CoAssociation MatrixBased MultiLayer Fusion for Community Detection in Attributed Networks
Abstract
:1. Introduction
 We propose a twolayer representation for attributed networks. In the view of the representation, the lowerlayer representation is the raw data from network topological structure and node attributes, respectively, while the higherlayer representation is a set of community partitions that are generated from lowerlayer data by using the existing community detection algorithms.
 We propose a weighted coassociation matrixbased community ensemble method for community detection in attributed networks. In order to reduce the uncertainty and data inconsistency, the WCMFA employs the coassociation matrix to learn optimum community structure with the twolayer representation of raw data.
 We also empirically evaluate the effectiveness of WCMFA. The experiment results show that our proposed community detection algorithm, WCMFA, is the optimal choice to detect community structure in attributed networks.
2. Related Work
3. Proposed Method
3.1. Notation and Method Overview
 ${P}^{\ast}$ should be robustness to small variations in $\mathcal{P}$, according to the fusion strategy;
 ${P}^{\ast}$ should have better performance than each candidate community partition $P\in \mathcal{P}$, statistically;
 ${P}^{\ast}$ should be similar to all single community partition.
3.2. TwoLayer Representation and Community Fusion
3.3. Community Fusion Algorithm
Algorithm 1 The weighted coassociation matrix based community fusion algorithm, WCMFA, which detects community structure in attributed networks based on the twolayer representation 

4. Experiments
4.1. Experiment Setup
4.2. Results
4.3. Impact of Varying Size of Candidate Community Partitions and Nodes
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Methods  RI  ARI  NMI  WQ 

LPACNS  0.5855  0.1717  0.3182  0.1024 
BGLLCNS  0.4889  0.0237  0.0014  0.0165 
KmedCNS  0.8019  0.6038  0.6007  0.1345 
WCMFA  0.9150  0.8299  0.7828  0.1970 
$\Delta $  0.1130  0.2261  0.1822  0.0625 
Methods  RI  ARI  NMI  WQ 

LPACNS  0.3788  0.0015  0.0003  0.0000 
BGLLCNS  0.5265  0.0138  0.1108  0.0032 
KmedCNS  0.3753  0.0353  0.0359  0.0005 
WCMFA  0.5514  0.0712  0.1008  0.0487 
$\Delta $  0.0249  0.0359  −0.0100  0.0455 
Methods  RI  ARI  NMI  WQ 

LPACNS  0.5513  0.2340  0.4312  0.0560 
BGLLCNS  0.6639  0.0110  0.2064  0.0283 
KmedCNS  0.7899  0.5146  0.6372  0.1151 
WCMFA  0.8739  0.6973  0.7785  0.3035 
$\Delta $  0.0840  0.1827  0.1413  0.1884 
Candidate Partitions  The Number of Communities in One Partition $\left\mathit{P}\right$  

2  4  8  16  32  
5  0.39  0.38  0.39  0.46  0.52 
10  0.40  0.43  0.46  0.57  0.65 
15  0.41  0.46  0.51  0.66  0.77 
20  0.44  0.51  0.59  0.78  0.94 
25  0.46  0.55  0.64  0.90  1.15 
30  0.49  0.57  0.71  1.09  1.30 
35  0.54  0.60  0.78  1.24  1.56 
40  0.55  0.65  0.81  1.36  1.74 
45  0.58  0.69  0.89  1.54  1.97 
50  0.64  0.78  1.02  1.66  2.29 
55  0.66  0.78  1.27  1.75  2.37 
60  0.69  0.83  1.28  2.05  2.79 
65  0.71  0.89  1.39  2.37  3.28 
70  0.74  0.93  1.53  2.47  3.30 
75  0.78  1.00  1.75  2.52  3.76 
80  0.80  1.02  1.76  2.95  4.13 
85  0.87  1.13  1.94  3.28  4.39 
90  0.89  1.14  2.00  3.49  4.73 
95  0.92  1.19  2.06  3.73  5.17 
100  0.94  1.24  2.37  4.05  5.43 
Node Size  The Number of Communities in One Partition $\left\mathit{P}\right$  

2  4  8  16  32  
200  0.93  1.25  2.30  4.90  5.65 
400  1.37  1.70  2.55  6.32  8.87 
600  1.92  2.14  2.99  6.82  15.50 
800  2.62  2.93  3.75  7.10  23.04 
1000  3.50  3.67  4.62  8.86  35.34 
1200  4.43  4.70  5.59  11.16  37.86 
1400  5.51  5.74  6.49  14.37  49.48 
1600  6.86  7.16  7.72  15.74  59.71 
1800  8.08  8.35  9.00  15.76  82.09 
2000  9.17  9.78  10.86  17.92  92.41 
2200  11.47  11.66  12.18  19.80  118.44 
2400  13.33  13.05  14.09  20.96  126.04 
2600  15.26  15.42  16.01  22.60  145.14 
2800  15.38  17.52  18.34  24.36  149.09 
3000  19.68  19.84  20.66  25.90  162.64 
3200  22.17  22.25  22.56  28.27  174.81 
3400  24.45  24.42  25.76  29.11  179.99 
3600  26.99  27.16  27.24  31.44  184.27 
3800  29.83  29.14  30.22  33.93  187.42 
4000  32.14  31.99  32.98  37.06  243.40 
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Luo, S.; Zhang, Z.; Zhang, Y.; Ma, S. CoAssociation MatrixBased MultiLayer Fusion for Community Detection in Attributed Networks. Entropy 2019, 21, 95. https://doi.org/10.3390/e21010095
Luo S, Zhang Z, Zhang Y, Ma S. CoAssociation MatrixBased MultiLayer Fusion for Community Detection in Attributed Networks. Entropy. 2019; 21(1):95. https://doi.org/10.3390/e21010095
Chicago/Turabian StyleLuo, Sheng, Zhifei Zhang, Yuanjian Zhang, and Shuwen Ma. 2019. "CoAssociation MatrixBased MultiLayer Fusion for Community Detection in Attributed Networks" Entropy 21, no. 1: 95. https://doi.org/10.3390/e21010095