Conclusion
ConclusionΒΆ
In this study, we build simple kernels using global, node-wise, and edge-wise properties of the network and assess their performances on matched and unmatched networks. We construct dissimilarity matrices based on each of these kernels and calculate their discriminability index values, then we cluster the dissimilarity matrix using Agglomerative clustering, GMM, and KMeans and report the adjusted rand index (ARI) values for each. We compare these simple kernels to a few well-established kernels, and we summarize the results in the discriminability and ARI plots in previous sections.
In general, we find that the kernels perform better on matched networks than unmatched networks. When we have matching between the nodes, we can make more direct comparisons between networks using their properties, which yields dissimilarity matrices with higher discriminability index values, leading to better clustering performances. For all discriminability and ARI plots, the kernels are ordered from highest to lowest performance, and the order in which the kernels are positioned in the discriminability plot seem to carry over to the ARI plot, suggesting that for both matched and unmatched networks, the kernel by which the dissimilarity matrix is generated has greater influence on its clustering performance than the clustering algorithm.
For matched networks, we find that node-wise and edge-wise kernels perform better than kernels based on global properties of the network, with simple kernels such as the Edge weight kernel or the Node strength kernel performing better than the Laplacian spectral kernel. For unmatched metworks, we observe the opposite, where global kernels such as the Density kernel or the Average of the adjacency matrix kernel performing better than the Latent distribution test kernel. When we look at the specific values, we see that the global kernels actually perform similarly for both matched and unmatched networks, while the performance for node-wise and edge-wise kernels decrease dramatically for unmatched networks. This suggests that kernel performance may depend more on network characteristics rather than the complexity of the kernel, as we have observed that simple kernels can outperform complex kernels based on whether or not the networks are matched.
More datasets should be incorporated into the study in order to solidify these claims, but our findings suggest that simple kernels can be a well-performing, yet much faster alternative to more complex algorithms that are computationally very expensive.