scholarly journals Spectral estimation for detecting low-dimensional structure in networks using arbitrary null models

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254057
Author(s):  
Mark D. Humphries ◽  
Javier A. Caballero ◽  
Mat Evans ◽  
Silvia Maggi ◽  
Abhinav Singh
Keyword(s):  
Community Structure ◽  
Real World ◽  
Spectral Estimation ◽  
Null Model ◽  
Generative Models ◽  
Detection Methods ◽  
Dimensional Structure ◽  
Spectral Approach ◽  
Low Dimensional ◽  
Noise Nodes

Discovering low-dimensional structure in real-world networks requires a suitable null model that defines the absence of meaningful structure. Here we introduce a spectral approach for detecting a network’s low-dimensional structure, and the nodes that participate in it, using any null model. We use generative models to estimate the expected eigenvalue distribution under a specified null model, and then detect where the data network’s eigenspectra exceed the estimated bounds. On synthetic networks, this spectral estimation approach cleanly detects transitions between random and community structure, recovers the number and membership of communities, and removes noise nodes. On real networks spectral estimation finds either a significant fraction of noise nodes or no departure from a null model, in stark contrast to traditional community detection methods. Across all analyses, we find the choice of null model can strongly alter conclusions about the presence of network structure. Our spectral estimation approach is therefore a promising basis for detecting low-dimensional structure in real-world networks, or lack thereof.

Detecting communities in networks using a Bayesian nonparametric method

2014 ◽  
Vol 28 (28) ◽  
pp. 1450199
Author(s):  
Shengze Hu ◽  
Zhenwen Wang
Keyword(s):  
Community Structure ◽  
Community Detection ◽  
Real World ◽  
Detection Method ◽  
Generative Models ◽  
Detection Methods ◽  
Model Parameters ◽  
Nonparametric Method ◽  
Bayesian Nonparametric ◽  
New Community

In the real world, a large amount of systems can be described by networks where nodes represent entities and edges the interconnections between them. Community structure in networks is one of the interesting properties revealed in the study of networks. Many methods have been developed to extract communities from networks using the generative models which give the probability of generating networks based on some assumption about the communities. However, many generative models require setting the number of communities in the network. The methods based on such models are lack of practicality, because the number of communities is unknown before determining the communities. In this paper, the Bayesian nonparametric method is used to develop a new community detection method. First, a generative model is built to give the probability of generating the network and its communities. Next, the model parameters and the number of communities are calculated by fitting the model to the actual network. Finally, the communities in the network can be determined using the model parameters. In the experiments, we apply the proposed method to the synthetic and real-world networks, comparing with some other community detection methods. The experimental results show that the proposed method is efficient to detect communities in networks.

Synthesizing Designs With Interpart Dependencies Using Hierarchical Generative Adversarial Networks

2019 ◽  
Vol 141 (11) ◽  
Author(s):  
Wei Chen ◽  
Mark Fuge
Keyword(s):  
Constraint Satisfaction ◽  
Real World ◽  
Generative Models ◽  
Dependency Graph ◽  
Generative Adversarial Networks ◽  
Engineering Systems ◽  
Adversarial Networks ◽  
Latent Space ◽  
Branching Factor ◽  
Low Dimensional

Abstract Real-world designs usually consist of parts with interpart dependencies, i.e., the geometry of one part is dependent on one or multiple other parts. We can represent such dependency in a part dependency graph. This paper presents a method for synthesizing these types of hierarchical designs using generative models learned from examples. It decomposes the problem of synthesizing the whole design into synthesizing each part separately but keeping the interpart dependencies satisfied. Specifically, this method constructs multiple generative models, the interaction of which is based on the part dependency graph. We then use the trained generative models to synthesize or explore each part design separately via a low-dimensional latent representation, conditioned on the corresponding parent part(s). We verify our model on multiple design examples with different interpart dependencies. We evaluate our model by analyzing the constraint satisfaction performance, the synthesis quality, the latent space quality, and the effects of part dependency depth and branching factor. This paper’s techniques for capturing dependencies among parts lay the foundation for learned generative models to extend to more realistic engineering systems where such relationships are widespread.

scholarly journals Multiview Community Discovery Algorithm via Nonnegative Factorization Matrix in Heterogeneous Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Wang Tao ◽  
Liu Yang
Keyword(s):  
Community Structure ◽  
Heterogeneous Networks ◽  
Real World ◽  
Rapid Development ◽  
Complex Structure ◽  
Nonnegative Matrix ◽  
Bipartite Graphs ◽  
Semisupervised Learning ◽  
Detection Methods ◽  
Target Mode

