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The Hyperspherical Geometry of Community Detection: Modularity as a Distance [article]

Martijn Gösgens, Remco van der Hofstad, Nelly Litvak
2022 arXiv   pre-print
In that sense, modularity-based community detection methods can be seen as a subclass of a more general class of projection methods, which we define as the community detection methods that adhere to the  ...  We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the angular distance to some modularity vector over the set of clustering vectors.  ...  The work of MG and RvdH is supported in part by the Netherlands Organisation for Scientific Research (NWO) through the Gravitation NETWORKS grant no. 024.002.003.  ... 
arXiv:2107.02645v2 fatcat:t4gzuqhyyffjnb3ruv3g65zhgi

The Hyperspherical Geometry of Community Detection: Modularity as a Distance [article]

Martijn Gösgens, Remco van der Hofstad, Nelly Litvak
2021
We extend this geometry to a hypersphere and prove that maximizing modularity is equivalent to minimizing the angular distance to some modularity vector over the set of clustering vectors.  ...  The Louvain algorithm is currently one of the most popular community detection methods. This algorithm finds communities by maximizing a quantity called modularity.  ...  This work is supported in part by the Netherlands Organisation for Scientific Research (NWO) through the Gravitation NETWORKS grant no. 024.002.003.  ... 
doi:10.48550/arxiv.2107.02645 fatcat:wcbgpal5knfgfp2gd5a37d7owu

Latent Space Approaches to Community Detection in Dynamic Networks

Daniel K. Sewell, Yuguo Chen
2017 Bayesian Analysis  
While clustering has been done using this approach for static networks, this paper gives two methods of community detection within dynamic network data, building upon the distance and projection models  ...  Embedding dyadic data into a latent space has long been a popular approach to modeling networks of all kinds.  ...  Acknowledgements The authors thank the editor, the associate editor, and the referees for valuable suggestions.  ... 
doi:10.1214/16-ba1000 fatcat:ldmow6ldifc4hoq7npol7hh73m

Nearest Neighbor search in Complex Network for Community Detection [article]

Suman Saha, S.P. Ghrera
2015 arXiv   pre-print
In general, a community detection algorithm represents an objective function and captures the communities by optimizing it to extract the interesting communities for the user.  ...  Community detection in complex network is an important problem of much interest.  ...  Acknowledgments This work is supported by the Jaypee University of Information Technology. Author Contributions  ... 
arXiv:1511.07210v1 fatcat:7gkkxbgfb5edxdwld2oe3qtjzq

Modular neural network architecture for detection of operational problems on urban arterials

1997 Transportation Research Part A: Policy and Practice  
In the case of detecting different types of traffic operational problems, a modular architecture was used as shown in To demonstrate the potential of using a modular architecture as presented in an earlier  ...  A front-end processor performs the task of controller communications, and a host computer does overall management. UTCS does vehicle detection and reports the data to the TMC.  ...  This architecture was used to develop a modular neural network model to detect different types of operational problems on signalized surface street networks. 0  ... 
doi:10.1016/s0965-8564(97)88292-4 fatcat:fq7qjflznndnrakg5et2d4yevq

Machine Learning Analysis of Complex Networks in Hyperspherical Space [article]

María Pereda, Ernesto Estrada
2018 arXiv   pre-print
We use one of the geometric parameters of this embedding, namely the angle between the position vectors of the nodes in the hyperspheres, to extract structural information from networks.  ...  A complex network is a condensed representation of the relational topological framework of a complex system.  ...  Fig. 4 : 4 (a) Illustration of a caveman graph in which modularity-based methods fail to detect the correct number of communities due to their merging of pairs of close clusters (clusters of nodes are  ... 
arXiv:1804.05960v1 fatcat:e3r3fx77arhw5orwvlx3xwbax4

The Geometry of Continuous Latent Space Models for Network Data

Anna L. Smith, Dena M. Asta, Catherine A. Calder
2019 Statistical Science  
In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks  ...  In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic  ...  ACKNOWLEDGMENTS Smith and Calder were partially supported by grants from the National Science Foundation (NSF DMS-1209161), the National Institutes of Health (NIH R01 HD088545) and The Ohio State University  ... 
doi:10.1214/19-sts702 pmid:33235407 pmcid:PMC7682928 fatcat:63innsk5xjhkbj5cru5buhhfsu

The Geometry of Continuous Latent Space Models for Network Data [article]

Anna L. Smith, Dena M. Asta, Catherine A. Calder
2019 arXiv   pre-print
In addition to reviewing the literature on continuous latent space models from a geometric perspective, we highlight the important role the geometry of the latent space plays on properties of networks  ...  In this way, these models provide a probabilistic framework for embedding network nodes in a continuous space equipped with a geometry that facilitates the description of dependence between random dyadic  ...  ACKNOWLEDGEMENTS Smith and Calder were partially supported by grants from the National Science Foundation (NSF DMS-1209161), the National Institutes of Health (NIH R01 HD088545), and The Ohio State University  ... 
arXiv:1712.08641v2 fatcat:ha6z2rspznhnzdzao55i7hsp6i

