Shape-based outlier detection in multivariate functional data

Outlier Detection for Pandemic-Related Data Using Compositional Functional Data Analysis

10.1007/978-3-030-78334-1_12 ◽

2021 ◽

pp. 251-266

Author(s):

Christopher Rieser ◽

Peter Filzmoser

Keyword(s):

Outlier Detection ◽

Functional Data Analysis ◽

Functional Data ◽

Subject Area ◽

Smooth Functions ◽

Related Data ◽

Relative Information ◽

The Subject ◽

Multivariate Functional Data ◽

Events Data

AbstractWith accurate data, governments can make the most informed decisions to keep people safer through pandemics such as the COVID-19 coronavirus. In such events, data reliability is crucial and therefore outlier detection is an important and even unavoidable issue. Outliers are often considered as the most interesting observations, because the fact that they differ from the data majority may lead to relevant findings in the subject area. Outlier detection has also been addressed in the context of multivariate functional data, thus smooth functions of several characteristics, often derived from measurements at different time points (Hubert et al. in Stat Methods Appl 24(2):177–202, 2015b). Here the underlying data are regarded as compositions, with the compositional parts forming the multivariate information, and thus only relative information in terms of log-ratios between these parts is considered as relevant for the analysis. The multivariate functional data thus have to be derived as smooth functions by utilising this relative information. Subsequently, already established multivariate functional outlier detection procedures can be used, but for interpretation purposes, the functional data need to be presented in an appropriate space. The methodology is illustrated with publicly available data around the COVID-19 pandemic to find countries displaying outlying trends.

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Multivariate Functional Data Visualization and Outlier Detection

Journal of Computational and Graphical Statistics ◽

10.1080/10618600.2018.1473781 ◽

2018 ◽

Vol 27 (4) ◽

pp. 923-934 ◽

Cited By ~ 12

Author(s):

Wenlin Dai ◽

Marc G. Genton

Keyword(s):

Outlier Detection ◽

Data Visualization ◽

Functional Data ◽

Multivariate Functional Data

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Detection of Anomalies in Water Networks by Functional Data Analysis

Mathematical Problems in Engineering ◽

10.1155/2018/5129735 ◽

2018 ◽

Vol 2018 ◽

pp. 1-13 ◽

Cited By ~ 8

Author(s):

Laura Millán-Roures ◽

Irene Epifanio ◽

Vicente Martínez

Keyword(s):

Data Analysis ◽

Outlier Detection ◽

Functional Data Analysis ◽

Functional Data ◽

Real Data ◽

Water Networks ◽

Archetypal Analysis ◽

Detection Techniques ◽

Second Stage ◽

Two Phases

A functional data analysis (FDA) based methodology for detecting anomalous flows in urban water networks is introduced. Primary hydraulic variables are recorded in real-time by telecontrol systems, so they are functional data (FD). In the first stage, the data are validated (false data are detected) and reconstructed, since there could be not only false data, but also missing and noisy data. FDA tools are used such as tolerance bands for FD and smoothing for dense and sparse FD. In the second stage, functional outlier detection tools are used in two phases. In Phase I, the data are cleared of anomalies to ensure that data are representative of the in-control system. The objective of Phase II is system monitoring. A new functional outlier detection method is also proposed based on archetypal analysis. The methodology is applied and illustrated with real data. A simulated study is also carried out to assess the performance of the outlier detection techniques, including our proposal. The results are very promising.

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