In a smart grid environment, we study coalition formation of prosumers that aim at entering the energy market. It is paramount for the grid operation that the energy producers are able to sustain the grid demand in terms of stability and minimum production requirement. We design an algorithm that seeks to form coalitions that will meet both of these requirements: a minimum energy level for the coalitions and a steady production level which leads to finding uncorrelated sources of energy to form a coalition. We propose an algorithm that uses graph tools such as correlation graphs or clique percolation to form coalitions that meet such complex constraints. We validate the algorithm against a random procedure and show that, it not only performs better in term of social welfare for the power grid, but also that it is more robust against unforeseen production variations due to changing weather conditions for instance.
Presented in this way, the time-series clustering task seems very close to graph community detection. Communities in networks are indeed often seen as groups of nodes exhibiting high internal densities of links as well as a low density across communities, and several topology oriented techniques for finding communities are present in the litterature ( @cite_12 @cite_13 @cite_18 ). For our purpose where decorrelation is the closeness notion, such algorithms tend to have some difficulties because only a few inclusions of very high correlations can strongly affect the stability of a coalition. However, local cliques, where all nodes are linked, provide uncorrelated groups of nodes. There exists greedy heuristics based on cliques in the litterature such as clique percolation @cite_17 which realizes local optimizations of a fitness function and results in overlaping community structures. Detection of overlapping communities is actually a very active field of research, especially in social networks where a person might belong to several communities.
@cite_18 @cite_13 @cite_12 @cite_17
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Recently community detection has attracted much interest in social media to understand the collective behaviours of users and allow individuals to be modeled in the context of the group. Most existing approaches for community detection exploit either users' social links or their published content, aiming at discovering groups of densely connected or highly similar users. They often fail to find effective communities due to excessive noise in content, sparsity in links, and heterogenous behaviours of users in social media. Further, they are unable to provide insights and rationales behind the formation of the group and the collective behaviours of the users. To tackle these challenges, we propose to discover communities in a low- dimensional latent space in which we simultaneously learn the representation of users and communities. In particular, we integrated different social views of the network into a low-dimensional latent space in which we sought dense clusters of users as communities. By imposing a Laplacian regularizer into affiliation matrix, we further incorporated prior knowledge into the community discovery process. Finally community profiles were computed by a linear operator integrating the profiles of members. Taking the wellness domain as an example, we conducted experiments on a large scale real world dataset of users tweeting about diabetes and its related concepts, which demonstrate the effectiveness of our approach in discovering and profiling user communities. Graph clustering has been widely applied in exploring regularities emerging in relational data. Recently, the rapid development of network theory correlates graph clustering with the detection of community structure, a common and important topological characteristic of networks. Most existing methods investigate the community structure at a single topological scale. However, as shown by empirical studies, the community structure of real world networks often exhibits multiple topological descriptions, corresponding to the clustering at different resolutions. Furthermore, the detection of multiscale community structure is heavily affected by the heterogeneous distribution of node degree. It is very challenging to detect multiscale community structure in heterogeneous networks. In this paper, we propose a novel, unified framework for detecting community structure from the perspective of dimensionality reduction. Based on the framework, we first prove that the well-known Laplacian matrix for network partition and the widely-used modularity matrix for community detection are two kinds of covariance matrices used in dimensionality reduction. We then propose a novel method to detect communities at multiple topological scales within our framework. We further show that existing algorithms fail to deal with heterogeneous node degrees. We develop a novel method to handle heterogeneity of networks by introducing a rescaling transformation into the covariance matrices in our framework. Extensive tests on real world and artificial networks demonstrate that the proposed correlation matrices significantly outperform Laplacian and modularity matrices in terms of their ability to identify multiscale community structure in heterogeneous networks. Detecting and analyzing dense groups or communities from social and information networks has attracted immense attention over the last decade due to its enormous applicability in different domains. Community detection is an ill-defined problem, as the nature of the communities is not known in advance. The problem has turned even more complicated due to the fact that communities emerge in the network in various forms such as disjoint, overlapping, and hierarchical. Various heuristics have been proposed to address these challenges, depending on the application in hand. All these heuristics have been materialized in the form of new metrics, which in most cases are used as optimization functions for detecting the community structure, or provide an indication of the goodness of detected communities during evaluation. Over the last decade, a large number of such metrics have been proposed. Thus, there arises a need for an organized and detailed survey of the metrics proposed for community detection and evaluation. Here, we present a survey of the start-of-the-art metrics used for the detection and the evaluation of community structure. We also conduct experiments on synthetic and real networks to present a comparative analysis of these metrics in measuring the goodness of the underlying community structure. Community detection is an important task in network analysis. A community (also referred to as a cluster) is a set of cohesive vertices that have more connections inside the set than outside. In many social and information networks, these communities naturally overlap. For instance, in a social network, each vertex in a graph corresponds to an individual who usually participates in multiple communities. In this paper, we propose an efficient overlapping community detection algorithm using a seed expansion approach. The key idea of our algorithm is to find good seeds, and then greedily expand these seeds based on a community metric. Within this seed expansion method, we investigate the problem of how to determine good seed nodes in a graph. In particular, we develop new seeding strategies for a personalized PageRank clustering scheme that optimizes the conductance community score. An important step in our method is the neighborhood inflation step where seeds are modified to represent their entire vertex neighborhood. Experimental results show that our seed expansion algorithm outperforms other state-of-the-art overlapping community detection methods in terms of producing cohesive clusters and identifying ground-truth communities. We also show that our new seeding strategies are better than existing strategies, and are thus effective in finding good overlapping communities in real-world networks.