Related papers: On the Weighted Top-Difference Distance: Axioms, A…
We introduce a correlation coefficient that is designed to deal with a variety of ranking formats including those containing non-strict (i.e., with-ties) and incomplete (i.e., unknown) preferences. The correlation coefficient is designed to…
In machine learning, distance-based algorithms, and other approaches, use information that is represented by propositional data. However, this kind of representation can be quite restrictive and, in many cases, it requires more complex…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
Graphs are used in almost every scientific discipline to express relations among a set of objects. Algorithms that compare graphs, and output a closeness score, or a correspondence among their nodes, are thus extremely important. Despite…
Our main interest is the low-rank approximation of a matrix in R^m.n under a weighted Frobenius norm. This norm associates a weight to each of the (m x n) matrix entries. We conjecture that the number of approximations is at most min(m, n).…
Ranking algorithms find extensive usage in diverse areas such as web search, employment, college admission, voting, etc. The related rank aggregation problem deals with combining multiple rankings into a single aggregate ranking. However,…
We present an automatic method for weighting the contributions of preference functions used in disambiguation. Initial scaling factors are derived as the solution to a least-squares minimization problem, and improvements are then made by…
Whether the goal is to analyze voting behavior, locate facilities, or recommend products, the problem of translating between (ordinal) rankings and (numerical) utilities arises naturally in many contexts. This task is commonly approached by…
Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a…
Given a distance $D$ on a finite set $X$ with $n$ elements, it is interesting to understand how the ranking $R_x = z_1,z_2,\dots,z_n$ obtained by ordering the elements in $X$ according to increasing distance $D(x,z_i)$ from $x$, varies with…
This paper studies the design and analysis of approximation algorithms for aggregating preferences over combinatorial domains, represented using Conditional Preference Networks (CP-nets). Its focus is on aggregating preferences over…
Ranking algorithms are deployed widely to order a set of items in applications such as search engines, news feeds, and recommendation systems. Recent studies, however, have shown that, left unchecked, the output of ranking algorithms can…
This work focuses on active learning of distance metrics from relative comparison information. A relative comparison specifies, for a data point triplet $(x_i,x_j,x_k)$, that instance $x_i$ is more similar to $x_j$ than to $x_k$. Such…
This paper reports the use of a document distance-based approach to automatically expand the number of available relevance judgements when these are limited and reduced to only positive judgements. This may happen, for example, when the…
We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three…
Quantifying the distance between datasets is a fundamental question in mathematics and machine learning. We propose \textit{magnitude distance}, a novel distance metric defined on finite datasets using the notion of the \emph{magnitude} of…
Motivated by an application of eliciting users' preferences, we investigate the problem of learning hemimetrics, i.e., pairwise distances among a set of $n$ items that satisfy triangle inequalities and non-negativity constraints. In our…
Comparing the ranking of candidates by different voters is an important topic in social and information science with a high relevance from the point of view of practical applications. In general, ties and pairs of incomparable candidates…
We construct a class of real-valued nonnegative binary functions on a set of jointly distributed random variables, which satisfy the triangle inequality and vanish at identical arguments (pseudo-quasi-metrics). These functions are useful in…