Related papers: Linear response theory for Google matrix
As the calculation of centrality in complex networks becomes increasingly vital across technological, biological, and social systems, precise and scalable ranking methods are essential for understanding these networks. This paper introduces…
A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…
We present new algorithms for Personalized PageRank estimation and Personalized PageRank search. First, for the problem of estimating Personalized PageRank (PPR) from a source distribution to a target node, we present a new bidirectional…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
In this paper, we propose a new ranking method inspired from previous results on the diffusion approach to solve linear equation. We describe new mathematical equations corresponding to this method and show through experimental results the…
Graph neural networks (GNNs) have emerged as a powerful approach for solving many network mining tasks. However, learning on large graphs remains a challenge - many recently proposed scalable GNN approaches rely on an expensive…
Computing accurate low rank approximations of large matrices is a fundamental data mining task. In many applications however the matrix contains sensitive information about individuals. In such case we would like to release a low rank…
Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…
Neural network models are one of the most successful approaches to machine learning, enjoying an enormous amount of development and research over recent years and finding concrete real-world applications in almost any conceivable area of…
In this paper new results on personalized PageRank are shown. We consider directed graphs that may contain dangling nodes. The main result presented gives an analytical characterization of all the possible values of the personalized…
Weighted low rank approximation (WLRA) is an important yet computationally challenging primitive with applications ranging from statistical analysis, model compression, and signal processing. To cope with the NP-hardness of this problem,…
Neuroscientific theory suggests that dopaminergic neurons broadcast global reward prediction errors to large areas of the brain influencing the synaptic plasticity of the neurons in those regions. We build on this theory to propose a…
Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…
In recent years, randomized algorithms have established themselves as fundamental tools in computational linear algebra, with applications in scientific computing, machine learning, and quantum information science. Many randomized matrix…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
Mass-action kinetics is frequently used in systems biology to model the behaviour of interacting chemical species. Many important dynamical properties are known to hold for such systems if they are weakly reversible and have a low…
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…
Recent literature highlights the potential of graph-based approaches within large language model (LLM) retrieval-augmented generation (RAG) pipelines for answering queries of varying complexity, particularly those that fall outside the…
Graph neural networks (GNNs) can learn effective node representations that significantly improve link prediction accuracy. However, most GNN-based link prediction algorithms are incompetent to predict weak ties connecting different…