After the phenomenal success of the PageRank algorithm, many researchers have extended the PageRank approach to ranking graphs with richer structures in addition to the simple linkage structure. Indeed, in some scenarios we have to deal with networks modeling multi-parameters data where each node has additional features and there are important relationships between such features.This paper addresses the need of a systematic approach to deal with multi-parameter data. We propose models and ranking algorithms that can be applied to a large variety of networks (bibliographic data, patent data, twitter and social data, healthcare data). We focus on several aspects not previously addressed in the literature: (1) we propose different models for ranking multi-parameters data and a class of numerical algorithms for efficiently computing the ranking score of such models, (2) we analyze stability and convergence of the proposed numerical schemes and we derive a fast and stable ranking algorithm, (3) we analyze the robustness of our models when data are incomplete. The comparison of the rank on the incomplete data with the rank on the full structure shows that our models compute consistent rankings whose correlation is up to 60 when just 10 of the links of the attributes are maintained.
In previous papers from the same authors @cite_18 @cite_20 @cite_15 a model is introduced in the contest of bibliographic data which is similar to one of the models (the one we called Stiff model ) of this paper. In particular in @cite_18 an integrated model for ranking scientific publications together with authors and journals was presented. In that context, particular weighting strategies were implemented @cite_15 and an exponential decay factor was introduced @cite_20 to take into account aging of citations, i.e. the fact that if an old paper is not cited recently its importance should fade over the time. In this paper we further generalize the original ideas introducing several models and other classes making the model suitable also for ranking other multi parameters data (patents, healthcare, social data etc. ). The new models are more adequate for example to handle updating of the datasets which can be done at a lower cost than in the Stiff model. In addition, in this paper the weighting strategies are problem independent, while in the previous papers they were designed ad hoc for dealing with bibliographic items.
@cite_18 @cite_20 @cite_15
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Some integrated models for ranking scientific publications together with authors and journals are presented and analyzed. The models rely on certain adjacency matrices obtained from the relationships between citations, authors and publications, which together give a suitable irreducible stochastic matrix whose Perron vector provides the ranking. Some perturbation theorems concerning the Perron vectors of nonnegative irreducible matrices are proved. These theoretical results provide a validation of the consistency and effectiveness of our models. Several examples are reported together with some results obtained on a real set of data. In this paper, we first give a quick review of the most used numerical indicators for evaluating research, and then we present an integrated model for ranking scientific publications together with authors and journals. Our model relies on certain adiacency matrices obtained from the relations of citation, authorship and publication. These matrices are first normalized to obtain stochastic matrices and then are combined together by means of weights to form a suitable irreducible stochastic matrix whose dominant eigenvector provides the ranking. We discuss various strategies for choosing the weights and we show on large synthetic datasets how the choice of a weighting criteria rather than another can change the behavior of our ranking algorithm. An integrated model for ranking scientific publications together with authors and journals recently presented in [Bini, Del Corso, Romani, ETNA 2008] is closely analyzed. The model, which relies on certain adjacency matrices H,K and F obtained from the relations of citation, authorship and publication, provides the ranking by means of the Perron vector of a stochastic matrix obtained by combining H,K and F. Some perturbation theorems concerning the Perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented. The theoretical results confirm the consistency and effectiveness of our model. Some paradigmatic examples are reported together with some results obtained on a real set of data.