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Louvain Method
The Louvain method for community detection is a method to extract non-overlapping communities from large networks created by Blondel ''et al''. from the University of Louvain (the source of this method's name). The method is a greedy optimization method that appears to run in time O(n \cdot \log n) where n is the number of nodes in the network. Modularity optimization The inspiration for this method of community detection is the optimization of modularity as the algorithm progresses. Modularity is a scale value between −0.5 (non-modular clustering) and 1 (fully modular clustering) that measures the relative density of edges inside communities with respect to edges outside communities. Optimizing this value theoretically results in the best possible grouping of the nodes of a given network. But because going through all possible iterations of the nodes into groups is impractical, heuristic algorithms are used. In the Louvain Method of community detection, first small communi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vincent Blondel
Vincent Daniel Blondel (born April 28, 1965) is a Belgian professor of applied mathematics and current rector of the University of Louvain (UCLouvain) and a visiting professor at the Massachusetts Institute of Technology (MIT). Blondel's research lies in the area of mathematical control theory and theoretical computer science. He is mostly known for his contributions in computational complexity in control, multi-agent coordination and complex networks. Education Blondel studied philosophy, mathematics, engineering and computer science in Louvain-la-Neuve, Grenoble, London and Oxford. He completed a master thesis in engineering at the Institut National Polytechnique de Grenoble, he holds a MSc in mathematics from Imperial College of Science and Technology and a degree in philosophy, a master's degree in engineering (summa cum laude) and a PhD in applied mathematics from Université catholique de Louvain. Career In 1993-1994 he was a Göran Gustafsson Fellow at the Royal I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Université Catholique De Louvain
The Université catholique de Louvain (also known as the Catholic University of Louvain, the English translation of its French name, and the University of Louvain, its official English name) is Belgium's largest French-speaking university. It is located in Louvain-la-Neuve, which was expressly built to house the university, and Brussels, Charleroi, Mons, Tournai and Namur. Since September 2018, the university has used the branding UCLouvain, replacing the acronym UCL, following a merger with Saint-Louis University, Brussels. The original University of Louvain (''Universitas Lovaniensis'') was founded at the centre of the historic town of Leuven (or ''Louvain'') in 1425, and abolished by the law in 1797 making it the first university in Belgium and the Low Countries. This university was the centre of Baianism, Jansenism and Febronianism in Europe. A new university, the State University of Louvain, was founded in 1817 and abolished by the law in 1835. A new catholic universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Community Structure
In the study of complex networks, a network is said to have community structure if the nodes of the network can be easily grouped into (potentially overlapping) sets of nodes such that each set of nodes is densely connected internally. In the particular case of ''non-overlapping'' community finding, this implies that the network divides naturally into groups of nodes with dense connections internally and sparser connections between groups. But ''overlapping'' communities are also allowed. The more general definition is based on the principle that pairs of nodes are more likely to be connected if they are both members of the same community(ies), and less likely to be connected if they do not share communities. A related but different problem is community search, where the goal is to find a community that a certain vertex belongs to. Properties In the study of networks, such as computer and information networks, social networks and biological networks, a number of different charac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modularity (networks)
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities). Networks with high modularity have dense connections between the nodes within modules but sparse connections between nodes in different modules. Modularity is often used in optimization methods for detecting community structure in networks. However, it has been shown that modularity suffers a resolution limit and, therefore, it is unable to detect small communities. Biological networks, including animal brains, exhibit a high degree of modularity. Motivation Many scientifically important problems can be represented and empirically studied using networks. For example, biological and social patterns, the World Wide Web, metabolic networks, food webs, neural networks and pathological networks are real world problems that can be mathematically represented and topologically studied to reveal some unexpected str ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kronecker Delta
In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: \delta_ = \begin 0 &\text i \neq j, \\ 1 &\text i=j. \end or with use of Iverson brackets: \delta_ = =j, where the Kronecker delta is a piecewise function of variables and . For example, , whereas . The Kronecker delta appears naturally in many areas of mathematics, physics and engineering, as a means of compactly expressing its definition above. In linear algebra, the identity matrix has entries equal to the Kronecker delta: I_ = \delta_ where and take the values , and the inner product of vectors can be written as \mathbf\cdot\mathbf = \sum_^n a_\delta_b_ = \sum_^n a_ b_. Here the Euclidean vectors are defined as -tuples: \mathbf = (a_1, a_2, \dots, a_n) and \mathbf= (b_1, b_2, ..., b_n) and the last step is obtained by using the values of the Kronecker delta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Network Science
Network science is an academic field which studies complex networks such as telecommunication networks, computer networks, biological networks, cognitive and semantic networks, and social networks, considering distinct elements or actors represented by ''nodes'' (or ''vertices'') and the connections between the elements or actors as ''links'' (or ''edges''). The field draws on theories and methods including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology. The United States National Research Council defines network science as "the study of network representations of physical, biological, and social phenomena leading to predictive models of these phenomena." Background and history The study of networks has emerged in diverse disciplines as a means of analyzing complex relational data. The earliest known paper in this f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-means Clustering
''k''-means clustering is a method of vector quantization, originally from signal processing, that aims to partition ''n'' observations into ''k'' clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid), serving as a prototype of the cluster. This results in a partitioning of the data space into Voronoi cells. ''k''-means clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem: the mean optimizes squared errors, whereas only the geometric median minimizes Euclidean distances. For instance, better Euclidean solutions can be found using k-medians and k-medoids. The problem is computationally difficult (NP-hard); however, efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation-maximization algorithm for mixtures of Gaussian distributions via an iterative refine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
