Elastic Depths for Detecting Shape Anomalies in Functional Data

Harris, Trevor A. Le V.; Tucker, James D.; Li, Bo; Shand, Lyndsay

doi:10.1080/00401706.2020.1811156

Cited by 22 publications

(28 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[12] found 6 outliers, Ref. [17] also found 6 outliers (2 scale outliers and 4 mild shape outliers) and [18] found 4 outliers (3 due to amplitude and 1 due to phase) with the recommended value of k = 2, which is the boxplot multiplier, while 9 outliers are found with the classical k = 1.5. However, with our methodology, we detect 8 outliers (the results are stable, we obtain the same outliers with k = 5, 10 or 15).…”

Section: Detection Of Outliersmentioning

confidence: 92%

“…The Karcher means of the ten spirals and of the ten circumferences are computed with the new metric (β new , Equation (18)) and by using the distance proposed by [5] in the shape and size space S 2 . These means are shown in Figure 2, where the original curves are plotted in light blue;β new is plotted in black color andβ 2 , the Karcher-mean using the distance d 2 , is plotted in red color.…”

Section: Application To a Simulated Data Setmentioning

confidence: 99%

“…Although there are a variety of techniques for outlier detection for different types of data in any metric space based on nearest-neighbor techniques (see [16] for a detailed explanation), they have not been fully exploited in the shape and size space of curves. Some of the main references are based on box-plots of the distances to the median to detect outliers, such as [12,17], and more recently the method based on elastic depths proposed by [18].…”

Section: Detection Of Outliersmentioning

confidence: 99%

“…We compare our procedure with that introduced in [12,17,18] using the data sets of open curves used in [12,17], which are available from [20]. For the Example 1 considered in [17] formed by 70 spirals, Ref.…”

Section: Detection Of Outliersmentioning

confidence: 99%

“…For the Example 3 in [17] formed by 176 fiber tracts in the human brain extracted from a diffusion tensor magnetic resonance image (DT-MRI), we detect the same 11 outliers also detected by [12,17], and all are due to shape, with percentages of contribution due to shape of 90%. However, [18] with k = 2 returned 62 outliers (62 due to amplitude, 23 of them are also outliers due to phase), i.e., 35% of points of the sample are considered outliers.…”

Section: Detection Of Outliersmentioning

confidence: 99%

See 4 more Smart Citations

A New Geometric Metric in the Shape and Size Space of Curves in R n

et al. 2020

View full text Add to dashboard Cite

Shape analysis of curves in Rn is an active research topic in computer vision. While shape itself is important in many applications, there is also a need to study shape in conjunction with other features, such as scale and orientation. The combination of these features, shape, orientation and scale (size), gives different geometrical spaces. In this work, we define a new metric in the shape and size space, S2, which allows us to decompose S2 into a product space consisting of two components: S4×R, where S4 is the shape space. This new metric will be associated with a distance function, which will clearly distinguish the contribution that the difference in shape and the difference in size of the elements considered makes to the distance in S2, unlike the previous proposals. The performance of this metric is checked on a simulated data set, where our proposal performs better than other alternatives and shows its advantages, such as its invariance to changes of scale. Finally, we propose a procedure to detect outlier contours in S2 considering the square-root velocity function (SRVF) representation. For the first time, this problem has been addressed with nearest-neighbor techniques. Our proposal is applied to a novel data set of foot contours. Foot outliers can help shoe designers improve their designs.

show abstract

Section: Detection Of Outliersmentioning

confidence: 92%

Section: Application To a Simulated Data Setmentioning

confidence: 99%

Section: Detection Of Outliersmentioning

confidence: 99%

Section: Detection Of Outliersmentioning

confidence: 99%

Section: Detection Of Outliersmentioning

confidence: 99%

See 3 more Smart Citations

A New Geometric Metric in the Shape and Size Space of Curves in R n

et al. 2020

View full text Add to dashboard Cite

show abstract

Elastic functional changepoint detection of climate impacts from localized sources

Tucker,

Yarger

2023

Environmetrics

Self Cite

View full text Add to dashboard Cite

Detecting changepoints in functional data has become an important problem as interest in monitoring of climate phenomenon has increased, where the data is functional in nature. The observed data often contains both amplitude (‐axis) and phase (‐axis) variability. If not accounted for properly, true changepoints may be undetected, and the estimated underlying mean change functions will be incorrect. In this article, an elastic functional changepoint method is developed which properly accounts for these types of variability. The method can detect amplitude and phase changepoints which current methods in the literature do not, as they focus solely on the amplitude changepoint. This method can easily be implemented using the functions directly or can be computed via functional principal component analysis to ease the computational burden. We apply the method and its nonelastic competitors to both simulated data and observed data to show its efficiency in handling data with phase variation with both amplitude and phase changepoints. We use the method to evaluate potential changes in stratospheric temperature due to the eruption of Mt. Pinatubo in the Philippines in June 1991. Using an epidemic changepoint model, we find evidence of a increase in stratospheric temperature during a period that contains the immediate aftermath of Mt. Pinatubo, with most detected changepoints occurring in the tropics as expected.

show abstract

Visualisation and outlier detection for probability density function ensembles

Murph,

Strait,

Moran

et al. 2024

Stat

View full text Add to dashboard Cite

Exploratory data analysis (EDA) for functional data—data objects where observations are entire functions—is a difficult problem that has seen significant attention in recent literature. This surge in interest is motivated by the ubiquitous nature of functional data, which are prevalent in applications across fields such as meteorology, biology, medicine and engineering. Empirical probability density functions (PDFs) can be viewed as constrained functional data objects that must integrate to one and be nonnegative. They show up in contexts such as yearly income distributions, zooplankton size structure in oceanography and in connectivity patterns in the brain, among others. While PDF data are certainly common in modern research, little attention has been given to EDA specifically for PDFs. In this paper, we extend several methods for EDA on functional data for PDFs and compare them on simulated data that exhibit different types of variation, designed to mimic that seen in real‐world applications. We then use our new methods to perform EDA on the breakthrough curves observed in gas transport simulations for underground fracture networks.

show abstract

Elastic Depths for Detecting Shape Anomalies in Functional Data

Cited by 22 publications

References 27 publications

A New Geometric Metric in the Shape and Size Space of Curves in R n

A New Geometric Metric in the Shape and Size Space of Curves in R n

Elastic functional changepoint detection of climate impacts from localized sources

Visualisation and outlier detection for probability density function ensembles

Contact Info

Product

Resources

About