Related papers: Central subspace data depth

Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…

Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…

'Big' high-dimensional data are commonly analyzed in low-dimensions, after performing a dimensionality-reduction step that inherently distorts the data structure. For the same purpose, clustering methods are also often used. These methods…

We initiate the rigorous study of classification in semimetric spaces, which are point sets with a distance function that is non-negative and symmetric, but need not satisfy the triangle inequality. For metric spaces, the doubling dimension…

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…

Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation…

This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…

Cluster analysis, or clustering, plays a crucial role across numerous scientific and engineering domains. Despite the wealth of clustering methods proposed over the past decades, each method is typically designed for specific scenarios and…

Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing…

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…

The halfspace depth is a well studied tool of nonparametric statistics in multivariate spaces, naturally inducing a multivariate generalisation of quantiles. The halfspace depth of a point with respect to a measure is defined as the infimum…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept is similar to those from Chen, Gao and Ren (2017) and Zhang (2002). Rather than focusing, as in these earlier works, on…

Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…

In many problems in data mining and machine learning, data items that need to be clustered or classified are not points in a high-dimensional space, but are distributions (points on a high dimensional simplex). For distributions, natural…

Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…

Group equivariance can overly constrain models if the symmetries in the group differ from those observed in data. While common methods address this by determining the appropriate level of symmetry at the dataset level, they are limited to…

High dimensional data can have a surprising property: pairs of data points may be easily separated from each other, or even from arbitrary subsets, with high probability using just simple linear classifiers. However, this is more of a rule…