The ground truth about metadata and community detection in networks
01 May 2017-Science Advances (American Association for the Advancement of Science)-Vol. 3, Iss: 5, pp 1602548
TL;DR: It is proved that no algorithm can uniquely solve community detection, and a general No Free Lunch theorem for community detection is proved, which implies that there can be no algorithm that is optimal for all possible community detection tasks.
Abstract: Across many scientific domains, there is a common need to automatically extract a simplified view or coarse-graining of how a complex system's components interact. This general task is called community detection in networks and is analogous to searching for clusters in independent vector data. It is common to evaluate the performance of community detection algorithms by their ability to find so-called ground truth communities. This works well in synthetic networks with planted communities because these networks' links are formed explicitly based on those known communities. However, there are no planted communities in real-world networks. Instead, it is standard practice to treat some observed discrete-valued node attributes, or metadata, as ground truth. We show that metadata are not the same as ground truth and that treating them as such induces severe theoretical and practical problems. We prove that no algorithm can uniquely solve community detection, and we prove a general No Free Lunch theorem for community detection, which implies that there can be no algorithm that is optimal for all possible community detection tasks. However, community detection remains a powerful tool and node metadata still have value, so a careful exploration of their relationship with network structure can yield insights of genuine worth. We illustrate this point by introducing two statistical techniques that can quantify the relationship between metadata and community structure for a broad class of models. We demonstrate these techniques using both synthetic and real-world networks, and for multiple types of metadata and community structures.
Citations
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TL;DR: In this article, the authors present the distinctive features and challenges of dynamic community discovery and propose a classification of published approaches, which can be used to identify the set of approaches that best fit their needs.
Abstract: Several research studies have shown that complex networks modeling real-world phenomena are characterized by striking properties: (i) they are organized according to community structure, and (ii) their structure evolves with time. Many researchers have worked on methods that can efficiently unveil substructures in complex networks, giving birth to the field of community discovery. A novel and fascinating problem started capturing researcher interest recently: the identification of evolving communities. Dynamic networks can be used to model the evolution of a system: nodes and edges are mutable, and their presence, or absence, deeply impacts the community structure that composes them. This survey aims to present the distinctive features and challenges of dynamic community discovery and propose a classification of published approaches. As a “user manual,” this work organizes state-of-the-art methodologies into a taxonomy, based on their rationale, and their specific instantiation. Given a definition of network dynamics, desired community characteristics, and analytical needs, this survey will support researchers to identify the set of approaches that best fit their needs. The proposed classification could also help researchers choose in which direction to orient their future research.
270 citations
TL;DR: In this paper, the authors apply a variety of complex network analysis tools to uncover the structure of embodied energy flow network (EEFN) at global, regional and national level, based on environmentally extended input-output analysis (EEIOA).
216 citations
TL;DR: A survey of the metrics used for community detection and evaluation can be found in this paper, where the authors 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.
Abstract: 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.
189 citations
03 Apr 2017
TL;DR: A modification of an existing module detection algorithm that allowed it to focus on connections that are unexpected under a cost-reduction wiring rule and to identify modules from among these connections, which support the hypothesis that brain networks are composed of modules and provide additional insight into the function of those modules.
Abstract: Brain networks are expected to be modular. However, existing techniques for estimating a network's modules make it difficult to assess the influence of organizational principles such as wiring cost reduction on the detected modules. Here we present a modification of an existing module detection algorithm that allowed us to focus on connections that are unexpected under a cost-reduction wiring rule and to identify modules from among these connections. We applied this technique to anatomical brain networks and showed that the modules we detected differ from those detected using the standard technique. We demonstrated that these novel modules are spatially distributed, exhibit unique functional fingerprints, and overlap considerably with rich clubs, giving rise to an alternative and complementary interpretation of the functional roles of specific brain regions. Finally, we demonstrated that, using the modified module detection approach, we can detect modules in a developmental dataset that track normative patterns of maturation. Collectively, these findings support the hypothesis that brain networks are composed of modules and provide additional insight into the function of those modules.
152 citations
TL;DR: An exhaustive search of known methods is performed and a classification of them based on when and how structure and attributes are fused is proposed, which pays attention to available information which methods outperform others and which datasets and quality measures are used for their evaluation.
139 citations
References
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TL;DR: This article proposes a method for detecting communities, built around the idea of using centrality indices to find community boundaries, and tests it on computer-generated and real-world graphs whose community structure is already known and finds that the method detects this known structure with high sensitivity and reliability.
Abstract: A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.
14,429 citations
"The ground truth about metadata and..." refers background or methods in this paper
...Other common approaches to community detection [9, 17], suggest that the best divisions of this network have more than two communities [10, 18]....
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...However, it is worth noting at this point that Zachary’s original network and metadata differ from those commonly used for community detection [9]....
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...Modularity [9], one of the most popular quality functions used for community detection, serves as an instructive example of the blockmodel entropy significance test in two ways....
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...Some methods, for example, search only for assortative [9, 37] or disassortative [38] community structures, while other are more flexible and can find mixtures of assortative, disassortative, and core-periphery structures [15, 16, 20, 39] and allow for nodes to belong to multiple communities [36, 37]....
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...It is also possible that human errors are introduced when handling the data, exemplified by the widely used American college football network [9] of teams that played each other in one season, whose associated metadata representing each team’s conference assignment were collected during a different season [10]....
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TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging.
13,789 citations
17 Jun 1997
TL;DR: This work treats image segmentation as a graph partitioning problem and proposes a novel global criterion, the normalized cut, for segmenting the graph, which measures both the total dissimilarity between the different groups as well as the total similarity within the groups.
Abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.
11,827 citations
"The ground truth about metadata and..." refers background in this paper
...Other common approaches to community detection [9, 17], suggest that the best divisions of this network have more than two communities [10, 18]....
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...[17] Jianbo Shi and Jitendra Malik, “Normalized cuts and image segmentation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 888–905 (2000)....
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TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Abstract: The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
9,057 citations
"The ground truth about metadata and..." refers methods in this paper
...Community detection has been used productively in many applications, including identifying allegiances or personal interests in social networks [1, 2], biological function in metabolic networks [3, 4], fraud in telecommunications networks [5], and homology in genetic similarity networks [6]....
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...[2] Santo Fortunato, “Community detection in graphs,” Physics Reports, 486, 75–174 (2010)....
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TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
8,432 citations