With the rapid development of the Internet and communication technologies, a large number of multimode or multidimensional networks widely emerge in real-world applications. Traditional community detection methods usually focus on homogeneous networks and simply treat different modes of nodes and connections in the same way, thus ignoring the inherent complexity and diversity of heterogeneous networks. It is challenging to effectively integrate the multiple modes of network information to discover the hidden community structure underlying heterogeneous interactions. In our work, a joint nonnegative matrix factorization (Joint-NMF) algorithm is proposed to discover the complex structure in heterogeneous networks. Our method transforms the heterogeneous dataset into a series of bipartite graphs correlated. Taking inspiration from the multiview method, we extend the semisupervised learning from single graph to several bipartite graphs with multiple views. In this way, it provides mutual information between different bipartite graphs to realize the collaborative learning of different classifiers, thus comprehensively considers the internal structure of all bipartite graphs, and makes all the classifiers tend to reach a consensus on the clustering results of the target-mode nodes. The experimental results show that Joint-NMF algorithm is efficient and well-behaved in real-world heterogeneous networks and can better explore the community structure of multimode nodes in heterogeneous networks.

scholarly journals Uncovering Hidden Community Structure in Multi-Layer Networks

2021 ◽  
Vol 11 (6) ◽  
pp. 2857
Author(s):  
Faiza Riaz Khawaja ◽  
Jinfang Sheng ◽  
Bin Wang ◽  
Yumna Memon
Keyword(s):  
Community Structure ◽  
Community Detection ◽  
Real World ◽  
Graph Clustering ◽  
Detection Methods ◽  
Connected Components ◽  
Natural Community ◽  
As Graph ◽  
Dominant Structure

Community detection, also known as graph clustering, in multi-layer networks has been extensively studied in the literature. The goal of community detection is to partition vertices in a network into densely connected components so called communities. Networks contain a set of strong, dominant communities, which may interfere with the detection of weak, natural community structure. When most of the members of the weak communities also belong to stronger communities, they are extremely hard to be uncovered. We call the weak communities the hidden or disguised community structure. In this paper, we present a method to uncover weak communities in a network by weakening the strength of the dominant structure. With the aim to detect the weak communities, through experiments, we observe real-world networks to answer the question of whether real-world networks have hidden community structure or not. Results of the hidden community detection (HCD) method showed the great variation in the number of communities detected in multiple layers when compared with the results of other community detection methods.

scholarly journals Community Detection Based on DeepWalk Model in Large-Scale Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Yunfang Chen ◽  
Li Wang ◽  
Dehao Qi ◽  
Tinghuai Ma ◽  
Wei Zhang
Keyword(s):  
Community Structure ◽  
Community Detection ◽  
Large Scale ◽  
Dimensional Space ◽  
Complex Structure ◽  
Gaussian Mixture ◽  
Detection Algorithm ◽  
Detection Methods ◽  
Large Scale Networks ◽  
Low Dimensional

The large-scale and complex structure of real networks brings enormous challenges to traditional community detection methods. In order to detect community structure in large-scale networks more accurately and efficiently, we propose a community detection algorithm based on the network embedding representation method. Firstly, in order to solve the scarce problem of network data, this paper uses the DeepWalk model to embed a high-dimensional network into low-dimensional space with topology information. Then, low-dimensional data are processed, with each node treated as a sample and each dimension of the node as a feature. Finally, samples are fed into a Gaussian mixture model (GMM), and in order to automatically learn the number of communities, variational inference is introduced into GMM. Experimental results on the DBLP dataset show that the model method of this paper can more effectively discover the communities in large-scale networks. By further analyzing the excavated community structure, the organizational characteristics within the community are better revealed.

scholarly journals Likelihood-free Out-of-Distribution Detection with Invertible Generative Models

2021 ◽  
Author(s):  
Amirhossein Ahmadian ◽  
Fredrik Lindsten
Keyword(s):  
Score Function ◽  
Generative Models ◽  
Generative Model ◽  
Training Data ◽  
Detection Methods ◽  
Representation Space ◽  
New Space ◽  
Low Dimensional ◽  
And Training ◽  
Low Dimensional Features

