Related papers: Comments on lumping the Google matrix
A $k$-ranking of a graph $G$ is a labeling of its vertices from $\{1,\ldots,k\}$ such that any nontrivial path whose endpoints have the same label contains a larger label. The least $k$ for which $G$ has a $k$-ranking is the ranking number…
Graph representation learning plays an important role in many graph mining applications, but learning embeddings of large-scale graphs remains a problem. Recent works try to improve scalability via graph summarization -- i.e., they learn…
We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…
Representation learning is the first step in automating tasks such as research paper recommendation, classification, and retrieval. Due to the accelerating rate of research publication, together with the recognised benefits of…
Censor-Hillel et al. [PODC'15] recently showed how to efficiently implement centralized algebraic algorithms for matrix multiplication in the congested clique model, a model of distributed computing that has received increasing attention in…
Large Language Models (LLMs) have demonstrated exceptional performance in the task of text ranking for information retrieval. While Pointwise ranking approaches offer computational efficiency by scoring documents independently, they often…
In the paper we compare well known numerical methods of finding PageRank vector. We propose Markov Chain Monte Carlo method and obtain a new estimation for this method. We also propose a new method for PageRank problem based on the…
Search engine has become an inevitable tool for retrieving information from the WWW. Web researchers introduce lots of algorithms to modify search engine based on different features. Sometimes those algorithms are domain related, sometimes…
We study the behavior of network diffusions based on the PageRank random walk from a set of seed nodes. These diffusions are known to reveal small, localized clusters (or communities) and also large macro-scale clusters by varying a…
Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank…
Node embedding is a central topic in graph representation learning. Computational efficiency and scalability can be challenging to any method that requires full-graph operations. We propose sampling approaches to node embedding, with or…
Straggler nodes are well-known bottlenecks of distributed matrix computations which induce reductions in computation/communication speeds. A common strategy for mitigating such stragglers is to incorporate Reed-Solomon based MDS (maximum…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
In this paper, we introduce InstantEmbedding, an efficient method for generating single-node representations using local PageRank computations. We theoretically prove that our approach produces globally consistent representations in…
In this research, we improve upon the current state of the art in entity retrieval by re-ranking the result list using graph embeddings. The paper shows that graph embeddings are useful for entity-oriented search tasks. We demonstrate…
We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…
Many problems in machine learning can be expressed by means of a graph with nodes representing training samples and edges representing the relationship between samples in terms of similarity, temporal proximity, or label information. Graphs…