Depth-based nonparametric description of functional data, with emphasis on use of spatial depth

Clustering functional data using forward search based on functional spatial ranks with medical applications

Cluster analysis of functional data is finding increasing application in the field of medical research and statistics. Here we introduce a functional version of the forward search methodology for the purpose of functional data clustering. The proposed forward search algorithm is based on the functional spatial ranks and is a data-driven non-parametric method. It does not require any preprocessing functional data steps, nor does it require any dimension reduction before clustering. The Forward Search Based on Functional Spatial Rank (FSFSR) algorithm identifies the number of clusters in the curves and provides the basis for the accurate assignment of each curve to its cluster. We apply it to three simulated datasets and two real medical datasets, and compare it with six other standard methods. Based on both simulated and real data, the FSFSR algorithm identifies the correct number of clusters. Furthermore, when compared with six standard methods used for clustering and classification, it records the lowest misclassification rate. We conclude that the FSFSR algorithm has the potential to cluster and classify functional data.

Analysis of the seasonal incidence of acute respiratory infections including influenza (ARI) in the Czech Republic - possible contribution of the functional data boxplot in epidemiology

AIMS

The detection of an epidemic outbreak is possible only if the baseline incidence level of a given disease is well defined. The determination of the baseline is complicated by the presence of epidemic outbreaks in historical data. The aim of the paper is to provide a new way of determining the baseline.

METHODS

The analyzed data containing weekly records on the incidence of acute respiratory infections including influenza (ARI) in the Czech Republic and its regions are taken from the nationwide surveillance system; data on 15 seasons from 2001/02 to 2015/16 are included. Functional boxplots of the data are constructed and five distinct methods (componentwise mean, componentwise median, median, trimmed mean, and adjusted mean) were used for the computation of the baseline level function.

RESULTS

It was shown that the methods based on functional data analysis could successfully overcome the problems that arise when the conventional methods are used for the determination of the baseline function.

CONCLUSION

The functional boxplot - a new statistical tool - can bring not only a transparent visualisation of comprehensive data, but can also help epidemiologists and other public health experts to determine the baseline incidence level of a given disease as well as to detect unusual epidemic seasons.