Corpus ID: 237503181

A geometric perspective on functional outlier detection

@article{Herrmann2021AGP,
  title={A geometric perspective on functional outlier detection},
  author={Moritz Herrmann and Fabian Scheipl},
  journal={ArXiv},
  year={2021},
  volume={abs/2109.06849}
}
We consider functional outlier detection from a geometric perspective, specifically: for functional data sets drawn from a functional manifold which is defined by the data’s modes of variation in amplitude and phase. Based on this manifold, we develop a conceptualization of functional outlier detection that is more widely applicable and realistic than previously proposed. Our theoretical and experimental analyses demonstrate several important advantages of this perspective: It considerably… Expand

References

SHOWING 1-10 OF 54 REFERENCES
A Decomposition of Total Variation Depth for Understanding Functional Outliers
TLDR
It is shown that the novel formation of the total variation depth leads to useful decomposition associated with shape and magnitude outlyingness of functional data, which has many desirable features and is well suited for outlier detection. Expand
Shape outlier detection and visualization for functional data: the outliergram.
TLDR
The relationship between two measures of depth for functional data is exploited to help to visualize curves in terms of shape and to develop an algorithm for shape outlier detection. Expand
Unsupervised Functional Data Analysis via Nonlinear Dimension Reduction
TLDR
A theoretical framework is defined which allows to systematically assess specific challenges that arise in the functional data context, several nonlinear dimension reduction methods for tabular and image data to functional data are transferred, and it is shown that manifold methods can be used successfully in this setting. Expand
Functional outlier detection and taxonomy by sequential transformations
TLDR
This work proposes turning the shape outliers into magnitude outliers through data transformation and detecting them using the functional boxplot, and applies several transformations sequentially to provide a reasonable taxonomy for the flagged outliers. Expand
Discussion of “Multivariate functional outlier detection”
TLDR
The paper discusses carefully the problem of outlier detection in this setting and starts by establishing a classification of different outlying behaviours, and compares the proposed taxonomy of functional outliers with the classification currently adopted in the literature. Expand
Elastic Depths for Detecting Shape Anomalies in Functional Data
Abstract We propose a new family of depth measures called the elastic depths that can be used to greatly improve shape anomaly detection in functional data. Shape anomalies are functions that haveExpand
A Measure of Directional Outlyingness With Applications to Image Data and Video
TLDR
The proposed directional outlyingness (DO) measure accounts for skewness in the data and only requires computation time per direction and is applied to spectra, MRI images, and video surveillance data. Expand
Multivariate Functional Data Visualization and Outlier Detection
  • Wenlin Dai, M. Genton
  • Computer Science, Mathematics
  • Journal of Computational and Graphical Statistics
  • 2018
TLDR
A new graphical tool, the magnitude-shape (MS) plot, is proposed, for visualizing both the magnitude and shape outlyingness of multivariate functional data, which builds on the recent notion of functional directionalOutlyingness. Expand
Nonlinear manifold representations for functional data
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and ofExpand
A Geometric Approach to Visualization of Variability in Functional Data
TLDR
This work uses a recent functional data analysis framework, based on a representation of functions called square-root slope functions, to decompose observed variation in functional data into three main components: amplitude, phase, and vertical translation. Expand
...
1
2
3
4
5
...