Related papers: Google matrix, dynamical attractors and Ulam netwo…
With the continuous popularity of deep learning and representation learning, fast vector search becomes a vital task in various ranking/retrieval based applications, say recommendation, ads ranking and question answering. Neural network…
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…
The aim of this paper is to study the finite-dimensional approximations of the nonautonomous lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z)\ (*)$. We show that the…
In this work, we investigate the presence of sub-diffusive behavior in the Chirikov-Taylor Standard Map. We show that the stickiness phenomena, present in the mixed phase space of the map setup, can be characterized as a Continuous Time…
Generative search engines (GEs) leverage large language models (LLMs) to deliver AI-generated summaries with website citations, establishing novel traffic acquisition channels while fundamentally altering the search engine optimization…
This note is focused on a novel technique in order to establish the boundedness in more regular spaces for global attractors of dissipative dynamical systems, without appealing to uniform-in-time estimates. As an application of the abstract…
Mobile robots frequently navigate on roadmaps, i.e., graphs where edges represent safe motions, in applications such as healthcare, hospitality, and warehouse automation. Often the environment is quasi-static, i.e., it is sufficient to…
We study the convergence of a variant of distributed gradient descent (DGD) on a distributed low-rank matrix approximation problem wherein some optimization variables are used for consensus (as in classical DGD) and some optimization…
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introduce a geometric description of the set of fixed rank matrices…
Recommendations are central to the utility of many websites including YouTube, Quora as well as popular e-commerce stores. Such sites typically contain a set of recommendations on every product page that enables visitors to easily navigate…
PageRank is a graph centrality metric that gives the importance of each node in a given graph. The PageRank algorithm provides important insights to understand the behavior of nodes through the connections they form with other nodes. It is…
We have proposed a model based upon flocking on a complex network, and then developed two clustering algorithms on the basis of it. In the algorithms, firstly a \textit{k}-nearest neighbor (knn) graph as a weighted and directed graph is…
Matrix factorization is a well-studied task in machine learning for compactly representing large, noisy data. In our approach, instead of using the traditional concept of matrix rank, we define a new notion of link-rank based on a…
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…
Google Earth (GE) has become a powerful tool for geological, geophysical and geographical modeling; yet GE can be accepted to acquire elevation data of terrain. In this paper, we present a real study case of building the discrete surface…
Recommender systems is one of the most successful AI technologies applied in the internet cooperations. Popular internet products such as TikTok, Amazon, and YouTube have all integrated recommender systems as their core product feature.…
The rank aggregation problem seeks to combine multiple rank orderings of the same set of candidates into a single consensus ordering. Such problems arise in diverse domains, including web search, employment, college admissions, and voting.…
Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged in learning problems. While most of the existing literature…
User interaction behavior is a valuable source of implicit relevance feedback. In Web image search a different type of search result presentation is used than in general Web search, which leads to different interaction mechanisms and user…
Gradient descent for matrix factorization exhibits an implicit bias toward approximately low-rank solutions. While existing theories often assume the boundedness of iterates, empirically the bias persists even with unbounded sequences. This…