相关论文: Efficiency analysis for the Perron vector of a rec…

We consider the multilinear pagerank problem studied in [Gleich, Lim and Yu, Multilinear Pagerank, 2015], which is a system of quadratic equations with stochasticity and nonnegativity constraints. We use the theory of quadratic vector…

Across a variety of ranking tasks, researchers use reciprocal rank to measure the effectiveness for users interested in exactly one relevant item. Despite its widespread use, evidence suggests that reciprocal rank is brittle when…

The computation of the sparse principal component of a matrix is equivalent to the identification of its principal submatrix with the largest maximum eigenvalue. Finding this optimal submatrix is what renders the problem…

We investigate an application of a mathematically robust minimization method -- the gradient method -- to the consistencization problem of a pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector…

The Peter principle has been recently investigated by means of an agent-based simulation and its validity has been numerically corroborated. It has been confirmed that, within certain conditions, it can really influence in a negative way…

Tubal scalars are usual vectors, and tubal matrices are matrices with every element being a tubal scalar. Such a matrix is often recognized as a third-order tensor. The product between tubal scalars, tubal vectors, and tubal matrices can be…

Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…

A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…

The standard approach for computing the trace of the inverse of a very large, sparse matrix $A$ is to view the trace as the mean value of matrix quadratures, and use the Monte Carlo algorithm to estimate it. This approach is heavily used in…

The Perron-Frobenius theorem of nonnegative matrices is a classical result on spectral theory of matrices, which has wide applications in many domains. In this paper, we give the Perron-Frobenius theorem for dual tensors, that is, a dual…

A framework to analyze inference performance in densely connected single-layer feed-forward networks is developed for situations where a given data set is composed of correlated patterns. The framework is based on the assumption that the…

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…

The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose…

Reinforcement learning has gained wide popularity as a technique for simulation-driven approximate dynamic programming. A less known aspect is that the very reasons that make it effective in dynamic programming can also be leveraged for…

It is tempting to assume that because effectiveness metrics have free choice to assign scores to search engine result pages (SERPs) there must thus be a similar degree of freedom as to the relative order that SERP pairs can be put into. In…

Search engine results pages are usually abstracted as binary relevance vectors and hence are categorical data, meaning that only a limited set of operations is permitted, most notably tabulation of occurrence frequencies, with determination…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object…

In this paper we analyze the PageRank of a complex network as a function of its personalization vector. By using this approach, a complete characterization of the existence and uniqueness of fixed points of PageRank of a graph is given in…