Related papers: On an application of multidimensional arrays

High-multiplicity signatures at particle colliders can arise in Standard Model processes and beyond. With such signatures, difficulties often arise from the large dimensionality of the kinematic space. For final states containing a single…

Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on…

In this paper, a class of combinatorial identities is proved. A method is used which is based on the following rule: counting elements of a given set in two ways and making equal the obtained results. This rule is known as "counting in two…

We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…

This paper studies the optimal solution of the classical problem of detecting the location of multiple image occurrences in a two-dimensional, noisy measurement. Assuming the image occurrences do not overlap, we formulate this task as a…

Two general algorithms based on opportunity costs are given for approximating a revenue-maximizing set of bids an auctioneer should accept, in a combinatorial auction in which each bidder offers a price for some subset of the available…

Teaching requires distilling a rich category distribution into a small set of informative exemplars. Although prior work shows that humans consider both representativeness and diversity when teaching, the computational principles underlying…

This paper describes serial and parallel compositional models of multiple objects with part sharing. Objects are built by part-subpart compositions and expressed in terms of a hierarchical dictionary of object parts. These parts are…

We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation…

Bilinear systems of equations are defined, motivated and analyzed for solvability. Elementary structure is mentioned and it is shown that all solutions may be obtained as rank one completions of a linear matrix polynomial derived from…

We briefly discuss linear algebraic, combinatorial, and applied aspects of an exact model representation of binary arrays. As an illustration, we present two linear algebraic portraits of a string of characters.

Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…

Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…

Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluation of scatterplots such as scagnostics have been presented and applied to…

Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

Binary relations are an important abstraction arising in many data representation problems. The data structures proposed so far to represent them support just a few basic operations required to fit one particular application. We identify…

K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance…

We consider methods for aggregating preferences that are based on the resolution of discrete optimization problems. The preferences are represented by arbitrary binary relations (possibly weighted) or incomplete paired comparison matrices.…

Algorithms to generate various combinatorial structures find tremendous importance in computer science. In this paper, we begin by reviewing an algorithm proposed by Rohl that generates all unique permutations of a list of elements which…