Related papers: Projection depth for functional data: Theoretical …

This paper explores the generalized projective Riemann curvature in Finsler geometry, focusing on the properties of projectively equivalent Finsler metrics and the invariance of their curvature structures under projective transformations.…

Estimation of the level set of a function (i.e., regions where the function exceeds some value) is an important problem with applications in digital elevation mapping, medical imaging, astronomy, etc. In many applications, the function of…

A new classification of real functions and other related real objects defined within a compact interval is proposed. The scope of the classification includes normal real functions and distributions in the sense of Schwartz, referred to…

Metric projection operators can be defined in similar wayin Hilbert and Banach spaces. At the same time, they differ signifitiantly in their properties. Metric projection operator in Hilbert space is a monotone and nonexpansive operator. It…

Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…

In the era of big data, integrating multi-source functional data to extract a subspace that captures the shared subspace across sources has attracted considerable attention. In practice, data collection procedures often follow…

In general Banach spaces, the metric projection map lacks the powerful properties it enjoys in Hilbert spaces. There are a few generalized projections that have been proposed in order to resolve many of the deficiencies of the metric…

The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires the consideration of all possible one-dimensional projections. In this paper we propose a random depth…

Tukey's halfspace depth can be seen as a stochastic program and as such it is not guarded against optimizer's curse, so that a limited training sample may easily result in a poor out-of-sample performance. We propose a generalized halfspace…

We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition…

Feedforward generalizable models for implicit shape reconstruction from unoriented point cloud present multiple advantages, including high performance and inference speed. However, they still suffer from generalization issues, ranging from…

This paper proposes an extension of Random Projection Depth (RPD) to cope with multiple modalities and non-convexity on data clouds. In the framework of the proposed method, the RPD is computed in a reproducing kernel Hilbert space. With…

The notion of statistical depth has been extensively studied in multivariate and functional data over the past few decades. In contrast, the depth on temporal point process is still under-explored. The problem is challenging because a point…

This paper addresses problems in functional metric geometry that arise in the study of data such as signals recorded on geometric domains or on the nodes of weighted networks. Datasets comprising such objects arise in many domains of…

In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…

Single image surface normal estimation and depth estimation are closely related problems as the former can be calculated from the latter. However, the surface normals computed from the output of depth estimation methods are significantly…

A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…

The merit of projecting data onto linear subspaces is well known from, e.g., dimension reduction. One key aspect of subspace projections, the maximum preservation of variance (principal component analysis), has been thoroughly researched…

We introduce an intrinsic notion of Hoelder-Zygmund regularity for Colombeau generalized functions. In case of embedded distributions belonging to some Zygmund-Hoelder space this is shown to be consistent. The definition is motivated by the…

The behaviour of statistical relational representations across differently sized domains has become a focal area of research from both a modelling and a complexity viewpoint.Recently, projectivity of a family of distributions emerged as a…