Network Capacity Bound for Personalized PageRank in Multimodal Networks

In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we introduce a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. we finally state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1702.0373

Approaches to “Cold-Start” in recommender systems

The paper explores the possibilities of handling cold start problems for recommenders associated with document-map based search engines

Cyclic Bayesian Network : Markov Process Approach

The paper proposes a new interpretation of the concept of cyclic Bayesian Networks, based on stationary Markov processes over feature vector state transitions

Random graph generator for bipartite networks modeling

The purpose of this article is to introduce a new bipartite graph generation algorithm. Bipartite graphs consist of two types of nodes and edges join only nodes of different types. This data structure appears in various applications (e.g. recommender systems or text clustering). Both real-life datasets and formal tools enable us to evaluate only a limited set of properties of the algorithms that are used in such situations. Therefore, artificial datasets are needed to enhance development and testing of the algorithms. Our generator can be used to produce a wide range of synthetic datasets

Random graphs for performance evaluation of recommender systems

The purpose of this article is to introduce a new analytical framework dedicated to measuring performance of recommender systems. A standard approach is to assess the quality of a system by means of accuracy related statistics. However, the specificity of the environments in which recommender systems are deployed requires paying much attention to speed and memory requirements of the algorithms. Unfortunately, it is implausible to assess accurately the complexity of various algorithms with formal tools. This can be attributed to the fact that such analyses are usually based on an assumption of dense representation of underlying data structures. In real life, though, the algorithms operate on sparse data and are implemented with collections dedicated for them. Therefore, we propose to measure the complexity of recommender systems with artificial datasets that posses real-life properties. We utilize a recently developed bipartite graph generator to evaluate how the state-of-art recommender system behavior is determined and diversified by topological properties of the generated datasets

Rozproszony protokół enumeracji dla systemów z wartościowaniami

The paper presents a new algorithm for the problem of an enumeration protocol for nodes in a network. The new algorithm, contrary to previous ones, is local both in information access (neighbourhood only) and information stored (proportional to the number of neighbours). This property is achieved at the expense of the type of connectivity the network is assumed to exhibit.W pracy przedstawiono nowy algorytm enumeracji węzłów sieci. W odróżnieniu od dotychczasowych algorytmów jest on lokalny zarówno w sensie dostępu do informacji (uwzględnia się wyłącznie informacje pochodzące od sąsiadów aktualnie przetwarzanego węzła) jak i przechowywania informacji (ilość informacji jest proporcjonalna do liczby sąsiadów danego węzła). Cechę lokalności uzyskano zawężając rozważania do rodziny grafów triangulowanych, które odgrywają podstawową rolę w teorii sieci bayesowskich. Uogólnieniem tych ostatnich są systemy z wartościowaniami, nazywane też grafowymi systemami ekspertowymi, czyli struktury grafowe służące do reprezentacji niedeterministycznych zależności między zmiennymi (odpowiadają im węzły grafu)

Dealing with Non-Convexity in Geographic Routing in Smart Dust Networks

The paper proposes a new approach to greedy geographic routing for sensor networks with non-convex covering structure