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1. BRIGHT: A Bridging Algorithm for Network Alignment

   Yuchen Yan, Si Zhang (April 2021, TheWebConf)

   null (Ed.)

   Multiple networks emerge in a wealth of high-impact applications. Network alignment, which aims to find the node correspondence across different networks, plays a fundamental role for many data mining tasks. Most of the existing methods can be divided into two categories: (1) consistency optimization based methods, which often explicitly assume the alignment to be consistent in terms of neighborhood topology and attribute across networks, and (2) network embedding based methods which learn low-dimensional node embedding vectors to infer alignment. In this paper, by analyzing certain methods of these two categories, we show that (1) the consistency optimization based methods are essentially specific random walk propagations from anchor links that might be restrictive; (2) the embedding based methods no longer explicitly assume alignment consistency but inevitably suffer from the space disparity issue. To overcome these two limitations, we bridge these methods and propose a novel family of network alignment algorithms BRIGHT to handle both non-attributed and attributed networks. Specifically, it constructs a space by random walk with restart (RWR) whose bases are one-hot encoding vectors of anchor nodes, followed by a shared linear layer. Our experiments on real-world networks show that the proposed family of algorithms BRIGHT outperform the state-of-the- arts for both non-attributed and attributed network alignment tasks. 

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2. ORIGIN: Non-Rigid Network Alignment

   https://doi.org/10.1109/BigData47090.2019.9005663  

   Zhang, Si; Tong, Hanghang; Xu, Jiejun; Hu, Yifan; Maciejewski, Ross (December 2019, BigData)

   Network alignment is a fundamental task in many high-impact applications. Most of the existing approaches either explicitly or implicitly consider the alignment matrix as a linear transformation to map one network to another, and might overlook the complicated alignment relationship across networks. On the other hand, node representation learning based alignment methods are hampered by the incomparability among the node representations of different networks. In this paper, we propose a unified semi-supervised deep model (ORIGIN) that simultaneously finds the non-rigid network alignment and learns node representations in multiple networks in a mutually beneficial way. The key idea is to learn node representations by the effective graph convolutional networks, which subsequently enable us to formulate network alignment as a point set alignment problem. The proposed method offers two distinctive advantages. First (node representations), unlike the existing graph convolutional networks that aggregate the node information within a single network, we can effectively aggregate the auxiliary information from multiple sources, achieving far-reaching node representations. Second (network alignment), guided by the highquality node representations, our proposed non-rigid point set alignment approach overcomes the bottleneck of the linear transformation assumption. We conduct extensive experiments that demonstrate the proposed non-rigid alignment method is (1) effective, outperforming both the state-of-the-art linear transformation-based methods and node representation based methods, and (2) efficient, with a comparable computational time between the proposed multi-network representation learning component and its single-network counterpart. 

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3. Quantifying functionally equivalent species and ecological network dissimilarity with optimal transport distances

   https://doi.org/10.1111/2041-210x.70130  

   Hung, Kai M; Beaudrot, Lydia; Finneran, Ann E; Zalles, Alex G; Uribe, César A (August 2025, Methods in Ecology and Evolution)

   Abstract Quantifying the structure and dynamics of species interactions in ecological communities is fundamental to studying ecology and evolution. While there are numerous approaches to analysing ecological networks, there is not yet an approach that can (1) quantify dissimilarity in the global structure of ecological networks that range from identical species and interaction composition to zero shared species or interactions and (2) map species between such networks while incorporating additional ecological information, such as species traits or abundances.To address these challenges, we introduce the use of optimal transport distances to quantify ecological network dissimilarity and functionally equivalent species between networks. Specifically, we describe the Gromov–Wasserstein (GW) and Fused Gromov–Wasserstein (FGW) distances. We apply these optimal transport methods to synthetic and empirical data, using mammal food webs throughout sub‐Saharan Africa for illustration. We showcase the application of GW and FGW distances to identify the most functionally similar species between food webs, incorporate additional trait information into network comparisons and quantify food web dissimilarity among geographic regions.Our results demonstrate that GW and FGW distances can effectively differentiate ecological networks based on their topological structure while identifying functionally equivalent species, even when networks have different species. The FGW distance further improves node mapping for basal species by incorporating node‐level traits. We show that these methods allow for a more nuanced understanding of the topological similarities in food web networks among geographic regions compared to an alternative measure of network dissimilarity based on species identities.Optimal transport distances offer a new approach for quantifying functional equivalence between networks and a measure of network dissimilarity suitable for a broader range of uses than existing approaches. OT methods can be harnessed to analyse ecological networks at large spatial scales and compare networks among ecosystems, realms or taxa. Optimal transport‐based distances, therefore, provide a powerful tool for analysing ecological networks with great potential to advance our understanding of ecological community structure and dynamics in a changing world. 

