arXiv subjects

Bryan Perozzi

Publications and source records attributed to Bryan Perozzi.

At least 55 records · Page 3Linked to original sources

arXiv2021

Graph Traversal with Tensor Functionals: A Meta-Algorithm for Scalable Learning

Graph Representation Learning (GRL) methods have impacted fields from chemistry to social science. However, their algorithmic implementations are specialized to specific use-cases e.g.message passing methods are run differently from node embedding ones. Despite their apparent differences, all these methods utilize the graph structure, and therefore, their learning can be approximated with stochastic graph traversals. We propose Graph Traversal via Tensor Functionals(GTTF), a unifying meta-algorithm framework for easing the implementation of diverse graph algorithms and enabling transparent and efficient scaling to large graphs. GTTF is founded upon a data structure (stored as a sparse tensor) and a stochastic graph traversal algorithm (described using tensor operations). The algorithm is a functional that accept two functions, and can be specialized to obtain a variety of GRL models and objectives, simply by changing those two functions. We show for a wide class of methods, our algorithm learns in an unbiased fashion and, in expectation, approximates the learning as if the specialized implementations were run directly. With these capabilities, we scale otherwise non-scalable methods to set state-of-the-art on large graph datasets while being more efficient than existing GRL libraries - with only a handful of lines of code for each method specialization. GTTF and its various GRL implementations are on: https://github.com/isi-usc-edu/gttf.

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arXiv2020

InstantEmbedding: Efficient Local Node Representations

In this paper, we introduce InstantEmbedding, an efficient method for generating single-node representations using local PageRank computations. We theoretically prove that our approach produces globally consistent representations in sublinear time. We demonstrate this empirically by conducting extensive experiments on real-world datasets with over a billion edges. Our experiments confirm that InstantEmbedding requires drastically less computation time (over 9,000 times faster) and less memory (by over 8,000 times) to produce a single node's embedding than traditional methods including DeepWalk, node2vec, VERSE, and FastRP. We also show that our method produces high quality representations, demonstrating results that meet or exceed the state of the art for unsupervised representation learning on tasks like node classification and link prediction.

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arXiv2020

Grale: Designing Networks for Graph Learning

How can we find the right graph for semi-supervised learning? In real world applications, the choice of which edges to use for computation is the first step in any graph learning process. Interestingly, there are often many types of similarity available to choose as the edges between nodes, and the choice of edges can drastically affect the performance of downstream semi-supervised learning systems. However, despite the importance of graph design, most of the literature assumes that the graph is static. In this work, we present Grale, a scalable method we have developed to address the problem of graph design for graphs with billions of nodes. Grale operates by fusing together different measures of(potentially weak) similarity to create a graph which exhibits high task-specific homophily between its nodes. Grale is designed for running on large datasets. We have deployed Grale in more than 20 different industrial settings at Google, including datasets which have tens of billions of nodes, and hundreds of trillions of potential edges to score. By employing locality sensitive hashing techniques,we greatly reduce the number of pairs that need to be scored, allowing us to learn a task specific model and build the associated nearest neighbor graph for such datasets in hours, rather than the days or even weeks that might be required otherwise. We illustrate this through a case study where we examine the application of Grale to an abuse classification problem on YouTube with hundreds of million of items. In this application, we find that Grale detects a large number of malicious actors on top of hard-coded rules and content classifiers, increasing the total recall by 89% over those approaches alone.

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arXiv2020

Examining COVID-19 Forecasting using Spatio-Temporal Graph Neural Networks

In this work, we examine a novel forecasting approach for COVID-19 case prediction that uses Graph Neural Networks and mobility data. In contrast to existing time series forecasting models, the proposed approach learns from a single large-scale spatio-temporal graph, where nodes represent the region-level human mobility, spatial edges represent the human mobility based inter-region connectivity, and temporal edges represent node features through time. We evaluate this approach on the US county level COVID-19 dataset, and demonstrate that the rich spatial and temporal information leveraged by the graph neural network allows the model to learn complex dynamics. We show a 6% reduction of RMSLE and an absolute Pearson Correlation improvement from 0.9978 to 0.998 compared to the best performing baseline models. This novel source of information combined with graph based deep learning approaches can be a powerful tool to understand the spread and evolution of COVID-19. We encourage others to further develop a novel modeling paradigm for infectious disease based on GNNs and high resolution mobility data.

