LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks
Abstract
:1. Introduction
2. Methodology
2.1. Measurement of Interlayer Correlation in Multiplex Networks
2.2. Probability Estimation of Potential Links in Multiplex Networks
3. Data Description and Evaluation Metric
3.1. Datasets
- Lazega [43]: The dataset consists of a multiplex network representing corporate law partnerships among employees. It contains three kinds of relationships, namely advice, co-work, and friendship. There are a total of 71 nodes, with the number of active nodes in each layer being 71, 70, and 69, respectively.
- C. elegans [44]: The Caenorhabditis elegans dataset comprises three layers that correspond to different synaptic junctions, namely electric links, chemical monadic links, and chemical polyadic links. The multiplex network consists of 279 nodes in total. Each layer has a different number of active nodes, with 253, 260, and 278 nodes, respectively.
- Kapferer [45]: The Kapferer tailor shop dataset describes the interactions in a tailor shop in Zambia over a period of ten months. The four layers of the network are generated by two different types of interaction. The first two layers, TS1 and TS2, represent “sociational” interactions, specifically friendship and socioemotional connections. The last two layers, TI1 and TI2, record “instrumental” interactions related to work and assistance at two different time points. The multiplex network consists of 39 nodes, with the number of active nodes in each layer being 39, 39, 35, and 37, respectively.
- Vicker [46]: This dataset is a multiplex social network depicting the relationships between 29 Grade 7 students in a school in Victoria, Australia. It consists of three layers, with each layer corresponding to different types of relationships, namely getting on, best friends, and preferring working together. There are 29 nodes in total. The number of active nodes in each layer is also 29.
- CKM [47]: This dataset constitutes a multiplex network that captures the interaction among physicians during the adoption of a new drug. It consists of three layers that represent different types of relationships: friendship, discussion, and asking for advice. There are 245 nodes in total. The number of active nodes in each layer is 215, 231, and 227, respectively.
- Rattus [48]: This dataset provides a multiplex network of genetic and protein interactions in Rattus Norvegicus. The raw data comprise 2640 nodes and 6 layers. In order to remove uninformative layers, we exclude those with only a few dozen edges. Within the paper, the multiplex network is analyzed using three layers: physical association, direct interaction, and colocalization. There are a total of 2538 nodes, with 1948, 979, and 149 active nodes in each layer, respectively.
3.2. Evaluation Metric
4. Experimental Analysis
4.1. Correlation Between Layers in Real Datasets
4.2. Tunable Parameter Analysis
4.3. Analysis of the Influence of Auxiliary Layers on Prediction Performance
4.4. Comparison of LPGRI with Other Methods
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
LPGRI | Link Prediction based on Global Relevance of Interlayer |
GR | Global Relevance |
AUC | Area Under the Curve |
RI | Ratio of Improvement |
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Notations | Explanations |
---|---|
the set of nodes in the -th layer () | |
the set of edges in the -th layer | |
the layer | |
