Related papers: A graph interpretation of the least squares rankin…
We present a physics-inspired method for inferring dynamic rankings in directed temporal networks - networks in which each directed and timestamped edge reflects the outcome and timing of a pairwise interaction. The inferred ranking of each…
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…
In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the…
While a plethora of research has been devoted to extoling the power and importance of data visualization, research on the effectiveness of data visualization methods from a human perceptual, and more generally, a cognitive standpoint…
Ranking is one of the most fundamental problems in machine learning with applications in many branches of computer science such as: information retrieval systems, recommendation systems, machine translation and computational biology.…
The problem of ranking/ordering instances, instead of simply classifying them, has recently gained much attention in machine learning. In this paper we formulate the ranking problem in a rigorous statistical framework. The goal is to learn…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
Integer data sets frequently appear in many applications in sciences and technology. To analyze these, integer low rank approximation has received much attention due to its capacity of representing the results in integers preserving the…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
Fluid-structure interaction models are used to study how a material interacts with different fluids at different Reynolds numbers. Examining the same model not only for different fluids but also for different solids allows to optimize the…
The minimum rank problem for a (simple) graph $G$ is to determine the smallest possible rank over all real symmetric matrices whose $ij$th entry (for $i\neq j$) is nonzero whenever $\{i,j\}$ is an edge in $G$ and is zero otherwise. This…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
Distributed algorithms, particularly Diffusion Least Mean Square, are widely favored for their reliability, robustness, and fast convergence in various industries. However, limited observability of the target can compromise the integrity of…
This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multi-agent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than…
Rational approximation appears in many contexts throughout science and engineering, playing a central role in linear systems theory, special function approximation, and many others. There are many existing methods for solving the rational…
For a simple graph, the minimum rank problem is to determine the smallest rank among the symmetric matrices whose off-diagonal nonzero entries occur in positions corresponding to the edges of the graph. Bounds on this minimum rank (and on…
Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these…