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Bipartite ranking is a fundamental ranking problem that learns to order relevant instances ahead of irrelevant ones. The pair-wise approach for bi-partite ranking construct a quadratic number of pairs to solve the problem, which is…
Dynamic arrays, also referred to as vectors, are fundamental data structures used in many programs. Modeling their semantics efficiently is crucial when reasoning about such programs. The theory of arrays is widely supported but is not…
This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…
The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…
Effectively inseparable pairs and their properties play an important role in the meta-mathematics of arithmetic and incompleteness. Different notions are introduced and shown in the literature to be equivalent to effective inseparability.…
Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\…
A learning algorithm for multilayer perceptrons is presented which is based on finding the principal components of a correlation matrix computed from the example inputs and their target outputs. For large networks our procedure needs far…
With automated measurements, large data sets can be assembled with relative ease. Often these data sets have a large degree of variance. Nonetheless, we hope to find groups within the data set with shared distinguishing characteristics.…
Improperly efficient solutions in the sense of Geoffrion in linear fractional vector optimization problems with unbounded constraint sets are studied in this paper. We give two sets of conditions which assure that all the efficient…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
Pairwise comparison matrices are widely used in Multicriteria Decision Making. This article applies incomplete pairwise comparison matrices in the area of sport tournaments, namely proposing alternative rankings for the 2010 Chess Olympiad…
We attack the problem of getting a strict ranking (i.e. a ranking without equally ranked items) of $n$ items from a pairwise comparisons matrix. Basic structures are described, a first heuristical approach based on a condition, the…
Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce…
In many situations, the choice of an adequate similarity measure or metric on the feature space dramatically determines the performance of machine learning methods. Building automatically such measures is the specific purpose of…
Markov-chain Monte Carlo algorithms rely on trial moves that are either rejected or accepted based on certain criteria. Here, we provide an efficient algorithm to generate random rotation matrices in four dimensions (4D) covering an…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
Complex networks are at the core of an intense research activity. However, in most cases, intricate and costly measurement procedures are needed to explore their structure. In some cases, these measurements rely on link queries: given two…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…