Related papers: A graph interpretation of the least squares rankin…
In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control…
We investigate the problem of estimating the structure factor, or spectra, of stationary spatial point processes. In the first part, we establish a minimax lower bound for this estimation problem, using an approach tailored to second-order…
In this paper, we consider the problem of diversity in ranking of the nodes in a graph. The task is to pick the top-k nodes in the graph which are both 'central' and 'diverse'. Many graph-based models of NLP like text summarization, opinion…
Given a set of n unit squares in the plane, the goal is to rank them in space in such a way that only few squares see each other vertically. We prove that ranking the squares according to the lexicographic order of their centers results in…
The divisor theory for graphs is compared to the theory of linear series on curves through the correspondence associating a curve to its dual graph. An algebro-geometric interpretation of the combinatorial rank is proposed, and proved in…
In several decision-making problems, alternatives should be ranked on the basis of paired comparisons between them. We present an axiomatic approach for the universal ranking problem with arbitrary preference intensities, incomplete and…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…
The problem of ranking is a multi-billion dollar problem. In this paper we present an overview of several production quality ranking systems. We show that due to conflicting goals of employing the most effective machine learning models and…
The method is based on the preliminary transformation of the traditionally used matrices or adjacency lists in the graph theory into refined projections free from redundant information, and their subsequent use in constructing shortest…
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…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…
Mathematical morphology provides a nonlinear framework for image and spatial data processing and analysis. Although there have been many successful applications of mathematical morphology to vector-valued images, such as color and…
The role of an expert in the decision-making process is crucial, as the final recommendation depends on his disposition, clarity of mind, experience, and knowledge of the problem. However, the recommendation also depends on their honesty.…
Feature selection is playing an increasingly significant role with respect to many computer vision applications spanning from object recognition to visual object tracking. However, most of the recent solutions in feature selection are not…
Strongly chordal digraphs are included in the class of chordal digraphs and generalize strongly chordal graphs and chordal bipartite graphs. They are the digraphs that admit a linear ordering of its vertex set for which their adjacency…
This paper provides a least squares formulation for the training of a 2-layer convolutional neural network using quadratic activation functions, a 2-norm loss function, and no regularization term. Using this method, an analytic expression…
The rankability of data is a recently proposed problem that considers the ability of a dataset, represented as a graph, to produce a meaningful ranking of the items it contains. To study this concept, a number of rankability measures have…
The best-worst method is an increasingly popular approach to solving multi-criteria decision-making problems. However, the usual prioritisation techniques may result in an ordinal violation if the best (worst) alternative identified in the…