Robust archetypoids for anomaly detection in big functional data

Archetypoid analysis (ADA) has proven to be a successful unsupervised statistical technique to identify extreme observations in the periphery of the data cloud, both in classical multivariate data and functional data. However, two questions remain open in this field: the use of ADA for outlier detection and its scalability. We propose to use robust functional archetypoids and adjusted boxplot to pinpoint functional outliers. Furthermore, we present a new archetypoid algorithm for obtaining results from large data sets in reasonable time. Functional time series are occurring in many practical problems, so this paper focuses on functional data settings. The new algorithm for detecting functional anomalies, called CRO-FADALARA, can be used with both univariate and multivariate curves. Our proposal for outlier detection is compared with all the state-of-the-art methods in a controlled study, showing a good performance. Furthermore, CRO-FADALARA is applied to two large time series data sets, where outliers curves are discussed and the reduction in computational time is clearly stated. A third case study with a small ECG data set is discussed, given its importance in functional data scenarios. All data, R code and a new R package are freely available.