Academic literature on the topic 'Classical PageRank'

ADI methods can be generalized to solve numerically multidimensional fractional diffusion equations, which describe fluid flows through porous media better than classical diffusion equations. A new, unconditionally stable, second-order and well balanced in space, third-order in time ADI scheme has been constructed and its convergence accelerated by an extrapolation technique coupled with the PageRank algorithm.

It is now generally accepted that an article written by influential authors often deserves a higher ranking in information retrieval. However, it is a challenging task to determine an author’s relative influence since information about the author is, much of the time, inaccessible. Actually, in scientific publications, the author is an important metadata item, which has been widely used in previous studies. In this paper, we bring an optimized AuthorRank, which is a topic-sensitive algorithm calculated by citation context, into citation analysis for testing whether and how topical AuthorRank can replace or enhance classical PageRank for publication ranking. For this purpose, we first propose a PageRank with Priors (PRP) algorithm to rank publications and authors. PRP is an optimized PageRank algorithm supervised by the Labeled Latent Dirichlet Allocation (Labeled-LDA) topic model with full-text information extraction. We then compared four methods of generating an AuthorRank score, looking, respectively, at the first author, the last author, the most famous author, and the “average” author (of a publication). Additionally, two combination methods (Linear and Cobb–Douglas) of AuthorRank and PRP were compared with several baselines. Finally, as shown in our evaluation results, the performance of AuthorRank combined with PRP is better (p < 0.001) than other baselines for publication ranking.

It is now generally accepted that an article written by influential authors often deserves a higher ranking in information retrieval. However, it is a challenging task to determine an author’s relative influence since information about the author is, much of the time, inaccessible. Actually, in scientific publications, the author is an important metadata item, which has been widely used in previous studies. In this paper, we bring an optimized AuthorRank, which is a topic-sensitive algorithm calculated by citation context, into citation analysis for testing whether and how topical AuthorRank can replace or enhance classical PageRank for publication ranking. For this purpose, we first propose a PageRank with Priors (PRP) algorithm to rank publications and authors. PRP is an optimized PageRank algorithm supervised by the Labeled Latent Dirichlet Allocation (Labeled-LDA) topic model with full-text information extraction. We then compared four methods of generating an AuthorRank score, looking, respectively, at the first author, the last author, the most famous author, and the “average” author (of a publication). Additionally, two combination methods (Linear and Cobb–Douglas) of AuthorRank and PRP were compared with several baselines. Finally, as shown in our evaluation results, the performance of AuthorRank combined with PRP is better (p < 0.001) than other baselines for publication ranking.

Let S be a column stochastic matrix with at least one full row. Then S describes a Pagerank-like random walk since the computation of the Perron vector x of S can be tackled by solving a suitable M-matrix linear system Mx = y, where M = I − τ A, A is a column stochastic matrix and τ is a positive coefficient smaller than one. The Pagerank centrality index on graphs is a relevant example where these two formulations appear. Previous investigations have shown that the Euler- Richardson (ER) method can be considered in order to approach the Pagerank computation problem by means of preconditioning strategies. In this work, it is observed indeed that the classical power method can be embedded into the ER scheme, through a suitable simple preconditioner. Therefore, a new preconditioner is proposed based on fast Householder transformations and the concept of low complexity weakly stochastic algebras, which gives rise to an effective alternative to the power method for large-scale sparse problems. Detailed mathematical reasonings for this choice are given and the convergence properties discussed. Numerical tests performed on real-world datasets are presented, showing the advantages given by the use of the proposed Householder-Richardson method.

A numerical method for solving fractional partial differential equations (fPDEs) of the diffusion and reaction–diffusion type, subject to Dirichlet boundary data, in three dimensions is developed. Such fPDEs may describe fluid flows through porous media better than classical diffusion equations. This is a new, fractional version of the Alternating Direction Implicit (ADI) method, where the source term is balanced, in that its effect is split in the three space directions, and it may be relevant, especially in the case of anisotropy. The method is unconditionally stable, second-order in space, and third-order in time. A strategy is devised in order to improve its speed of convergence by means of an extrapolation method that is coupled to the PageRank algorithm. Some numerical examples are given.

