Related papers: Proximity Induced by Order Relations
Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…
S.B. Rao conjectured in 1971 that graphic degree sequences are well quasi ordered by a relation defined in terms of the induced subgraph relation. In 2008, M. Chudnovsky and P. Seymour proved this long standing Rao's Conjecture by giving…
Given a set of people and a set of events they attend, we address the problem of measuring connectedness or tie strength between each pair of persons given that attendance at mutual events gives an implicit social network between people. We…
Visual relationship detection, as a challenging task used to find and distinguish the interactions between object pairs in one image, has received much attention recently. In this work, we propose a novel visual relationship detection…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
Earlier papers \cite{VB2022,VB2023a,VB2023b} introduced the notions of a core and an index of a relation (an index being a special case of a core). A limited form of the axiom of choice was postulated -- specifically that all partial…
We derive an entropic uncertainty relation for generalized positive-operator-valued measure (POVM) measurements via a direct-sum majorization relation using Schur concavity of entropic quantities in a finite-dimensional Hilbert space. Our…
We explore the problems of classification of composite object (images, speech signals) with low number of models per class. We study the question of improving recognition performance for medium-sized database (thousands of classes). The key…
Visual relation detection methods rely on object information extracted from RGB images such as 2D bounding boxes, feature maps, and predicted class probabilities. We argue that depth maps can additionally provide valuable information on…
We consider the problem of computing reachable sets directly from noisy data without a given system model. Several reachability algorithms are presented for different types of systems generating the data. First, an algorithm for computing…
This paper proposes a new graph proximity measure. This measure is a derivative of network reliability. By analyzing its properties and comparing it against other proximity measures through graph examples, we demonstrate that it is more…
We develop the foundations of the theory of quasi-visual approximations of bounded metric spaces. Roughly speaking, these are sequences of covers of a given space for which the diameters of the sets in the covers shrink to zero and for…
The effect that weighted summands have on each other in approximations of $S=w_1S_1+w_2S_2+\cdots+w_NS_N$ is investigated. Here, $S_i$'s are sums of integer-valued random variables, and $w_i$ denote weights, $i=1,\dots,N$. Two cases are…
Rank-based linkage is a new tool for summarizing a collection $S$ of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between objects need be neither numerical nor symmetrical. All an…
Statistical pattern classification methods based on data-random graphs were introduced recently. In this approach, a random directed graph is constructed from the data using the relative positions of the data points from various classes.…
The focus of this article is to define the descriptively approximations in proximal relator spaces. Afterwards, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with…
A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new ``normalized information distance'', based on the noncomputable notion of…
A non-parametric k-nearest neighbour based entropy estimator is proposed. It improves on the classical Kozachenko-Leonenko estimator by considering non-uniform probability densities in the region of k-nearest neighbours around each sample…
Distinction among nearby poses and among symmetries of an object is challenging. In this paper, we propose a unified, group-theoretic approach to tackle both. Different from existing works which directly predict absolute pose, our method…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…