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4. JADE: Joint Alignment and Deep Embedding for Multi-Slice Spatial Transcriptomics

   https://doi.org/10.1101/2025.11.21.689823  

   Guo, Yuanchuan; Liu, Jun S; Cheng, Huimin; Ma, Ying (November 2025, bioRxiv)

   Abstract As spatially resolved transcriptomics (SRT) datasets increasingly span multiple adjacent or replicated slices, effective joint analysis across slices is needed to reconstruct tissue structures and identify consistent spatial gene expression patterns. This requires resolving spatial correspondences between slices while capturing shared transcriptomic features, two tasks that are typically addressed in isolation. Multi-slice analysis remains challenging due to physical distortions, technical variability, and batch effects. To address these challenges, we introduce Joint Alignment and Deep Embedding for multi-slice SRT (JADE), a unified computational framework that simultaneously learns spatial location-wise alignments and shared low-dimensional embeddings across tissue slices. Unlike existing methods, JADE adopts a roundtrip framework in which each iteration alternates between alignment and embedding refinement. To infer alignment, we employ attention mechanisms that dynamically assess and weight the importance of different embedding dimensions, allowing the model to focus on the most alignment-relevant features while suppressing noise. To the best of our knowledge, JADE is the first method that jointly optimizes alignment and representation learning in a shared latent space, enabling robust multi-slice integration. We demonstrate that JADE outperforms existing alignment and embedding methods across multiple evaluation metrics in the 10x Visium human dorsolateral prefrontal cortex (DLPFC) and Stereo-seq axolotl brain datasets. By bridging spatial alignment and feature integration, JADE provides a scalable and accurate solution for cross-slice analysis of SRT data. 

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5. MrMine: Multi-resolution Multi-network Embedding

   https://doi.org/10.1145/3357384.3357944  

   Du, Boxin; Tong, Hanghang (November 2019, CIKM)

   Network embedding has become the cornerstone of a variety of mining tasks, such as classification, link prediction, clustering, anomaly detection and many more, thanks to its superior ability to encode the intrinsic network characteristics in a compact low-dimensional space. Most of the existing methods focus on a single network and/or a single resolution, which generate embeddings of different network objects (node/subgraph/network) from different networks separately. A fundamental limitation with such methods is that the intrinsic relationship across different networks (e.g., two networks share same or similar subgraphs) and that across different resolutions (e.g., the node-subgraph membership) are ignored, resulting in disparate embeddings. Consequentially, it leads to sub-optimal performance or even becomes inapplicable for some downstream mining tasks (e.g., role classification, network alignment. etc.). In this paper, we propose a unified framework MrMine to learn the representations of objects from multiple networks at three complementary resolutions (i.e., network, subgraph and node) simultaneously. The key idea is to construct the cross-resolution cross-network context for each object. The proposed method bears two distinctive features. First, it enables and/or boosts various multi-network downstream mining tasks by having embeddings at different resolutions from different networks in the same embedding space. Second, Our method is efficient and scalable, with a O(nlog(n)) time complexity for the base algorithm and a linear time complexity w.r.t. the number of nodes and edges of input networks for the accelerated version. Extensive experiments on real-world data show that our methods (1) are able to enable and enhance a variety of multi-network mining tasks, and (2) scale up to million-node networks. 

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