Related papers: Distance-based Depths for Directional Data
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…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to…
We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a…
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 propose new small-sphere distributional families for modeling multivariate directional data on $(\mathbb{S}^{p-1})^K$ for $p \ge 3$ and $K \ge 1$. In a special case of univariate directions in $\Re^3$, the new densities model random…
Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate…
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…
The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…
During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and…
Recent work on depth estimation up to now has only focused on projective images ignoring 360 content which is now increasingly and more easily produced. We show that monocular depth estimation models trained on traditional images produce…
Estimating the distance to objects is crucial for autonomous vehicles when using depth sensors is not possible. In this case, the distance has to be estimated from on-board mounted RGB cameras, which is a complex task especially in…
Zonoid depth, as a well-known ordering tool, has been widely used in multivariate analysis. However, since its depth value vanishes outside the convex hull of the data cloud, it suffers from the so-called `outside problem', which…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
Existing approaches to depth or disparity estimation output a distribution over a set of pre-defined discrete values. This leads to inaccurate results when the true depth or disparity does not match any of these values. The fact that this…