roahd Package: Robust Analysis of High Dimensional Data

Abstract

The focus of this paper is on the open-source R package roahd (RObust Analysis of High dimensional Data), see Tarabelloni et al. (2017). roahd has been developed to gather recently proposed statistical methods that deal with the robust inferential analysis of univariate and multivariate functional data. In particular, efficient methods for outlier detection and related graphical tools, methods to represent and simulate functional data, as well as inferential tools for testing differences and dependency among families of curves will be discussed, and the associated functions of the package will be described in details.Even if the research in FDA dates back to 1970s -1980s, the first edition of Ramsay and Silverman (2005) and Ramsay and Silverman (2002) made the methods available to a larger audience with an enormous impact on the spread of this topic. The authors mainly cover explorative methods, parametric and semi-parametric approaches. Other important books on functional data analysis are Ferraty and Vieu (2006), Horvath andKokoszka (2012) and Kokoszka and Reimherr (2017). In addition to these monographs there is a vast quantity of scientific papers ranging from theoretical to applied techniques aimed at modelling and analysing functions.In the open-source R software development the number of packages focused on general functional data analysis is rapidly increasing. In particular, fda (Ramsay et al. ( 2014)) presents functions to implement many methods of functional data analysis, including smoothing, plotting and regression models (see Ramsay and Silverman (2005), Ramsay et al. ( 2009)). The package fda.usc (Febrero-Bande and Oviedo de la Fuente (2012)) carries out exploratory and descriptive analysis of functional data such as depth measurements or functional outliers detection, as well as functional regression models (univariate, nonparametric), basis representation and Functional Principal Component Analysis (FPCA). The package fdasrvf (Tucker (2017)) performs alignment, FPCA, and modeling of univariate and multivariate functions, allowing for elastic analysis of functional data through phase and amplitude separation. The core of the package fdapace (Dai et al. ( 2018)) is FPCA for sparsely or densely sampled random trajectories and time courses, via the Principal Analysis by Conditional Estimation (PACE) algorithm or numerical integration. The package rainbow (Shang and Hyndman ( 2019)) provides tools for functional data display, explorqatory analysis (plots, bagplots and boxplots) and outlier detection, while the package fds (cite(fds) contains 19 data sets with functional data. There are also a lot of other packages, focused on more specific methods for functional data analysis, like regression, classification and clustering, registering and aligning, studying time series of functional data (see Zeileis ( 2005))The focus of this paper is on the open-source R package roahd (RObust Analysis of High dimensional Data), see Tarabelloni et al. (2017). roahd has been developed to gather recently proposed stati...

Detecting and classifying outliers in big functional data

“…These methods are available in the mrfDepth package (Segaert et al, 2020). Finally, the roahd package (Ieva et al, 2019) contains an implementation of the outliergram method proposed in Arribas-Gil and Romo (2014), as well as its multivariate generalisation proposed in Ieva and Paganoni (2020).…”

Smoothing method for unit quaternion time series in a classification problem: an application to motion data

“…In order to understand the influence of noise on the performance of the different smoothing methods, we applied the methods described in “ Methods and experimental settings ” section to data to which different levels of noise had been added. We generated these noisy data sets by adding Gaussian noise to the logarithm of the curves in the original data set 22 . The quaternion time series were transformed to through the logarithm transformation and then Gaussian noise was added independently to each component.…”

A Geometric Perspective on Functional Outlier Detection

“…Figure A5 shows results for the MBD-MEI "Outliergram" by Aribas-Gil and Romo [41] (implementation: [42]) for shape outlier detection, and the magnitude-shape plot method of Dai and Genton [34] for the example datasets shown in Figures 5 and 8. Figures A6 and A7 show the results for the translation-phase-amplitude boxplots by Xie et al [15] and the elastic depth boxplot for shape outlier detection by Harris et al [9] for these datasets.…”

“…For the sake of clarity, only the results are summarized here. The figures for the various alternative methods can be found in Appendix D. Figure A5 shows the results for the MBD-MEI "Outliergram" by Aribas-Gil and Romo [41] (implementation: [42]) for shape outlier detection and the magnitude-shape plot method of Dai and Genton [34]. Figures A6 and A7 show the results for the translation-phase-amplitude boxplots by Xie et al [15] and the elastic depth boxplot for shape outlier detection by Harris et al [9].…”