An official website of the United States government
Learning discriminative node representations benefits various downstream tasks in graph analysis such as community detection and node classification. Existing graph representation learning methods (e.g., based on random walk and contrastive learning) are limited to maximizing the local similarity of connected nodes. Such pair-wise learning schemes could fail to capture the global distribution of representations, since it has no explicit constraints on the global geometric properties of representation space. To this end, we propose Geometric Graph Representation Learning (G2R) to learn node representations in an unsupervised manner via maximizing rate reduction. In this way, G2R maps nodes in distinct groups (implicitly stored in the adjacency matrix) into different subspaces, while each subspace is compact and different subspaces are dispersedly distributed. G2R adopts a graph neural network as the encoder and maximizes the rate reduction with the adjacency matrix. Furthermore, we theoretically and empirically demonstrate that rate reduction maximization is equivalent to maximizing the principal angles between different subspaces. Experiments on real-world datasets show that G2R outperforms various baselines on node classification and community detection tasks.
more »
« less
Fast and Accurate Network Embeddings via Very Sparse Random Projection
We present FastRP, a scalable and performant algorithm for learning distributed node representations in a graph. FastRP is over 4,000 times faster than state-of-the-art methods such as DeepWalk and node2vec, while achieving comparable or even better performance as evaluated on several real-world networks on various downstream tasks. We observe that most network embedding methods consist of two components: construct a node similarity matrix and then apply dimension reduction techniques to this matrix. We show that the success of these methods should be attributed to the proper construction of this similarity matrix, rather than the dimension reduction method employed. FastRP is proposed as a scalable algorithm for network embeddings. Two key features of FastRP are: 1) it explicitly constructs a node similarity matrix that captures transitive relationships in a graph and normalizes matrix entries based on node degrees; 2) it utilizes very sparse random projection, which is a scalable optimization-free method for dimension reduction. An extra benefit from combining these two design choices is that it allows the iterative computation of node embeddings so that the similarity matrix need not be explicitly constructed, which further speeds up FastRP. FastRP is also advantageous for its ease of implementation, parallelization and hyperparameter tuning. The source code is available at https://github.com/GTmac/FastRP.
more »
« less
- Award ID(s):
- 1927227
- PAR ID:
- 10283034
- Date Published:
- Journal Name:
- CIKM '19: Proceedings of the 28th ACM International Conference on Information and Knowledge Management
- Page Range / eLocation ID:
- 399 to 408
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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.more » « less
-
Graph contrastive learning (GCL) has emerged as a successful method for self-supervised graph learning. It involves generating augmented views of a graph by augmenting its edges and aims to learn node embeddings that are invariant to graph augmentation. Despite its effectiveness, the potential privacy risks associated with GCL models have not been thoroughly explored. In this paper, we delve into the privacy vulnerability of GCL models through the lens of link membership inference attacks (LMIA). Specifically, we focus on the federated setting where the adversary has white-box access to the node embeddings of all the augmented views generated by the target GCL model. Designing such white-box LMIAs against GCL models presents a significant and unique challenge due to potential variations in link memberships among node pairs in the target graph and its augmented views. This variability renders members indistinguishable from non-members when relying solely on the similarity of their node embeddings in the augmented views. To address this challenge, our in-depth analysis reveals that the key distinguishing factor lies in the similarity of node embeddings within augmented views where the node pairs share identical link memberships as those in the training graph. However, this poses a second challenge, as information about whether a node pair has identical link membership in both the training graph and augmented views is only available during the attack training phase. This demands the attack classifier to handle the additional “identical-membership information which is available only for training and not for testing. To overcome this challenge, we propose GCL-LEAK, the first link membership inference attack against GCL models. The key component of GCL-LEAK is a new attack classifier model designed under the “Learning Using Privileged Information (LUPI)” paradigm, where the privileged information of “same-membership” is encoded as part of the attack classifier's structure. Our extensive set of experiments on four representative GCL models showcases the effectiveness of GCL-LEAK. Additionally, we develop two defense mechanisms that introduce perturbation to the node embeddings. Our empirical evaluation demonstrates that both defense mechanisms significantly reduce attack accuracy while preserving the accuracy of GCL models.more » « less
-
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.more » « less
-
We propose a new randomized algorithm for solving L2-regularized least-squares problems based on sketching. We consider two of the most popular random embeddings, namely, Gaussian embeddings and the Subsampled Randomized Hadamard Transform (SRHT). While current randomized solvers for least-squares optimization prescribe an embedding dimension at least greater than the data dimension, we show that the embedding dimension can be reduced to the effective dimension of the optimization problem, and still preserve high-probability convergence guarantees. In this regard, we derive sharp matrix deviation inequalities over ellipsoids for both Gaussian and SRHT embeddings. Specifically, we improve on the constant of a classical Gaussian concentration bound whereas, for SRHT embeddings, our deviation inequality involves a novel technical approach. Leveraging these bounds, we are able to design a practical and adaptive algorithm which does not require to know the effective dimension beforehand. Our method starts with an initial embedding dimension equal to 1 and, over iterations, increases the embedding dimension up to the effective one at most. Hence, our algorithm improves the state-of-the-art computational complexity for solving regularized least-squares problems. Further, we show numerically that it outperforms standard iterative solvers such as the conjugate gradient method and its pre-conditioned version on several standard machine learning datasets.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3357384.3357879