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arXiv2020

Just SLaQ When You Approximate: Accurate Spectral Distances for Web-Scale Graphs

Graph comparison is a fundamental operation in data mining and information retrieval. Due to the combinatorial nature of graphs, it is hard to balance the expressiveness of the similarity measure and its scalability. Spectral analysis provides quintessential tools for studying the multi-scale structure of graphs and is a well-suited foundation for reasoning about differences between graphs. However, computing full spectrum of large graphs is computationally prohibitive; thus, spectral graph comparison methods often rely on rough approximation techniques with weak error guarantees. In this work, we propose SLaQ, an efficient and effective approximation technique for computing spectral distances between graphs with billions of nodes and edges. We derive the corresponding error bounds and demonstrate that accurate computation is possible in time linear in the number of graph edges. In a thorough experimental evaluation, we show that SLaQ outperforms existing methods, oftentimes by several orders of magnitude in approximation accuracy, and maintains comparable performance, allowing to compare million-scale graphs in a matter of minutes on a single machine.

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arXiv2020

MONET: Debiasing Graph Embeddings via the Metadata-Orthogonal Training Unit

Are Graph Neural Networks (GNNs) fair? In many real world graphs, the formation of edges is related to certain node attributes (e.g. gender, community, reputation). In this case, standard GNNs using these edges will be biased by this information, as it is encoded in the structure of the adjacency matrix itself. In this paper, we show that when metadata is correlated with the formation of node neighborhoods, unsupervised node embedding dimensions learn this metadata. This bias implies an inability to control for important covariates in real-world applications, such as recommendation systems. To solve these issues, we introduce the Metadata-Orthogonal Node Embedding Training (MONET) unit, a general model for debiasing embeddings of nodes in a graph. MONET achieves this by ensuring that the node embeddings are trained on a hyperplane orthogonal to that of the node metadata. This effectively organizes unstructured embedding dimensions into an interpretable topology-only, metadata-only division with no linear interactions. We illustrate the effectiveness of MONET though our experiments on a variety of real world graphs, which shows that our method can learn and remove the effect of arbitrary covariates in tasks such as preventing the leakage of political party affiliation in a blog network, and thwarting the gaming of embedding-based recommendation systems.

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arXiv2019

MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixing

Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operators, by repeatedly mixing feature representations of neighbors at various distances. Mixhop requires no additional memory or computational complexity, and outperforms on challenging baselines. In addition, we propose sparsity regularization that allows us to visualize how the network prioritizes neighborhood information across different graph datasets. Our analysis of the learned architectures reveals that neighborhood mixing varies per datasets.

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arXiv2019

Is a Single Embedding Enough? Learning Node Representations that Capture Multiple Social Contexts

Recent interest in graph embedding methods has focused on learning a single representation for each node in the graph. But can nodes really be best described by a single vector representation? In this work, we propose a method for learning multiple representations of the nodes in a graph (e.g., the users of a social network). Based on a principled decomposition of the ego-network, each representation encodes the role of the node in a different local community in which the nodes participate. These representations allow for improved reconstruction of the nuanced relationships that occur in the graph -- a phenomenon that we illustrate through state-of-the-art results on link prediction tasks on a variety of graphs, reducing the error by up to $90\%$. In addition, we show that these embeddings allow for effective visual analysis of the learned community structure.

