# Uncovering Hidden Community Structure in Multi-Layer Networks
## 6 Evaluation of Results and Comparison
### Attribute Based Comparison  
In this section, we compare some multi-layer community detection algorithms with the proposed method according to four attributes as shown in Table 3.  
For the comparison, we choose five multiple layer community detection approaches. The first method ([PERSON] et al. [27]) is basically a hierarchical community detection algorithm consisting of four major steps: core probing, core merging, affiliation, and classification. According to the results, this approach usually detects communities in just two-layer networks effectively. The second approach is from [PERSON] et al. [20], and is a matrix factorization category based community detection algorithm. The main contribution of this algorithm is using edge content for the community detection process and it can be a useful source of information when nodes interact with multiple communities. Another method proposed by [PERSON] et al. [28] is based on structural correlation pattern mining, called SCPM, which uncovers the interaction between vertex attributes and dense subgraphs using both frequent item-set mining and quasi-clique mining. [PERSON] et al. [29] proposed a model-based community detection approach based on both structural and attribute aspects of a graph in a multi-layer network. The last method for comparison is the one of an online auction network [12] with fraudsters as a random network with hidden communities. * **Attribute 1: Applicability to the multi-layer graph. ** Defines whether an algorithm is able to detect communities in a multiple layer graph (i.e., should detect more than 2 layers) or not. Undoubtedly, there have been many studies done for community detection in both single layer and multiple layer graphs. The overall phenomenon of each approach might be different from the perspective of hidden community detection, but the general results show that the proposed method is applicable to the multiple \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Attribute 1** & **Attribute 2** & **Attribute 3** & **Attribute 4** \\ \hline [PERSON] et al. [27] & ✗ & ✗ & ✗ & ✓ \\ [PERSON] et al. [20] & ✗ & ✓ & ✓ & ✓ \\ [PERSON] et al. [28] & ✗ & ✗ & ✗ & ✓ \\ [PERSON] et al. [29] & ✗ & ✓ & ✗ & ✗ \\ [PERSON] et al. [12] & ✗ & ✗ & ✗ & ✗ \\ HCD & ✓ & ✓ & ✓ & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of the HCD method with other multi-layer and hidden community detection methods. layer graphs and can detect the communities that often go undetected by most of the community detection algorithms. * **Attribute 2: Equal consideration of each layer. ** Since each aspect of the relationships may have a different importance in the real world, considering the importance of each layer differently is more applicable than assigning uniform importance. Thus, it is crucial to automatically find the importance of each layer based on the layer's characteristics. It has been observed that among the selected approaches and the hidden community detection method, some approaches satisfy the property of equally considering each layer during operation; the hidden community detection clearly satisfies this property because it weakens the communities at each layer and in the second phase it also clarifies the whole graph. It also gives better results in the next layer while considering the performance at the prior one. * **Attribute 3: Insensitivity of the algorithm. ** Some approaches are tightly coupled so that they can only be used for a specific kind of network. This tight coupling may limit the freedom of users to choose a network while experimenting and evaluating. It is well-known that certain algorithms tend to perform particularly well or poorly on certain kinds of graphs or networks. From the results given below, it is clear that except one, all other approaches failed to satisfy this property and the HCD method is not a very tightly coupled approach when experimented with in real-world datasets of different domains. * **Attribute 4: Applicability to the graph with overlapping layers.