Network Geometry [article]

Marian Boguna, Ivan Bonamassa, Manlio De Domenico, Shlomo Havlin, Dmitri Krioukov, M. Angeles Serrano
2020 arXiv   pre-print
Yet the geometry induced by shortest path distances in a network is definitely not its only geometry.  ...  Network geometry is also of great utility in a variety of practical applications, ranging from the understanding how the brain works, to routing in the Internet.  ...  The colours of the nodes correspond to the community structure detected by the Louvain algorithm.  ... 
arXiv:2001.03241v2 fatcat:n3kqsgmpxffr5klzoihs525mrm

Spherical harmonic shape descriptors of nodal force demands for quantifying spatial truss connection complexity [article]

Keith J. Lee, Renaud Danhaive, Caitlin T. Mueller
2021 arXiv   pre-print
By representing nodal forces as a geometric object, we leverage the spherical harmonic shape descriptor, developed for applications in computational geometry, to characterize each node by a rotation and  ...  The connections of a spatial truss structure play a critical role in the safe and efficient transfer of axial forces between members.  ...  Statements and Declarations The authors have no competing interests, financial or otherwise, pertaining to this work.  ... 
arXiv:2111.10454v1 fatcat:giybubv5bvdhjej5mg3ugigby4

Consciousness in the Universe is Scale Invariant and Implies an Event Horizon of the Human Brain

Dirk K.F. Meijer, Hans J H Geesink
2017 NeuroQuantology  
Its functional structure is adequately defined by the geometry of the torus, that is envisioned as a basic unit (operator) of space-time.  ...  In order to explain earlier reported ultra-rapid brain responses and effective operation of the meta-stable neural system, a field-receptive mental workspace is proposed to be communicating with the brain  ...  The presence of a glome or hypersphere can be detected invoking the Borsuk-Ulam Theorem (BUT), which states that every continuous map from a hypersphere to a 3D Euclidean space must identify a pair of  ... 
doi:10.14704/nq.2017.15.3.1079 fatcat:3ru3ihfcqbfwfdwdrupgq6n76m

Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials

Richard Le Blanc
2022 Entropy  
When constructed in terms of translated uniform distributions on unit radius hyperspheres, these translation factors become generating functions for classical families of orthogonal polynomials.  ...  Invoking the moment problem and the duality principle, modelization can be reduced to the direct determination of the prior moments in parametric space in terms of the Bayes factor's orthogonal polynomial  ...  In order to proceed, one needs to master some very simple notions concerning the hypersphere geometry.  ... 
doi:10.3390/e24050709 pmid:35626592 pmcid:PMC9141810 fatcat:73fsauljofd6hejpvpgdzmw3xq

Cluster-Based Spectral-Spatial Segmentation of Hyperspectral Imagery

Sean M. Kennedy, William Williamson, James W. Scrofani
2019 2019 10th Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing (WHISPERS)  
the data needed, and completing and reviewing the collection of information.  ...  Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching existing data sources, gathering and maintaining  ...  As modularity merely provides a figure-of-merit for an already known partition of a given network, modularity must be coupled with a community detection method that can produce multiple "guesses" of acceptable  ... 
doi:10.1109/whispers.2019.8921232 dblp:conf/whispers/KennedyWS19 fatcat:j2dujaoexjdv7gmgfpwldhdxkq

Life and Consciousness are Guided by a Semi-Harmonic EM Background Field

Dirk K.F. Meijer, Geesink Hans
2019 NeuroQuantology  
Consciousness is seen as arising through interaction of life systems with a holographic, field-receptive workspace, that is associated with the brain as a global supervening memory horizon, that is organized  ...  through toroidal geometry.  ...  The proposed 4-D aspect of brain memory was directly shown in the fMRI studies of Peters, 2016, 2017 , demonstrating repetitive modular electric oscillations, that were modeled as a 4-D-hypersphere that  ... 
doi:10.14704/nq.2019.17.4.2074 fatcat:t57cptrqcbhsjclwesfm74qp7u

A secure multidimensional point inclusion protocol

Juan Ramón Troncoso-Pastoriza, Stefan Katzenbeisser, Mehmet Celik, Aweke Lemma
2007 Proceedings of the 9th workshop on Multimedia & security - MM&Sec '07  
We subsequently extend the protocol to inclusion in multiple hyperellipsoidal regions. Considering possible reduction strategies such as input packing, we analyze the complexity of both protocols.  ...  Several such applications reduce to a multidimensional point inclusion problem where two participants decide whether a point known to the first lies inside a region specified by the second.  ...  The information in this paper is provided as is, and no guarantee or warranty is given or implied that the information is fit for any particular purpose.  ... 
doi:10.1145/1288869.1288884 dblp:conf/mmsec/Troncoso-PastorizaKCL07 fatcat:z7ltdyh6qfgzjja43uhgtudroi
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