Related papers: Depth and depth-based classification with R-packag…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
The $DD\alpha$-classifier, a nonparametric fast and very robust procedure, is described and applied to fifty classification problems regarding a broad spectrum of real-world data. The procedure first transforms the data from their original…
In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…
John W. Tukey (1975) defined statistical data depth as a function that determines centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved…
Determining the representativeness of a point within a data cloud has recently become a desirable task in multivariate analysis. The concept of statistical depth function, which reflects centrality of an arbitrary point, appears to be…
Data depths are score functions that quantify in an unsupervised fashion how central is a point inside a distribution, with numerous applications such as anomaly detection, multivariate or functional data analysis, arising across various…
Laboratory scientists are well equipped with statistical tools for univariate data, yet many phenomena of scientific interest are time-variant or otherwise multidimensional. Functional data analysis is one way of approaching such data: by…
DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for…
A data depth measures the centrality of a point with respect to an empirical distribution. Postulates are formulated, which a depth for functional data should satisfy, and a general approach is proposed to construct multivariate data depths…
Data depth is a powerful nonparametric tool originally proposed to rank multivariate data from center outward. In this context, one of the most archetypical depth notions is Tukey's halfspace depth. In the last few decades notions of depth…
For computing the exact value of the halfspace depth of a point w.r.t. a data cloud of $n$ points in arbitrary dimension, a theoretical framework is suggested. Based on this framework a whole class of algorithms can be derived. In all of…
Data depth functions are a generalization of one-dimensional order statistics and medians to real spaces of dimension greater than one; in particular, a data depth function quantifies the centrality of a point with respect to a data set or…
We present a short tutorial and introduction to using the R package TDA, which provides some tools for Topological Data Analysis. In particular, it includes implementations of functions that, given some data, provide topological information…
The notion of data depth has long been in use to obtain robust location and scale estimates in a multivariate setting. The depth of an observation is a measure of its centrality, with respect to a data set or a distribution. The data depths…
The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite…
Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…
Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…
This paper studies how to generalize Tukey's depth to problems defined in a restricted space that may be curved or have boundaries, and to problems with a nondifferentiable objective. First, using a manifold approach, we propose a broad…
Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…
In this article we introduce a notion of depth functions for data types that are not given in standard statistical data formats. We focus on data that cannot be represented by one specific data structure, such as normed vector spaces. This…