Optimizing modularity with nonnegative matrix factorization

Community structure detection is one of the fundamental problems in complex network analysis towards understanding the topology structure and function of the network. Modularity is a criterion to evaluate the quality of community structures, and optimization of this quality function over the possible divisions of a network is a sensitive detection method for community structure. However, the direct application of this method is computationally costly. Nonnegative matrix factorization (NMF) is a widely used method for community detection. In this paper, we show that modularity maximization can be approximately reformulated under the framework of NMF with Frobenius norm, especially when [Formula: see text] is large. A new algorithm for detecting community structure is proposed based on the above finding. The new method is compared with four state-of-the-art methods on both synthetic and real-world networks, showing its higher clustering quality over the existing methods.

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Community Detection Based on Modularized Deep Nonnegative Matrix Factorization

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001421590060 ◽

2020 ◽

pp. 2159006

Author(s):

Jin Huang ◽

Tinghua Zhang ◽

Weihao Yu ◽

Jia Zhu ◽

Ercong Cai

Keyword(s):

Community Structure ◽

Community Detection ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Complex Data ◽

Original Matrix ◽

Latent Features ◽

Topology Information ◽

Structure Properties

Community detection is a well-established problem and nontrivial task in complex network analysis. The goal of community detection is to discover community structures in complex networks. In recent years, many existing works have been proposed to handle this task, particularly nonnegative matrix factorization-based method, e.g. HNMF, BNMF, which is interpretable and can learn latent features of complex data. These methods usually decompose the original matrix into two matrixes, in one matrix, each column corresponds to a representation of community and each column of another matrix indicates the membership between overall pairs of communities and nodes. Then they discover the community by updating the two matrices iteratively and learn the shallow feature of the community. However, these methods either ignore the topological structure characteristics of the community or ignore the microscopic community structure properties. In this paper, we propose a novel model, named Modularized Deep NonNegative Matrix Factorization (MDNMF) for community detection, which preserves both the topology information and the instinct community structure properties of the community. The experimental results show that our proposed models can significantly outperform state-of-the-art approaches on several well-known dataset.

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CDCN: A New NMF-Based Community Detection Method with Community Structures and Node Attributes

Wireless Communications and Mobile Computing ◽

10.1155/2021/5517204 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Zhiwen Ye ◽

Hui Zhang ◽

Libo Feng ◽

Zhangming Shan

Keyword(s):

Community Structure ◽

Community Detection ◽

Network Topology ◽

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Original Network ◽

Community Structures ◽

Structure Matrix ◽

Node Attributes

Community discovery can discover the community structure in a network, and it provides consumers with personalized services and information pushing. It plays an important role in promoting the intelligence of the network society. Most community networks have a community structure whose vertices are gathered into groups which is significant for network data mining and identification. Existing community detection methods explore the original network topology, but they do not make the full use of the inherent semantic information on nodes, e.g., node attributes. To solve the problem, we explore networks by considering both the original network topology and inherent community structures. In this paper, we propose a novel nonnegative matrix factorization (NMF) model that is divided into two parts, the community structure matrix and the node attribute matrix, and we present a matrix updating method to deal with the nonnegative matrix factorization optimization problem. NMF can achieve large-scale multidimensional data reduction processing to discover the internal relationships between networks and find the degree of network association. The community structure matrix that we proposed provides more information about the network structure by considering the relationships between nodes that connect directly or share similar neighboring nodes. The use of node attributes provides a semantic interpretation for the community structure. We conduct experiments on attributed graph datasets with overlapping and nonoverlapping communities. The results of the experiments show that the performances of the F1-Score and Jaccard-Similarity in the overlapping community and the performances of normalized mutual information (NMI) and accuracy (AC) in the nonoverlapping community are significantly improved. Our proposed model achieves significant improvements in terms of its accuracy and relevance compared with the state-of-the-art approaches.

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Comparison of Initialization Techniques for the Accurate Extraction of Muscle Synergies from Myoelectric Signals via Nonnegative Matrix Factorization

Applied Bionics and Biomechanics ◽

10.1155/2018/3629347 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Mumtaz Hussain Soomro ◽

Silvia Conforto ◽

Gaetano Giunta ◽

Simone Ranaldi ◽

Cristiano De Marchis

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Simulated Data ◽

Surface Emg ◽

Muscle Synergies ◽

Accurate Identification ◽

Experimental Surface ◽

Factorization Algorithms

The main goal of this work was to assess the performance of different initializations of matrix factorization algorithms for an accurate identification of muscle synergies. Currently, nonnegative matrix factorization (NNMF) is the most commonly used method to identify muscle synergies. However, it has been shown that NNMF performance might be affected by different kinds of initialization. The present study aims at optimizing the traditional NNMF initialization for data with partial or complete temporal dependencies. For this purpose, three different initializations are used: random, SVD-based, and sparse. NNMF was used to identify muscle synergies from simulated data as well as from experimental surface EMG signals. Simulated data were generated from synthetic independent and dependent synergy vectors (i.e., shared muscle components), whose activation coefficients were corrupted by simulating controlled degrees of correlation. Similarly, EMG data were artificially modified, making the extracted activation coefficients temporally dependent. By measuring the quality of identification of the original synergies underlying the data, it was possible to compare the performance of different initialization techniques. Simulation results demonstrate that sparse initialization performs significantly better than all other kinds of initialization in reconstructing muscle synergies, regardless of the correlation level in the data.

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A Review on Initialization Methods for Nonnegative Matrix Factorization: Towards Omics Data Experiments

Mathematics ◽

10.3390/math9091006 ◽

2021 ◽

Vol 9 (9) ◽

pp. 1006

Author(s):

Flavia Esposito

Keyword(s):

Matrix Factorization ◽

Nonnegative Matrix Factorization ◽

Nonnegative Matrix ◽

Biological Information ◽

Relevant Role ◽

Initialization Scheme ◽

The Cost ◽

The Impact ◽

Omic Data

Nonnegative Matrix Factorization (NMF) has acquired a relevant role in the panorama of knowledge extraction, thanks to the peculiarity that non-negativity applies to both bases and weights, which allows meaningful interpretations and is consistent with the natural human part-based learning process. Nevertheless, most NMF algorithms are iterative, so initialization methods affect convergence behaviour, the quality of the final solution, and NMF performance in terms of the residual of the cost function. Studies on the impact of NMF initialization techniques have been conducted for text or image datasets, but very few considerations can be found in the literature when biological datasets are studied, even though NMFs have largely demonstrated their usefulness in better understanding biological mechanisms with omic datasets. This paper aims to present the state-of-the-art on NMF initialization schemes along with some initial considerations on the impact of initialization methods when microarrays (a simple instance of omic data) are evaluated with NMF mechanisms. Using a series of measures to qualitatively examine the biological information extracted by a given NMF scheme, it preliminary appears that some information (e.g., represented by genes) can be extracted regardless of the initialization scheme used.

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