## 4 Results and Discussion
### Real-World Multiplex Networks  
Multiple well-known real-world multiplex networks were adopted to validate the performance of the proposed **Mx-CRTSA**, including:  
* **Nokia Research Center (NRC).** ([[https://bitbucket.org/uuinfolab/20](https://bitbucket.org/uuinfolab/20) csur/src/masster/algorithms/spectral/data/]([https://bitbucket.org/uuinfolab/20](https://bitbucket.org/uuinfolab/20) csur/src/masster/algorithms/spectral/data/)) (accessed on 15 January 2023) Mobile phone data of 136 users living and working in Switzerland with eight communities and three layers, including physical location, Bluetooth scans and phone calls [33].
* **CKM physicians innovation.** ([[https://manliodededomenico.com/data.php](https://manliodededomenico.com/data.php)]([https://manliodededomenico.com/data.php](https://manliodededomenico.com/data.php))) (accessed on 15 January 2023) A network that reflects data on medical innovation, considering physicians in four towns in Illinois (Peoria, Bloomington, Quincy and Galesburg) with three layers and four communities [34].
* **C. Elegans.** A three-layer multiplex network of the Caenorhabditis Elegans connectome that reflects the synaptic junctions between the neurons including electric, chemical monadic and polyadic junctions. The network consists of 279 nodes and 12 communities representing the neuron groups [35; 36].
* **Cora.** ([[https://people.cs.umass.edu/~mccallum/data.html](https://people.cs.umass.edu/~mccallum/data.html)]([https://people.cs.umass.edu/~mccallum/data.html](https://people.cs.umass.edu/~mccallum/data.html))) (accessed on 15 January 2023) A subset of the Cora bibliographic dataset consisting of 292 research papers with three communities, including natural language processing, data mining and robotics, and three layers, including title similarity, abstract similarity and citation relationship.
* **BBCSPORT.** ([[http://mlg.ucd.ie/datasets/bbc.html](http://mlg.ucd.ie/datasets/bbc.html)]([http://mlg.ucd.ie/datasets/bbc.html](http://mlg.ucd.ie/datasets/bbc.html))) (accessed on 15 January 2023) A collection of BBC sport articles (\(n=544\)) with two layers and grouped into five clusters: athletics, cricket, football, rugby and tennis. [37].
* **Wikipedia.** ([[http://www.svcl.ucsd.edu/projects/crossmodal/](http://www.svcl.ucsd.edu/projects/crossmodal/)]([http://www.svcl.ucsd.edu/projects/crossmodal/](http://www.svcl.ucsd.edu/projects/crossmodal/))) (accessed on 15 January 2023) A dataset containing 693 articles, where each article is considered a node with two layers and ten communities.
* **COIL-20.** ([[https://www.cs.columbia.edu/CAVE/software/softlib/](https://www.cs.columbia.edu/CAVE/software/softlib/)]([https://www.cs.columbia.edu/CAVE/software/softlib/](https://www.cs.columbia.edu/CAVE/software/softlib/))) (accessed on 15 January 2023) An image dataset that consists of 1440 images collected from the Columbia object image library with three layers that reflect intensity, LBP and Gabor, and twenty communities.
* 100**Leaves.** ([[https://archive.ics.uci.edu/ml/datasets/One-hundred+plant+species+leaves+](https://archive.ics.uci.edu/ml/datasets/One-hundred+plant+species+leaves+)]([https://archive.ics.uci.edu/ml/datasets/One-hundred+plant+species+leaves+](https://archive.ics.uci.edu/ml/datasets/One-hundred+plant+species+leaves+))) (accessed on 15 January 2023) A plant species leaf database with 1600 samples, 100 communities and 3 layers, where the edges in the layers reflect shape descriptor, fine-scale margin and texture.  
Figure 6: The scalability of **Mx-CRTSA** compared with other existing methods as the number of nodes increases.