OrthoNet: Multilayer Network Data Clustering

Abstract

Network data appears in very diverse applications, like biological, social, or sensor networks. Clustering of network nodes into categories or communities has thus become a very common task in machine learning and data mining. Network data comes with some information about the network edges. In some cases, this network information can even be given with multiple views or multiple layers, each one representing a different type of relationship between the network nodes. Increasingly often, network nodes also carry a feature vector. We propose in this paper to extend the node clustering problem, that commonly considers only the network information, to a problem where both the network information and the node features are considered together for learning a clustering-friendly representation of the feature space. Specifically, we design a generic two-step algorithm for multilayer network data clustering. The first step aggregates the different layers of network information into a graph representation given by the geometric mean of the network Laplacian matrices. The second step uses a neural net to learn a feature embedding that is consistent with the structure given by the network layers. We propose a novel algorithm for efficiently training the neural net via stochastic gradient descent, which encourages the neural net outputs to span the leading eigenvectors of the aggregated Laplacian matrix, in order to capture the pairwise interactions on the network, and provide a clustering-friendly representation of the feature space. We demonstrate with an extensive set of experiments on synthetic and real datasets that our method leads to a significant improvement w.r.t. state-of-the-art multilayer graph clustering algorithms, as it judiciously combines nodes features and network information in the node embedding algorithms.

Multilayer network analyses as a toolkit for measuring social structure

“…See Section 4.2.3 in Kivelä et al (2014 ) for a review and discussion of multilayer clustering methods, and numerous other recent clustering analyses for multilayer networks ( Chen and Hero 2017 ; Chen et al. 2019 ; El Gheche et al. 2020 ).…”

Figlearn: Filter and Graph Learning Using Optimal Transport

“…Both optimization problems are fully differentiable, and thus can be solved via accelerated gradient descent algorithm (ADAM) [20]. 3 Graph learning To facilitate the optimization defined in equation ( 9) with respect to the graph structure, we seek for a valid adjacency matrix 4 instead of a Laplacian. Moreover, we can exploit the symmetry of the adjacency matrix by only optimizing the upper triangular part w. If we denote as L : R (N −1)N/2 → R N ×N the linear operator that converts the upper-triangular part w of an adjacency matrix into the corresponding Laplacian matrix, we can reformulate the problem as…”

“…Smoothness is typically related to the signal variations between nodes that are connected through an edge. In frameworks exploiting this assumption, graph learning amounts to finding the GSO that corresponds to the topology on which the signal differences across edges are minimized [1,2,3,4].…”

Community detection with node attributes in multilayer networks

“…However, the majority of these methods do not consider node attributes as input along with the network information. In fact, the few methods developed for community detection in multilayer networks with node attributes are based on first aggregating the multilayer network into a single layer, either by combining directly the adjacency matrices of each layer 20 or by using similarity matrices derived from them along with the node attributes 21 , 22 . In the context of data mining, a similar problem can be framed for learning low dimensional representations of heterogeneous data with both content and linkage structure (what we call attributes and edges).…”

“…These works show the impact of adding nodes attributes in community detection a priori into the models to uncover meaningful patterns. One might then be tempted to adopt such methods also in multilayer networks by collapsing the topological structure into a suitable single network that can then be given in input to these single-layer and node-attributed methods as done by Gheche et al 20 . However, collapsing a multilayer network often leads to important loss of information, and one needs to be careful in determining when this collapse is appropriate and how it should be implemented, as shown for community detection methods without attribute information 39,40 .…”