Related papers: Interval-Valued Rank in Finite Ordered Sets

Topological entropy is a widely studied indicator of chaos in topological dynamics. Here we give a generalized definition of topological entropy which may be applied to set-valued functions. We demonstrate that some of the well-known…

In problems involving approximation, completion, denoising, dimension reduction, estimation, interpolation, modeling, order reduction, regression, etc, we argue that the near-universal practice of assuming that a function, matrix, or tensor…

Data can be visually represented using visual channels like position, length or luminance. An existing ranking of these visual channels is based on how accurately participants could report the ratio between two depicted values. There is an…

Centrality measures have been defined to quantify the importance of a node in complex networks. The relative importance of a node can be measured using its centrality rank based on the centrality value. In the present work, we predict the…

The consecutive pattern poset is the infinite partially ordered set of all permutations where $\sigma\le\tau$ if $\tau$ has a subsequence of adjacent entries in the same relative order as the entries of $\sigma$. We study the structure of…

Rank-based inference methods are applied in various disciplines, typically when procedures relying on standard normal theory are not justifiable, for example when data are not symmetrically distributed, contain outliers, or responses are…

We consider the problem of exact low-rank matrix completion from a geometric viewpoint: given a partially filled matrix M, we keep the positions of specified and unspecified entries fixed, and study how the minimal completion rank depends…

Higher-order networks are efficient representations of sequential data. Unlike the classic first-order network approach, they capture indirect dependencies between items composing the input sequences by the use of \textit{memory-nodes}. We…

Overlap functions are a class of aggregation functions that measure the overlapping degree between two values. Interval-valued overlap functions were defined as an extension to express the overlapping of interval-valued data, and they have…

In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a…

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all…

We consider the problem of statistical inference for ranking data, specifically rank aggregation, under the assumption that samples are incomplete in the sense of not comprising all choice alternatives. In contrast to most existing methods,…

Many randomized optimization algorithms are rank-invariant, relying solely on the relative ordering of solutions rather than absolute fitness values. We introduce a stronger notion of rank landscape invariance: two problems are equivalent…

Instance ranking problems intend to recover the true ordering of the instances in a data set with a variety of applications in for example scientific, social and financial contexts. Robust statistics studies the behaviour of estimators in…

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth value to a proposition that the…

The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…

We propose a new data mining approach in ranking documents based on the concept of cone-based generalized inequalities between vectors. A partial ordering between two vectors is made with respect to a proper cone and thus learning the…

Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical…

For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…

Tree-based methods are powerful nonparametric techniques in statistics and machine learning. However, their effectiveness, particularly in finite-sample settings, is not fully understood. Recent applications have revealed their surprising…