Related papers: Distances Between Partial Preference Orderings
For many years, the intuitions underlying partial-order planning were largely taken for granted. Only in the past few years has there been renewed interest in the fundamental principles underlying this paradigm. In this paper, we present a…
We consider a finite fields version of the Erd\H{o}s-Falconer distance problem for two different sets. In a certain range for the sizes of the two sets we obtain results of the conjectured order of magnitude.
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Representational similarity metrics typically force all units to be matched, making them susceptible to noise and outliers common in neural representations. We extend the soft-matching distance to a partial optimal transport setting that…
Given two distributions $\mathcal{P}$ and $\mathcal{Q}$ over a high-dimensional domain $\{0,1\}^n$, and a parameter $\varepsilon$, the goal of distance estimation is to determine the statistical distance between $\mathcal{P}$ and…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
New quantum distance is introduced as a half-sum of several singular values of difference between two density operators. This is, up to factor, the metric induced by so-called Ky Fan norm. The partitioned trace distances enjoy similar…
In higher education, data is collected that indicate the term(s) that a course is taken and when it is passed. Often, study plans propose a suggested course order to students. Study planners can adjust these based on detected deviations…
In combinatorial optimization, ordinal costs can be used to model the quality of elements whenever numerical values are not available. When considering, for example, routing problems for cyclists, the safety of a street can be ranked in…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
The Two Alternative Forced Choice (2AFC) paradigm offers advantages over the Mean Opinion Score (MOS) paradigm in psychophysics (PF), such as simplicity and robustness. However, when evaluating perceptual distance models, MOS enables direct…
The binary relation framework has been shown to be applicable to many real-life preference handling scenarios. Here we study preference contraction: the problem of discarding selected preferences. We argue that the property of minimality…
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…
In this study I proposed a filtering beliefs method for improving performance of Partially Observable Markov Decision Processes(POMDPs), which is a method wildly used in autonomous robot and many other domains concerning control policy. My…
Human preferences are not always represented via complete linear orders: It is natural to employ partially-ordered preferences for expressing incomparable outcomes. In this work, we consider decision-making and probabilistic planning in…
Modern parcel logistic networks are designed to ship demand between given origin, destination pairs of nodes in an underlying directed network. Efficiency dictates that volume needs to be consolidated at intermediate nodes in typical…
The ability to generate multiple plans is central to using planning in real-life applications. Top-quality planners generate sets of such top-cost plans, allowing flexibility in determining equivalent ones. In terms of the order between…
The natural pseudo-distance of spaces endowed with filtering functions is precious for shape classification and retrieval; its optimal estimate coming from persistence diagrams is the bottleneck distance, which unfortunately suffers from…
We study the shortcut Fr\'{e}chet distance, a natural variant of the Fr\'{e}chet distance, that allows us to take shortcuts from and to any point along one of the curves. The classic Fr\'echet distance is a bottle-neck distance measure and…