Wireless sensor network (WSN) is a classical self-organizing communication network, and its topology evolution currently becomes one of the attractive issues in this research field. Accordingly, the problem is divided into two subproblems: one is to design a new preferential attachment method and the other is to analyze the dynamics of the network topology evolution. To solve the first subproblem, a revised PageRank algorithm, called Con-rank, is proposed to evaluate the node importance upon the existing node contraction, and then a novel preferential attachment is designed based on the node importance calculated by the proposed Con-rank algorithm. To solve the second one, we firstly analyze the network topology evolution dynamics in a theoretical way and then simulate the evolution process. Theoretical analysis proves that the network topology evolution of our model agrees with power-law distribution, and simulation results are well consistent with our conclusions obtained from the theoretical analysis and simultaneously show that our topology evolution model is superior to the classic BA model in the average path length and the clustering coefficient, and the network topology is more robust and can tolerate the random attacks.

In this study, we sorted out the research hotspots in sports science by bibliometric method and also used social network analysis to explore the relationship between knowledge networks and their scientific performance. We found 38 high-frequency keywords with obvious curricular nature or classical direction of sports science research and 4 high-frequency research groups. The topics of hotspots covered the secondary disciplines of sports science: physical education and training, national traditional sports, sports human science, and sports humanities and sociology. However, sports human science research is less; therefore, accelerating the research of sports human science is the focus of future research. Meanwhile, we use social network structure analysis (i.e., centrality, clustering coefficient, PageRank, and structural holes) to study the relationship between knowledge elements in knowledge networks and their scientific performance. In addition to betweenness centrality, the closeness centrality, clustering coefficient, and structural holes of knowledge elements are significantly and positively related to their influence. In the relationship between knowledge elements and productivity, betweenness centrality and closeness centrality show significant positive correlations, and clustering coefficient and structural hole show significant negative correlations. Therefore, knowledge networks can be used to predict the scientific performance of knowledge elements.

Large datasets from -omics studies need to be deeply investigated. The aim of this paper is to provide a new method (LEM method) for the search of transcriptome and metabolome connections. The heuristic algorithm here described extends the classical canonical correlation analysis (CCA) to a high number of variables (without regularization) and combines well-conditioning and fast-computing in “R.” Reduced CCA models are summarized in PageRank matrices, the product of which gives a stochastic matrix that resumes the self-avoiding walk covered by the algorithm. Then, a homogeneous Markov process applied to this stochastic matrix converges the probabilities of interconnection between genes, providing a selection of disjointed subsets of genes. This is an alternative to regularized generalized CCA for the determination of blocks within the structure matrix. Each gene subset is thus linked to the whole metabolic or clinical dataset that represents the biological phenotype of interest. Moreover, this selection process reaches the aim of biologists who often need small sets of genes for further validation or extended phenotyping. The algorithm is shown to work efficiently on three published datasets, resulting in meaningfully broadened gene networks.

The integration of the classical Web (of documents) with the emerging Web of Data is a challenging vision. In this paper we focus on an integration approach during searching which aims at enriching the responses of non-semantic search systems with semantic information, i.e. Linked Open Data (LOD), and exploiting the outcome for offering advanced exploratory search services which provide an overview of the search space and allow the users to explore the related LOD. We use named entities identified in the search results for automatically connecting search hits with LOD and we consider a scenario where this entity-based integration is performed at query time with no human effort and no a-priori indexing which is beneficial in terms of configurability and freshness. However, the number of identified entities can be high and the same is true for the semantic information about these entities that can be fetched from the available LOD. To this end, in this paper we propose a Link Analysis-based method which is used for ranking (and thus selecting to show) the more important semantic information related to the search results. We report the results of a survey regarding the marine domain with promising results, and comparative results that illustrate the effectiveness of the proposed (PageRank-based) ranking scheme. Finally, we report experimental results regarding efficiency showing that the proposed functionality can be offered even at query time.

