Network Alignment Using Topological And Node Embedding Features

Abstract

In today’s big data environment, development of robust knowledge discovery solutions depends on integration of data from various sources. For example, intelligence agencies fuse data from multiple sources to identify criminal activities; e-commerce platforms consolidate user activities on various platforms and devices to build better user profile; scientists connect data from various modality to develop new drugs, and treatments. In all such activities, entities from different data sources need to be aligned—first, to ensure accurate analysis and more importantly, to discover novel knowledge regarding these entities. If the data sources are networks, aligning entities from different sources leads to the task of network alignment, which is the focus of this thesis. The main objective of this task is to find an optimal one-to-one correspondence among nodes in two or more networks utilizing graph topology and nodes/edges attributes.

In existing works, diverse computational schemes have been adopted for solving the network alignment task; these schemes include finding eigen-decomposition of similarity matrices, solving quadratic assignment problems via sub-gradient optimization, and designing iterative greedy matching techniques. Contemporary works approach this problem using a deep learning framework by learning node representations to identify matches. Node matching’s key challenges include computational complexity and scalability. However, privacy concerns or unavailability often prevent the utilization of node attributes in real-world scenarios. In light of this, we aim to solve this problem by relying solely on the graph structure, without the need for prior knowledge, external attributes, or guidance from landmark nodes. Clearly, topology-based matching emerges as a hard problem when compared to other network matching tasks.

In this thesis, I propose two original works to solve network topology-based alignment task. The first work, Graphlet-based Alignment (Graphlet-Align), employs a topological approach to network alignment. Graphlet-Align represents each node with a local graphlet count based signature and use that as feature for deriving node to node similarity across a pair of networks. By using these similarity values in a bipartite matching algorithm GraphletAlign obtains a preliminary alignment. It then uses high-order information extending to k-hop neighborhood of a node to further refine the alignment, achieving better accuracy. We validated Graphlet-Align’s efficacy by applying it to various large real-world networks, achieving accuracy improvements ranging from 20% to 72% over state-of-the-art methods on both duplicated and noisy graphs.

Expanding on this paradigm that focuses solely on topology for solving graph alignment, in my second work, I develop a self-supervised learning framework known as Self-Supervised Topological Alignment (SST-Align). SST-Align uses graphlet-based signature for creating self-supervised node alignment labels, and then use those labels to generate node embedding vectors of both the networks in a joint space from which node alignment task can be effectively and accurately solved. It starts with an optimization process that applies average pooling on top of the extracted graphlet signature to construct an initial node assignment. Next, a self-supervised Siamese network architecture utilizes both the initial node assignment and graph convolutional networks to generate node embeddings through a contrastive loss. By applying kd-tree similarity to the two networks’ embeddings, we achieve the final node mapping. Extensive testing on real-world graph alignment datasets shows that our developed methodology has competitive results compared to seven existing competing models in terms of node mapping accuracy. Additionally, we establish the Ablation Study to evaluate the two-stage accuracy, excluding the learning representation part and comparing the mapping accuracy accordingly.

This thesis enhances the theoretical understanding of topological features in the analysis of graph data for network alignment task, hence facilitating future advancements toward the field.