Related papers: Enhanced preprocessed multi-step splitting iterati…
We introduce AlphaRank, an artificial intelligence approach to address the fixed-budget ranking and selection (R&S) problems. We formulate the sequential sampling decision as a Markov decision process and propose a Monte Carlo…
PageRank is an algorithm introduced in 1998 and used by the Google Internet search engine. It assigns a numerical value to each element of a set of hyperlinked documents (that is, web pages) within the World Wide Web with the purpose of…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov…
PageRank is a Web page ranking technique that has been a fundamental ingredient in the development and success of the Google search engine. The method is still one of the many signals that Google uses to determine which pages are most…
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher-order power…
In this paper, we propose three methods to solve the PageRank problem for the transition matrices with both row and column sparsity. Our methods reduce the PageRank problem to the convex optimization problem over the simplex. The first…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
It has recently been shown that ISTA, an unaccelerated optimization method, presents sparse updates for the $\ell_1$-regularized personalized PageRank problem, leading to cheap iteration complexity and providing the same guarantees as the…
The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Rayleigh quotient to an unconstrained difference formulation,…
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…
The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors…
PageRank (PR) is an algorithm originally developed by Google to evaluate the importance of web pages. Considering how deeply rooted Google's PR algorithm is to gathering relevant information or to the success of modern businesses, the…
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which…
PageRank is a well-known algorithm whose robustness helps set a standard benchmark when processing graphs and analytical problems. The PageRank algorithm serves as a standard for many graph analytics and a foundation for extracting graph…
An important method for search engine result ranking works by finding the principal eigenvector of the "Google matrix." Recently, a quantum algorithm for preparing this eigenvector and evidence of an exponential speedup for some scale-free…
Recently Ahmadi et al. (2021) and Tagliaferro (2022) proposed some iterative methods for the numerical solution of linear systems which, under the classical hypothesis of strict diagonal dominance, typically converge faster than the Jacobi…