Rainbow Plots, Bagplots, and Boxplots for Functional Data

Abstract

We propose new tools for visualizing large numbers of functional data in the form of smooth curves or surfaces. The proposed tools include functional versions of the bagplot and boxplot, and make use of the first two robust principal component scores, Tukey's data depth and highest density regions. By-products of our graphical displays are outlier detection methods for functional data. We compare these new outlier detection methods with existing methods for detecting outliers in functional data and show that our methods are better able to identify the outliers.

Functional data analysis in shape analysis

“…Some additional points to study are as follows: Firstly, from the statistical point of view, the use of ICA in other statistical problems such as functional logistic regression or visualization (Hyndman and Shang, 2010), or the use of ICA in the construction of a semi-metric for use with non-parametric techniques (Ferraty and Vieu, 2006) (PCA-type semi-metrics could be replaced by ICA-type semi-metrics by just considering the ICA expansion instead of the PCA-based expansion. This is a very interesting field of study, since compared with PCA, ICA allows better observation of the underlying structure of the data.…”

The impact of special days in call arrivals forecasting: A neural network approach to modelling special days

“…In contrast to normal outliers, functional outliers differ not only in level, but also in shape over the duration of a fixed period. This means that outliers may lie outside the range of the vast majority of data or they may be within the range of the rest of the data but have a very different shape than other curves; the former referred to as magnitude outliers and the latter called shape outliers (Hyndman and Shang, 2010). In some cases outliers will exhibit a combination of both features.…”

Visualization tools for uncertainty and sensitivity analyses on thermal-hydraulic transients

“…This section presents two methods from an article by Hyndman and Shang 6) for the construction of "functional boxplots", which are both based on a dimension reduction. Classical boxplot for scalar variables is a very common statistical tool that allows summarizing the main information of a data sample: median, first and third quartiles, and an interquartile-based interval which define the limit of non-outliers data.…”

“…Two classes of methods have been identified as potential useful tools: a classical way to handle functional variables in statistics is to reduce their dimension via projection or regression techniques 4) ; another one is to consider the concept of band depth 5) . The first part of this article presents two methods introduced by Hyndman and Shang 6) , based on dimension reduction. The second part is dedicated to the functional boxplot of Sun and Genton 7) , which implies depth of band concept.…”