Related papers: Pythagorean Centrality for Data Selection
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Summarizing data samples by quantitative measures has a long history, with descriptive statistics being a case in point. However, as natural language processing methods flourish, there are still insufficient characteristic metrics to…
Hierarchical clustering is a popular method for analyzing data which associates a tree to a dataset. Hartigan consistency has been used extensively as a framework to analyze such clustering algorithms from a statistical point of view.…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
Symmetry plays a central role in accelerating symbolic computation involving polynomials. This chapter surveys recent developments and foundational methods that leverage the inherent symmetries of polynomial systems to reduce complexity,…
Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…
Extraction of structure, in particular of group symmetries, is increasingly crucial to understanding and building intelligent models. In particular, some information-theoretic models of parsimonious learning have been argued to induce…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
A \emph{strong coreset} for the mean queries of a set $P$ in ${\mathbb{R}}^d$ is a small weighted subset $C\subseteq P$, which provably approximates its sum of squared distances to any center (point) $x\in {\mathbb{R}}^d$. A \emph{weak…
We study quantum statistical inference tasks of hypothesis testing and their canonical variations, in order to review relations between their corresponding figures of merit---measures of statistical distance---and demonstrate the crucial…
We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has $\mathbb{R}^2$ as its ambient space, and is…
Pythagoras' theorem, the area of a triangle as one half the base times the height, and Heron's formula are amongst the most important and useful results of ancient Greek geometry. Here we look at all three in a new and improved light, using…
Centrality metrics aim to identify the most relevant nodes in a network. In literature, a broad set of metrics exists, either measuring local or global centrality characteristics. Nevertheless, when networks exhibit a high spectral gap, the…
Spherical symmetry arguments are used to produce a general device to convert identities and inequalities for the $p$th absolute moments of real-valued random variables into the corresponding identities and inequalities for the $p$th moments…
The spherical centroid body of a centrally-symmetric convex body in the Euclidean unit sphere is introduced. Two alternative definitions - one geometric, the other probabilistic in nature - are given and shown to lead to the same objects.…
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical…
Vertex centrality measures are a multi-purpose analysis tool, commonly used in many application environments to retrieve information and unveil knowledge from the graphs and network structural properties. However, the algorithms of such…
The mean shift algorithm is a non-parametric and iterative technique that has been used for finding modes of an estimated probability density function. It has been successfully employed in many applications in specific areas of machine…