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arXiv2019

DDGK: Learning Graph Representations for Deep Divergence Graph Kernels

Can neural networks learn to compare graphs without feature engineering? In this paper, we show that it is possible to learn representations for graph similarity with neither domain knowledge nor supervision (i.e.\ feature engineering or labeled graphs). We propose Deep Divergence Graph Kernels, an unsupervised method for learning representations over graphs that encodes a relaxed notion of graph isomorphism. Our method consists of three parts. First, we learn an encoder for each anchor graph to capture its structure. Second, for each pair of graphs, we train a cross-graph attention network which uses the node representations of an anchor graph to reconstruct another graph. This approach, which we call isomorphism attention, captures how well the representations of one graph can encode another. We use the attention-augmented encoder's predictions to define a divergence score for each pair of graphs. Finally, we construct an embedding space for all graphs using these pair-wise divergence scores. Unlike previous work, much of which relies on 1) supervision, 2) domain specific knowledge (e.g. a reliance on Weisfeiler-Lehman kernels), and 3) known node alignment, our unsupervised method jointly learns node representations, graph representations, and an attention-based alignment between graphs. Our experimental results show that Deep Divergence Graph Kernels can learn an unsupervised alignment between graphs, and that the learned representations achieve competitive results when used as features on a number of challenging graph classification tasks. Furthermore, we illustrate how the learned attention allows insight into the the alignment of sub-structures across graphs.

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arXiv2018

Enhanced Network Embeddings via Exploiting Edge Labels

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. While achieving competitive performance on a variety of network inference tasks such as node classification and link prediction, these methods treat the relations between nodes as a binary variable and ignore the rich semantics of edges. In this work, we attempt to learn network embeddings which simultaneously preserve network structure and relations between nodes. Experiments on several real-world networks illustrate that by considering different relations between different node pairs, our method is capable of producing node embeddings of higher quality than a number of state-of-the-art network embedding methods, as evaluated on a challenging multi-label node classification task.

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arXiv2018

Watch Your Step: Learning Node Embeddings via Graph Attention

Graph embedding methods represent nodes in a continuous vector space, preserving information from the graph (e.g. by sampling random walks). There are many hyper-parameters to these methods (such as random walk length) which have to be manually tuned for every graph. In this paper, we replace random walk hyper-parameters with trainable parameters that we automatically learn via backpropagation. In particular, we learn a novel attention model on the power series of the transition matrix, which guides the random walk to optimize an upstream objective. Unlike previous approaches to attention models, the method that we propose utilizes attention parameters exclusively on the data (e.g. on the random walk), and not used by the model for inference. We experiment on link prediction tasks, as we aim to produce embeddings that best-preserve the graph structure, generalizing to unseen information. We improve state-of-the-art on a comprehensive suite of real world datasets including social, collaboration, and biological networks. Adding attention to random walks can reduce the error by 20% to 45% on datasets we attempted. Further, our learned attention parameters are different for every graph, and our automatically-found values agree with the optimal choice of hyper-parameter if we manually tune existing methods.

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arXiv2018

A Tutorial on Network Embeddings

Network embedding methods aim at learning low-dimensional latent representation of nodes in a network. These representations can be used as features for a wide range of tasks on graphs such as classification, clustering, link prediction, and visualization. In this survey, we give an overview of network embeddings by summarizing and categorizing recent advancements in this research field. We first discuss the desirable properties of network embeddings and briefly introduce the history of network embedding algorithms. Then, we discuss network embedding methods under different scenarios, such as supervised versus unsupervised learning, learning embeddings for homogeneous networks versus for heterogeneous networks, etc. We further demonstrate the applications of network embeddings, and conclude the survey with future work in this area.

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arXiv2018

N-GCN: Multi-scale Graph Convolution for Semi-supervised Node Classification

Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations.

