Multivariate Outlier Detection in Precipitation Series by Using Two-Dimensional Correlation

The accuracy of descriptive statistics might be influenced by the existence of outliers in data sets. An observation which might not be considered as an outlier in the univariate case might be a multivariate outlier. Therefore, determination of outliers might make multivariate analysis more robust by providing an opportunity for making required corrections before modelling studies. This paper presents the implementation of the two-dimensional correlation method in the determination of multivariate outliers among the observations of six precipitation stations in Turkey. The two-dimensional correlation method considers the averages of the parts of the whole series instead of the average of the whole series and enables determination of the location of the outlier in the compared series. The obtained results point out that an outlier analysis for hydrologic variables should consider the two-directional behavior and the presented two-dimensional correlation method proves to be a strong alternative to be used in outlier and irregularity detection studies even with a limited number of available data. The 2DCorr software used in the study is freely provided as a supplementary material.

Multivariate Outlier Detection by Using Two-Dimensional Correlation

The accuracy of descriptive statistics might be influenced by the existence of outliers in data sets. An observation which might not be considered as an outlier in the univariate case might be a multivariate outlier. Therefore, determination of outliers might make multivariate analysis more robust by providing an opportunity for making required corrections before modelling studies. This paper presents the implementation of the two-dimensional correlation method in the determination of multivariate outliers among the observations of six precipitation stations in Turkey. The two-dimensional correlation method considers the averages of the parts of the whole series instead of the average of the whole series and enables determination of the location of the outlier in the compared series. The obtained results point out that an outlier analysis for hydrologic variables should consider the two-directional behavior and the presented two-dimensional correlation method proves to be a strong alternative to be used in outlier and irregularity detection studies even with a limited number of available data. The 2DCorr software used in the study is freely provided as a supplementary material.

Multivariate Outlier Detection in Applied Data Analysis: Global, Local, Compositional and Cellwise Outliers

Outliers are encountered in all practical situations of data analysis, regardless of the discipline of application. However, the term outlier is not uniformly defined across all these fields since the differentiation between regular and irregular behaviour is naturally embedded in the subject area under consideration. Generalized approaches for outlier identification have to be modified to allow the diligent search for potential outliers. Therefore, an overview of different techniques for multivariate outlier detection is presented within the scope of selected kinds of data frequently found in the field of geosciences. In particular, three common types of data in geological studies are explored: spatial, compositional and flat data. All of these formats motivate new outlier concepts, such as local outlyingness, where the spatial information of the data is used to define a neighbourhood structure. Another type are compositional data, which nicely illustrate the fact that some kinds of data require not only adaptations to standard outlier approaches, but also transformations of the data itself before conducting the outlier search. Finally, the very recently developed concept of cellwise outlyingness, typically used for high-dimensional data, allows one to identify atypical cells in a data matrix. In practice, the different data formats can be mixed, and it is demonstrated in various examples how to proceed in such situations.