al (2019). 7 presents a real data application aimed at clustering aircraft trajectories that motivated our interest in clustering functional directional data This real data example serves to illustrate all the material introduced in previous sections. Explaining why they exhibit such strange behavior, can be an interesting task
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