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arXiv2017

ASYMP: Fault-tolerant Mining of Massive Graphs

We present ASYMP, a distributed graph processing system developed for the timely analysis of graphs with trillions of edges. ASYMP has several distinguishing features including a robust fault tolerance mechanism, a lockless architecture which scales seamlessly to thousands of machines, and efficient data access patterns to reduce per-machine overhead. ASYMP is used to analyze the largest graphs at Google, and the graphs we consider in our empirical evaluation here are, to the best of our knowledge, the largest considered in the literature. Our experimental results show that compared to previous graph processing frameworks at Google, ASYMP can scale to larger graphs, operate on more crowded clusters, and complete real-world graph mining analytic tasks faster. First, we evaluate the speed of ASYMP, where we show that across a diverse selection of graphs, it runs Connected Component 3-50x faster than state of the art implementations in MapReduce and Pregel. Then we demonstrate the scalability and parallelism of this framework: first by showing that the running time increases linearly by increasing the size of the graphs (without changing the number of machines), and then by showing the gains in running time while increasing the number of machines. Finally, we demonstrate the fault-tolerance properties for the framework, showing that inducing 50% of our machines to fail increases the running time by only 41%.

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arXiv2017

HARP: Hierarchical Representation Learning for Networks

We present HARP, a novel method for learning low dimensional embeddings of a graph's nodes which preserves higher-order structural features. Our proposed method achieves this by compressing the input graph prior to embedding it, effectively avoiding troublesome embedding configurations (i.e. local minima) which can pose problems to non-convex optimization. HARP works by finding a smaller graph which approximates the global structure of its input. This simplified graph is used to learn a set of initial representations, which serve as good initializations for learning representations in the original, detailed graph. We inductively extend this idea, by decomposing a graph in a series of levels, and then embed the hierarchy of graphs from the coarsest one to the original graph. HARP is a general meta-strategy to improve all of the state-of-the-art neural algorithms for embedding graphs, including DeepWalk, LINE, and Node2vec. Indeed, we demonstrate that applying HARP's hierarchical paradigm yields improved implementations for all three of these methods, as evaluated on both classification tasks on real-world graphs such as DBLP, BlogCatalog, CiteSeer, and Arxiv, where we achieve a performance gain over the original implementations by up to 14% Macro F1.

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arXiv2017

Learning Edge Representations via Low-Rank Asymmetric Projections

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the "graph likelihood", which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76% and 55%, on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller.

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arXiv2017

Don't Walk, Skip! Online Learning of Multi-scale Network Embeddings

We present Walklets, a novel approach for learning multiscale representations of vertices in a network. In contrast to previous works, these representations explicitly encode multiscale vertex relationships in a way that is analytically derivable. Walklets generates these multiscale relationships by subsampling short random walks on the vertices of a graph. By `skipping' over steps in each random walk, our method generates a corpus of vertex pairs which are reachable via paths of a fixed length. This corpus can then be used to learn a series of latent representations, each of which captures successively higher order relationships from the adjacency matrix. We demonstrate the efficacy of Walklets's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, DBLP, Flickr, and YouTube. Our results show that Walklets outperforms new methods based on neural matrix factorization. Specifically, we outperform DeepWalk by up to 10% and LINE by 58% Micro-F1 on challenging multi-label classification tasks. Finally, Walklets is an online algorithm, and can easily scale to graphs with millions of vertices and edges.

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arXiv2017

Ties That Bind - Characterizing Classes by Attributes and Social Ties

Given a set of attributed subgraphs known to be from different classes, how can we discover their differences? There are many cases where collections of subgraphs may be contrasted against each other. For example, they may be assigned ground truth labels (spam/not-spam), or it may be desired to directly compare the biological networks of different species or compound networks of different chemicals. In this work we introduce the problem of characterizing the differences between attributed subgraphs that belong to different classes. We define this characterization problem as one of partitioning the attributes into as many groups as the number of classes, while maximizing the total attributed quality score of all the given subgraphs. We show that our attribute-to-class assignment problem is NP-hard and an optimal $(1 - 1/e)$-approximation algorithm exists. We also propose two different faster heuristics that are linear-time in the number of attributes and subgraphs. Unlike previous work where only attributes were taken into account for characterization, here we exploit both attributes and social ties (i.e. graph structure). Through extensive experiments, we compare our proposed algorithms, show findings that agree with human intuition on datasets from Amazon co-purchases, Congressional bill sponsorships, and DBLP co-authorships. We also show that our approach of characterizing subgraphs is better suited for sense-making than discriminating classification approaches.

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