相关论文: A Correlation-Based Distance

Minimizing the Euclidean distance to a set arises frequently in applications. When the set is algebraic, a measure of complexity of this optimization problem is its number of critical points. In this paper we provide a general framework to…

Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…

In off-equilibrium dynamics we define a dynamical correlation length which is proportional to the size of the region in which the atoms move in a correlated way. General arguments indicate that this dynamical correlation length diverges at…

Given a dataset of finitely many elements $\mathcal{T} = \{\mathbf{x}_i\}_{i = 1}^N$, the goal of dataset condensation (DC) is to construct a synthetic dataset $\mathcal{S} = \{\tilde{\mathbf{x}}_j\}_{j = 1}^M$ which is significantly…

We seek for lines of minimal distance to finitely many points in the plane. The distance between a line and a set of points is defined by the L^p-norm, 1\leq p\leq \infty, of the vector of vertical or orthogonal distances from the single…

We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of…

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…

In this paper we tackle the issue of clustering trajectories of geolocalized observations. Using clustering technics based on the choice of a distance between the observations, we first provide a comprehensive review of the different…

Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using…

The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…

We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…

In machine learning, observation features are measured in a metric space to obtain their distance function for optimization. Given similar features that are statistically sufficient as a population, a statistical distance between two…

When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…

A compact metric space $(X, \rho)$ is given. Let $\mu$ be a Borel measure on $X$. By $r$-cluster we mean a measurable subset of $X$ with diameter at most $r$. A family of $k$ $2r$-clusters is called a $r$-cluster structure of order $k$ if…

Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…

It is shown that space-time may possess the differentiability properties of manifolds as well as the ultraviolet finiteness properties of lattices. Namely, if a field's amplitudes are given on any sufficiently dense set of discrete points…

We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…

The redshift-space distortion (RSD) in the observed distribution of galaxies is known as a powerful probe of cosmology. Observations of large-scale RSD have given tight constraints on the linear growth rate of the large-scale structures in…

A structural genetic model incorporating a modern understanding of the genome and common practice in genome-wide association studies is derived mathematically. The model shows the Haldane map distance as a direct consequence of the…

An R package SpatialPack that implements routines to compute point estimators and perform hypothesis testing of the spatial association between two stochastic sequences is introduced. These methods address the spatial association between…