Rainbow Plots, Bagplots, and Boxplots for Functional Data

By Rob J Hyndman, Han Lin Shang. 2010

323 citations recorded by the source corpus.

We propose new tools for visualizing large amounts of functional data in the form of smooth curves. The proposed tools include functional versions of the bagplot and boxplot, which 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 outliers. An R-package containing computer code and datasets is available in the online supplements.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8091181fc405c8aa8416adaffd0e0a2d11dafe86

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Citations in the corpus

Multivariate Functional Halfspace Depth (2014, methodology): “The resulting depth values can be visualized by means of the so-called rainbow plot (Hyndman and Shang 2010).”
A survey of functional principal component analysis (2014, methodology): “2009 , Hyndman & Shang 2010 ) .”
Large-Scale Unusual Time Series Detection (2015, methodology): “Our approach achieves a detection accuracy of over 80% (compared to 42% for baseline methods) and requires less than 0.5 seconds to process 1000 time series which is at least 3x faster than baseline algorithms.”
Anomaly detection by robust statistics (2017, background): “The literature on outlier detection in functional data is rather young, and several graphical tools have been developed 67–69 , mainly for univariate functions.”
Functional Data Analysis (2016, methodology): “Current approaches to deal with outliers and contamination and more generally visual exploration of functional data include exploratory box plots (Hyndman & Shang 2010; Sun & Genton 2011) and robust versions of FPCA (Crambes, Delsol & Laksaci 2008; Gervini 2008; Bali et al. 2011; Kraus & Panaretos…”
Applications of functional data analysis: A systematic review (2013, unknown): “Most recently, Ullah and Finch [23] used constrained penalized Table 1 Areas of application and the functional data analysis (FDA) features used in the 84 peer-review papers reporting application of FDA Year Field of study Outcome of interest FDA features Reference Smoothing Data reduction Clusterin”
Statistical Computing in Functional Data Analysis: The R Package fda.usc (2012, methodology): “The package rainbow (Shang and Hyndman 2012) for functional data representation, the package ftsa (Hyndman and Shang 2012) for functional time series analysis, the package refund (Crainiceanu, Reiss, Goldsmith, Huang, Huo, and Scheipl 2012) for functional penalized regression, the package fpca…”