The one-mode projecting is extensively used to compress the bipartite networks. Since the onemode projection is always less informative than the bipartite representation, a proper weighting method is required to better retain the original information. In this article, inspired by the networkbased resource-allocation dynamics, we raise a weighting method, which can be directly applied in extracting the hidden information of networks, with remarkably better performance than the widely used global ranking method as well as collaborative filtering. This work not only provides a creditable method in compressing bipartite networks, but also highlights a possible way for the better solution of a long-standing challenge in modern information science: How to do personal recommendation?

Recommender systems use data on past user preferences to predict possible future likes and interests. A key challenge is that while the most useful individual recommendations are to be found among diverse niche objects, the most reliably accurate results are obtained by methods that recommend objects based on user or object similarity. In this paper we introduce a new algorithm specifically to address the challenge of diversity and show how it can be used to resolve this apparent dilemma when combined in an elegant hybrid with an accuracy-focused algorithm. By tuning the hybrid appropriately we are able to obtain, without relying on any semantic or context-specific information, simultaneous gains in both accuracy and diversity of recommendations.etting what you want, as the saying goes, is easy; the hard part is working out what it is that you want in the first place (1). Whereas information filtering tools like search engines typically require the user to specify in advance what they are looking for (2-5), this challenge of identifying user needs is the domain of recommender systems (5-8), which attempt to anticipate future likes and interests by mining data on past user activities.Many diverse recommendation techniques have been developed, including collaborative filtering (6, 9), content-based analysis (10), spectral analysis (11, 12), latent semantic models and Dirichlet allocation (13,14), and iterative self-consistent refinement (15-17). What most have in common is that they are based on similarity, either of users or objects or both: for example, e-commerce sites such as Amazon.com use the overlap between customers' past purchases and browsing activity to recommend products (18,19), while the TiVo digital video system recommends TV shows and movies on the basis of correlations in users' viewing patterns and ratings (20). The risk of such an approach is that, with recommendations based on overlap rather than difference, more and more users will be exposed to a narrowing band of popular objects, while niche items that might be very relevant will be overlooked.The focus on similarity is compounded by the metrics used to assess recommendation performance. A typical method of comparison is to consider an algorithm's accuracy in reproducing known user opinions that have been removed from a test dataset. An accurate recommendation, however, is not necessarily a useful one: real value is found in the ability to suggest objects users would not readily discover for themselves, that is, in the novelty and diversity of recommendation (21). Despite this, most studies of recommender systems focus overwhelmingly on accuracy as the only important factor [for example, the Netflix Prize (22) challenged researchers to increase accuracy without any reference to novelty or personalization of results]. Where diversification is addressed, it is typically as an adjunct to the main recommendation process, based on restrictive features such as semantic or other context-specific information (23, 24).The clear concern is that an alg...

The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has a great scientific depth and combines diverse research fields which makes it of interests for physicists as well as interdisciplinary researchers.