the adjacency matrix of | |
the target layer | |
the i-th row of the adjacency matrix of layer | |
the i-th column of the adjacency matrix of layer | |
the mean value of | |
the standard deviation of | |
probability of potential links between node pair in the target layer |
Network Type | Dataset | L | N | Layer Name | D | |||
---|---|---|---|---|---|---|---|---|
undirected | Lazega | 3 | 71 | 71 | 1 | advice | 717 | 0.298 |
70 | 2 | work | 378 | 0.152 | ||||
69 | 3 | friend | 399 | 0.161 | ||||
C. elegans | 3 | 279 | 253 | 1 | electric | 514 | 0.013 | |
260 | 2 | mono | 888 | 0.023 | ||||
278 | 3 | poly | 1703 | 0.044 | ||||
Kapferer | 4 | 39 | 39 | 1 | TS1 | 158 | 0.213 | |
39 | 2 | TS2 | 223 | 0.301 | ||||
35 | 3 | TI1 | 76 | 0.103 | ||||
37 | 4 | TI2 | 95 | 0.128 | ||||
directed | Vicker | 3 | 29 | 29 | 1 | get on | 361 | 0.445 |
29 | 2 | friend | 181 | 0.223 | ||||
29 | 3 | co-work | 198 | 0.244 | ||||
CKM | 3 | 245 | 215 | 1 | advice | 480 | 0.008 | |
231 | 2 | discussion | 565 | 0.009 | ||||
227 | 3 | friend | 504 | 0.008 | ||||
Rattus | 3 | 2538 | 1948 | 1 | physical association | 2894 | 0.00052 | |
979 | 2 | direct interaction | 1024 | 0.00018 | ||||
149 | 3 | colocalization | 119 | 0.00002 |
Type | Dataset | Layer Name | Method | RI | ||||
---|---|---|---|---|---|---|---|---|
LPGRI | NSILR | LPIS | NBS | LPPON | ||||
undirected | Lazega | advice | 0.8513 | 0.8498 | 0.8417 | 0.8245 | 0.8011 | 0.18% |
work | 0.8407 | 0.8101 | 0.7625 | 0.7983 | 0.7788 | 0.38% | ||
friend | 0.8664 | 0.8769 | 0.8639 | 0.8245 | 0.8011 | −0.12% | ||
C. elegans | electric | 0.8141 | 0.8522 | 0.7901 | 0.7011 | 0.7441 | −4.47% | |
mono | 0.8880 | 0.8648 | 0.8047 | 0.7585 | 0.8139 | 2.68% | ||
poly | 0.8527 | 0.8493 | 0.8571 | 0.8292 | 0.7952 | −0.51% | ||
Kapferer | TS1 | 0.7922 | 0.7875 | 0.7289 | 0.7540 | 0.7212 | 0.60% | |
TS2 | 0.7899 | 0.7786 | 0.7554 | 0.7391 | 0.7148 | 1.45% | ||
TI1 | 0.8042 | 0.7914 | 0.7561 | 0.7096 | 0.7072 | 1.62% | ||
TI2 | 0.8225 | 0.8225 | 0.7685 | 0.7330 | 0.7517 | 0.00% | ||
directed | Vicker | get on | 0.8253 | 0.7755 | 0.8046 | 0.7576 | 0.7256 | 2.57% |
friend | 0.8448 | 0.8026 | 0.8208 | 0.7585 | 0.7889 | 2.92% | ||
co-work | 0.8906 | 0.7924 | 0.8443 | 0.7741 | 0.7926 | 5.48% | ||
CKM | advice | 0.8225 | 0.7117 | 0.5913 | 0.6792 | 0.7006 | 15.57% | |
discussion | 0.7816 | 0.7667 | 0.5791 | 0.6022 | 0.6848 | 1.94% | ||
friend | 0.6897 | 0.7397 | 0.5875 | 0.5442 | 0.5971 | −6.76% | ||
Rattus | physical association | 0.6830 | 0.5458 | 0.5464 | 0.6647 | 0.5872 | 2.75% | |
direct interaction | 0.6702 | 0.5175 | 0.5601 | 0.6229 | 0.5923 | 7.59% | ||
colocalization | 0.7252 | 0.5742 | 0.5938 | 0.5588 | 0.5757 | 22.13% |
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Wang, C.; Tang, F.; Zhao, X. LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks. Mathematics 2023, 11, 3256. https://doi.org/10.3390/math11143256
Wang C, Tang F, Zhao X. LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks. Mathematics. 2023; 11(14):3256. https://doi.org/10.3390/math11143256
Chicago/Turabian StyleWang, Chunning, Fengqin Tang, and Xuejing Zhao. 2023. "LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks" Mathematics 11, no. 14: 3256. https://doi.org/10.3390/math11143256
APA StyleWang, C., Tang, F., & Zhao, X. (2023). LPGRI: A Global Relevance-Based Link Prediction Approach for Multiplex Networks. Mathematics, 11(14), 3256. https://doi.org/10.3390/math11143256