All online sharing systems gather data that reflects users' collective behaviour and their shared activities. This data can be used to extract different kinds of relationships, which can be grouped into layers, and which are basic components of the multidimensional social network proposed in the paper. The layers are created on the basis of two types of relations between humans, i.e. direct and object-based ones which respectively correspond to either social or semantic links between individuals. For better understanding of the complexity of the social network structure, layers and their profiles were identified and studied on two, spanned in time, snapshots of the Flickr population. Additionally, for each layer, a separate strength measure was proposed. The experiments on the Flickr photo sharing system revealed that the relationships between users result either from semantic links between objects they operate on or from social connections of these users. Moreover, the density of the social network increases in time. The second part of the study is devoted to building a social recommender system that supports the creation of new relations between users in a multimedia sharing system. Its main goal is to generate personalized suggestions that are continuously adapted to users' needs depending on the personal weights assigned to each layer in the multidimensional social network. The conducted experiments confirmed the usefulness of the proposed model.Comment: social recommender system;Multidimensional social network (MSN);Web 2.0;multi-layered social network;multimedia sharing system (MSS);recommender system;social network analysi

Abstract:We propose using five data-driven community detection approaches from social networks to partition the label space in the task of multi-label classification as an alternative to random partitioning into equal subsets as performed by RAkELd. We evaluate modularity-maximizing using fast greedy and leading eigenvector approximations, infomap, walktrap and label propagation algorithms. For this purpose, we propose to construct a label co-occurrence graph (both weighted and unweighted versions) based on training data and perform community detection to partition the label set. Then, each partition constitutes a label space for separate multi-label classification sub-problems. As a result, we obtain an ensemble of multi-label classifiers that jointly covers the whole label space. Based on the binary relevance and label powerset classification methods, we compare community detection methods to label space divisions against random baselines on 12 benchmark datasets over five evaluation measures. We discover that data-driven approaches are more efficient and more likely to outperform RAkELd than binary relevance or label powerset is, in every evaluated measure. For all measures, apart from Hamming loss, data-driven approaches are significantly better than RAkELd (α = 0.05), and at least one data-driven approach is more likely to outperform RAkELd than a priori methods in the case of RAkELd's best performance. This is the largest RAkELd evaluation published to date with 250 samplings per value for 10 values of RAkELd parameter k on 12 datasets published to date.

Information spreading in complex networks is often modeled as diffusing information with certain probability from nodes that possess it to their neighbors that do not. Information cascades are triggered when the activation of a set of initial nodes -seeds -results in diffusion to large number of nodes. Here, several novel approaches for seed initiation that replace the commonly used activation of all seeds at once with a sequence of initiation stages are introduced. Sequential strategies at later stages avoid seeding highly ranked nodes that are already activated by diffusion active between stages. The gain arises when a saved seed is allocated to a node difficult to reach via diffusion. Sequential seeding and a single stage approach are compared using various seed ranking methods and diffusion parameters on real complex networks. The experimental results indicate that, regardless of the seed ranking method used, sequential seeding strategies deliver better coverage than single stage seeding in about 90% of cases. Longer seeding sequences tend to activate more nodes but they also extend the duration of diffusion. Various variants of sequential seeding resolve the trade-off between the coverage and speed of diffusion differently.The process of making the complex decisions is difficult, so it is often worth making partial decisions and to track their consequences before proceeding further. Such strategy was proven useful in areas such as: general theory of decision making 1, 2 , financial markets 3, 4 , epidemiology 5 and marketing 6 . Here, we show that sequential, consecutive approach is also highly efficient in choosing the individuals, called seeds, that when activated will widely spread information or opinion in a social network. The current research on influence maximization and information spread in complex networks focuses mainly on single stage seed initiation. An exception is new product adaptation with early diffusion of product samples 7,8 to benefit from consumer responses and product spread. The main challenge is finding a method for selection of seeds to maximize the final spread of information within the network. If the total number of seeds to be used is limited, e.g. due to restricted budget, a typical approach is to rank all nodes in the network according to some criteria, select top n nodes as seeds and activate them at once to initiate the diffusion.Influence maximization problem in complex networks was defined by Kempe 9 . Analyses of various factors affecting the diffusion and social influence in complex networks include the efficiency of using different centrality measures for ranking influencers for selection 10 , impact of homophily for successful seeding 11 , and heterogeneous thresholds on congestion 12 , finding the critical initiator fraction beyond which the cascade becomes global 13 or importance of different network features in predicting spread 14 . Selection of initial seeds was also analyzed, including incentives for innovators to start diffusion 15 and the multi-market entry pe...

One of the most popular methods of estimating the complexity of networks is to measure the entropy of network invariants, such as adjacency matrices or degree sequences. Unfortunately, entropy and all entropy-based information-theoretic measures have several vulnerabilities. These measures neither are independent of a particular representation of the network nor can capture the properties of the generative process, which produces the network. Instead, we advocate the use of the algorithmic entropy as the basis for complexity definition for networks. Algorithmic entropy (also known as Kolmogorov complexity or -complexity for short) evaluates the complexity of the description required for a lossless recreation of the network. This measure is not affected by a particular choice of network features and it does not depend on the method of network representation. We perform experiments on Shannon entropy and -complexity for gradually evolving networks. The results of these experiments point to -complexity as the more robust and reliable measure of network complexity. The original contribution of the paper includes the introduction of several new entropy-deceiving networks and the empirical comparison of entropy and -complexity as fundamental quantities for constructing complexity measures for networks.