Related papers: A Geometric Approach to Visualization of Variabili…
This article proposes a new graphical tool, the magnitude-shape (MS) plot, for visualizing both the magnitude and shape outlyingness of multivariate functional data. The proposed tool builds on the recent notion of functional directional…
Functional data analysis can be seriously impaired by abnormal observations, which can be classified as either magnitude or shape outliers based on their way of deviating from the bulk of data. Identifying magnitude outliers is relatively…
There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the…
With the development of data-monitoring techniques in various fields of science, multivariate functional data are often observed. Consequently, an increasing number of methods have appeared to extend the general summary statistics of…
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,…
Visualization and assessment of copula structures are crucial for accurately understanding and modeling the dependencies in multivariate data analysis. In this paper, we introduce an innovative method that employs functional boxplots and…
This paper introduces the sparse functional boxplot and the intensity sparse functional boxplot as practical exploratory tools. Besides being available for complete functional data, they can be used in sparse univariate and multivariate…
Angular observations, or observations lying on the unit circle, arise in many disciplines and require special care in their description, analysis, interpretation and visualization. We provide methods to construct concentric circular boxplot…
The direction of outlyingness is crucial to describing the centrality of multivariate functional data. Motivated by this idea, we generalize classical depth to directional outlyingness for functional data. We investigate theoretical…
The advent of high resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high resolution data require a functional approach. The starting point is a…
Data depth is an efficient tool for robustly summarizing the distribution of functional data and detecting potential magnitude and shape outliers. Commonly used functional data depth notions, such as the modified band depth and extremal…
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 of functional manifold components. These constitute…
This article introduces trimmed estimators for the mean and covariance function of general functional data. The estimators are based on a new measure of outlyingness or data depth that is well defined on any metric space, although this…
We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA).…
Surface, image and video data can be considered as functional data with a bivariate domain. To detect outlying surfaces or images, a new method is proposed based on the mean and the variability of the degree of outlyingness at each grid…
We propose two new outlier detection methods, for identifying and classifying different types of outliers in (big) functional data sets. The proposed methods are based on an existing method called Massive Unsupervised Outlier Detection…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which…
The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…