We show that to explain the growth of the citation network by preferential attachment (PA), one has to accept that individual nodes exhibit heterogeneous fitness values that decay with time. While previous PAbased models assumed either heterogeneity or decay in isolation, we propose a simple analytically treatable model that combines these two factors. Depending on the input assumptions, the resulting degree distribution shows an exponential, log-normal or power-law decay, which makes the model an apt candidate for modeling a wide range of real systems.Over the years, models with preferential attachment (PA) were independently proposed to explain the distribution of the number of species in a genus [1], the power-law distribution of the number of citations received by scientific papers [2], and the number of links pointing to World Wide Web (WWW) pages [3]. A theoretical description of this class of processes and the observation that they generally lead to power-law distributions are due to Simon [4]. Notably, the application of PA to WWW data by Barabási and Albert helped to initiate the lively field of complex networks [5]. Their network model, which stands at the center of attention of this work, was much studied and generalized to include effects such as presence of purely random connections [6], nonlinear dependence on the degree [7], node fitness [8], and others ([9], Chap. 8).Despite its success in providing a common roof for many theoretical models and empirical data sets, preferential attachment is still little developed to take into account the temporal effects of network growth. For example, it predicts a strong relation between a node's age and its degree. While such first-mover advantage [10] plays a fundamental role for the emergence of scale-free topologies in the model, it is a rather unrealistic feature for several real systems (e.g., it is entirely absent in the WWW [11] and significant deviations are found in citation data [10,12]). This motivates us to study a model of a growing network where a broad degree distribution does not result from strong time bias in the system. To this end we assign fitness to each node and assume that this fitness decays with time-we refer it as relevance henceforth. Instead of simply classifying the vertices as active or inactive, as done in [13,14], we use real data to investigate the relevance distribution and decay therein and build a model where decaying and heterogeneous relevance are combined.Models with decaying fitness values (''aging'') were shown to produce narrow degree distributions (except for very slow decay) [15] and widely distributed fitness values were shown to produce extremely broad distributions or even a condensation phenomenon where a single node attracts a macroscopic fraction of all links [16]. We show that when these two effects act together, they produce various classes of behavior, many of which are compatible with structures observed in real data sets.Before specifying a model and attempting to solve it, we turn to data to provide sup...

Complex networks have emerged as a simple yet powerful framework to represent and analyze a wide range of complex systems. The problem of ranking the nodes and the edges in complex networks is critical for a broad range of real-world problems because it affects how we access online information and products, how success and talent are evaluated in human activities, and how scarce resources are allocated by companies and policymakers, among others. This calls for a deep understanding of how existing ranking algorithms perform, and which are their possible biases that may impair their effectiveness. Well-established ranking algorithms (such as the popular Google's PageRank) are static in nature and, as a consequence, they exhibit important shortcomings when applied to real networks that rapidly evolve in time. The recent advances in the understanding and modeling of evolving networks have enabled the development of a wide and diverse range of ranking algorithms that take the temporal dimension into account. The aim of this review is to survey the existing ranking algorithms, both static and time-aware, and their applications to evolving networks. We emphasize both the impact of network evolution on well-established static algorithms and the benefits from including the temporal dimension for tasks such as prediction of real network traffic, prediction of future links, and identification of highly-significant nodes.Comment: 54 pages, 16 figure

Abstract. Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applications, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products-typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable.

-Information overload in the modern society calls for highly efficient recommendation algorithms. In this letter we present a novel diffusion-based recommendation model, with users' ratings built into a transition matrix. To speed up computation we introduce a Green function method. The numerical tests on a benchmark database show that our prediction is superior to the standard recommendation methods.Introduction. -The exponential growth of the Internet [1] and the World-Wide-Web [2] confronts us with the information overload: we face too many data and data sources, making us unable to find the relevant results. As a consequence we need automated ways to deal with the data. Recently, a lot of work has been done in this field. The two main directions of the research are correlationbased methods [3,4] and spectral methods [5]. A good overview of the achieved results can be found in [6,7].Despite the amount of work done, the problem is not satisfactorily exploited yet as both the prediction accuracy and the computational complexity can be further improved. In this letter we propose a new method based on diffusion of the users' opinions in an object-to-object network. This method can be used for any data where users evaluate objects on an integer scale. Using data from a real recommender application (GroupLens project) we show that the present model performs better than the standard recommendation methods. In addition, a Green function method is proposed here to further reduce computation in some cases.

-Most news recommender systems try to identify users' interests and news' attributes and use them to obtain recommendations. Here we propose an adaptive model which combines similarities in users' rating patterns with epidemic-like spreading of news on an evolving network. We study the model by computer agent-based simulations, measure its performance and discuss its robustness against bias and malicious behavior. Subject to the approval fraction of news recommended, the proposed model outperforms the widely adopted recommendation of news according to their absolute or relative popularity. This model provides a general social mechanism for recommender systems and may find its applications also in other types of recommendation.