Abstract Is it always beneficial to create a new relationship (have a new follower/friend) in a social network? This question can be formally stated as a property of the centrality measure that defines the importance of the actors of the network. Score monotonicity means that adding an arc increases the centrality score of the target of the arc; rank monotonicity means that adding an arc improves the importance of the target of the arc relatively to the remaining nodes. It is known that most centralities are both score and rank monotone on directed, strongly connected graphs. In this paper, we study the problem of score and rank monotonicity for classical centrality measures in the case of undirected networks: in this case, we require that score, or relative importance, improves at both endpoints of the new edge. We show that, surprisingly, the situation in the undirected case is very different, and in particular that closeness, harmonic centrality, betweenness, eigenvector centrality, Seeley’s index, Katz’s index, and PageRank are not rank monotone; betweenness and PageRank are not even score monotone. In other words, while it is always a good thing to get a new follower, it is not always beneficial to get a new friend.

ABSTRACT In the modern day , we are witnessing two complementary trends, exponential growth in data and shrinking of chip size. The Data is approaching to 44 zettabytes by 2020 and the chips are now available with 10nm technology. The hyperconnectivity between machine-to-machine and humanto- machine creates multi-dimensional data which is more complex. Our thesis addresses the quantum meta layer abstraction which provides the interface to the Application layer to design quantum and classical algorithms. The first part of the thesis addresses the quantum algorithms and second part address classical algorithms running on top of quantum meta layer. In the first part of our thesis we explored quantum stochastic algorithm for ranking Quantum Webpages, analogous to the classical Google PageRank. The architecture is a six-waveguide photonic lattice that runs finely-tuned quantum stochastic walk. The evolution of density matrix solves the ranking of quantum webpages. We force the photon stochastic walk for quantum PageRank by matching the entries of Google matrix with parameters of the Kossakowski-Lindblad master equation. We have done extensive simulation to observe the density matrix evolution with different parameter settings. We have used noise in the Kossakowski-Lindblad master equation to break the symmetry (reciprocity) property of quantum system, which helps in distinguishable measurement of the quantum PageRank. We next propose a new quantum deep learning with photonic lattice waveguide as a feedforward neural network. The proposed deep photonic neural network uses the quantum properties for learning. The hidden layers of our deep photonic neural network can be designed to learn object representation and mentains the quantum quantum properties for longer time for optimal learning. The second part of the thesis discusses the data based learning. We have used data graph method which captures the system representation. The proposed data graph model captures and encodes the data efficiently and then the data graph is updated and trained with new data to provide efficient predictions. The model retains the previously learned knowledge by transfer learning and improves it with new training. The proposed method is highly adaptive and scalable for different real-time scenarios. Data graph models the system where every node (object) is associated with data and if two objects are related then they are linked with a data edge. The proposed algorithm is an incremental algorithm which learns hidden objects and hidden relationships through the data pattern over time and updates the model accordingly. We have used algebraic graph transformation methods to trigger the mutation of the Data Graph. This new updated Data Graph behaves differently for the data it observes. We explore more into machine learning algorithms and have proposed a complete framework to predict the state of the system based on the system parameters. We have proposed the discretization of the data points using the symbol algebra and used Bayesian machine learning algorithm to select the best model to represent the new data. Symbol algebra provides unified language platform to different sensor data and it can process both, the discrete and continuous data. The portability of unified language platform in processing heterogeneous and homogeneous data increases the hypotheses space and Bayesian machine learning gets more degrees of freedom in choosing the best model with high measure of confidence level in the predicted state.

Influence is a concept found in nature and society and is related to the interdependency among a set of objects. In the context of a stock market, the variation in price of shares can influence the variation in price of other shares, leading to influential and influenced shares. In this work we leverage the notion of transfer entropy to build a network of shares and pairwise directed influence that is used to rank the most influential and influenced shares. Classical network centrality metrics such as PageRank and HITS are leveraged to rank the nodes. We apply our methodology to the shares in the greater stock market in Brazil, we rank nodes to find source and destination of influence in that market, while also comparing the different rankings and their correlation with traded volume.

In recent years, the axiomatic approach to centrality measures has attracted attention in the literature. However, most papers propose a collection of axioms dedicated to one or two considered centrality measures. In result, it is hard to capture the differences and similarities between various measures. In this paper, we propose an axiom system for four classic feedback centralities: Eigenvector centrality, Katz centrality, Katz prestige and PageRank. We prove that each of these four centrality measures can be uniquely characterized with a subset of our axioms. Our system is the first one in the literature that considers all four feedback centralities.