Outlier detection

Functional outlier detection is the identification of functions that do not seem to behave like the others in the dataset. There are several ways in which a function may be different from the others. For example, a function may have a different shape than the others, or its values could be more extreme. Thus, outlyingness is difficult to categorize exactly as each outlier detection method looks at different features of the functions in order to identify the outliers.

Each of the outlier detection methods in scikit-fda has the same API as the outlier detection methods of scikit-learn.

Boxplot Outlier Detector

One of the most common ways of outlier detection is given by the functional data boxplot. An observation is marked as an outlier if it has points \(1.5 \cdot IQR\) times outside the region containing the deepest 50% of the curves (the central region), where \(IQR\) is the interquartile range.

skfda.exploratory.outliers.BoxplotOutlierDetector(*)

Outlier detector using the interquartile range.

MSPlotOutlierDetector

Other more novel way of outlier detection is the one presented in the Magnitude-Shape plot, or MS-plot. It takes into account the magnitude and shape of the curves. Curves which have a very different shape or magnitude are considered outliers.

skfda.exploratory.outliers.MSPlotOutlierDetector(*)

Outlier detector using directional outlyingness.

For this method, it is necessary to compute the mean and variation of the directional outlyingness, which can be done with the following function.

skfda.exploratory.outliers.directional_outlyingness_stats(...)

Compute the directional outlyingness of the functional data.