Title: Total variation depth and its decomposition for functional-data outlier detection
Authors: Huang Huang - NCAR (United States) [presenting]
Ying Sun - KAUST (Saudi Arabia)
Abstract: There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have involved infinite-dimensional objects such as functional data. We propose a notion of depth, the total variation depth, for functional data, which has many desirable features and is well suited for outlier detection. The proposed depth is of the form of an integral of a univariate depth function. We show that the novel formation of the total variation depth leads to useful decomposition associated with shape and magnitude outlyingness of functional data. Compared to magnitude outliers, shape outliers are often masked among the rest of samples and more difficult to identify. We then further develop an effective procedure and visualization tools for detecting both types of outliers, while naturally accounting for the correlation in functional data.