Likelihood of generative models has been used traditionally as a score to detect atypical (Out-of-Distribution, OOD) inputs. However, several recent studies have found this approach to be highly unreliable, even with invertible generative models, where computing the likelihood is feasible. In this paper, we present a different framework for generative model--based OOD detection that employs the model in constructing a new representation space, instead of using it directly in computing typicality scores, where it is emphasized that the score function should be interpretable as the similarity between the input and training data in the new space. In practice, with a focus on invertible models, we propose to extract low-dimensional features (statistics) based on the model encoder and complexity of input images, and then use a One-Class SVM to score the data. Contrary to recently proposed OOD detection methods for generative models, our method does not require computing likelihood values. Consequently, it is much faster when using invertible models with iteratively approximated likelihood (e.g. iResNet), while it still has a performance competitive with other related methods.

scholarly journals Community detection in networks: a game-theoretic framework

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yan Chen ◽  
Xuanyu Cao ◽  
K. J. Ray Liu
Keyword(s):  
Community Detection ◽  
Real World ◽  
Expectation Maximization ◽  
Detection Method ◽  
Detection Algorithm ◽  
Generative Models ◽  
Detection Methods ◽  
Game Theoretic ◽  
Community Detection Algorithm ◽  
General Community

AbstractReal-world networks are often cluttered and hard to organize. Recent studies show that most networks have the community structure, i.e., nodes with similar attributes form a certain community, which enables people to better understand the constitution of the networks and thus gain more insights into the complicated networks. Strategic nodes belonging to different communities interact with each other to decide mutual links in the networks. Hitherto, various community detection methods have been proposed in the literature, yet none of them takes the strategic interactions among nodes into consideration. Additionally, many real-world observations of networks are noisy and incomplete, i.e., with some missing links or fake links, due to either technology constraints or privacy regulations. In this work, a game-theoretic framework of community detection is established, where nodes interact and produce links with each other in a rational way based on mutual benefits, i.e., maximizing their own utility functions when forming a community. Given the proposed game-theoretic generative models for communities, we present a general community detection algorithm based on expectation maximization (EM). Simulations on synthetic networks and experiments on real-world networks demonstrate that the proposed detection method outperforms the state of the art.

scholarly journals Modelling community structure and temporal spreading on complex networks

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Vesa Kuikka
Keyword(s):  
Community Structure ◽  
Complex Networks ◽  
Community Detection ◽  
Network Structure ◽  
Network Connectivity ◽  
Network Models ◽  
Building Blocks ◽  
Detection Algorithm ◽  
Research Area ◽  
Detection Methods

AbstractWe present methods for analysing hierarchical and overlapping community structure and spreading phenomena on complex networks. Different models can be developed for describing static connectivity or dynamical processes on a network topology. In this study, classical network connectivity and influence spreading models are used as examples for network models. Analysis of results is based on a probability matrix describing interactions between all pairs of nodes in the network. One popular research area has been detecting communities and their structure in complex networks. The community detection method of this study is based on optimising a quality function calculated from the probability matrix. The same method is proposed for detecting underlying groups of nodes that are building blocks of different sub-communities in the network structure. We present different quantitative measures for comparing and ranking solutions of the community detection algorithm. These measures describe properties of sub-communities: strength of a community, probability of formation and robustness of composition. The main contribution of this study is proposing a common methodology for analysing network structure and dynamics on complex networks. We illustrate the community detection methods with two small network topologies. In the case of network spreading models, time development of spreading in the network can be studied. Two different temporal spreading distributions demonstrate the methods with three real-world social networks of different sizes. The Poisson distribution describes a random response time and the e-mail forwarding distribution describes a process of receiving and forwarding messages.

scholarly journals Generative Models for Relief Perspective Architectures

2021 ◽  
Author(s):  
Leonardo Baglioni ◽  
Federico Fallavollita
Keyword(s):  
Research Methodology ◽  
Affine Space ◽  
Three Dimensional ◽  
Generative Models ◽  
Linear Perspective ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
Present Essay ◽  
Santa Maria

AbstractThe present essay investigates the potential of generative representation applied to the study of relief perspective architectures realized in Italy between the sixteenth and seventeenth centuries. In arts, and architecture in particular, relief perspective is a three-dimensional structure able to create the illusion of great depths in small spaces. A method of investigation applied to the case study of the Avila Chapel in Santa Maria in Trastevere in Rome (Antonio Gherardi 1678) is proposed. The research methodology can be extended to other cases and is based on the use of a Relief Perspective Camera, which can create both a linear perspective and a relief perspective. Experimenting mechanically and automatically the perspective transformations from the affine space to the illusory space and vice versa has allowed us to see the case study in a different light.

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