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Graph mining

Our mission is to build the most scalable library for graph algorithms and analysis and apply it to a multitude of Google products.

graphs

Graph mining

About the team

We formalize data mining and machine learning challenges as graph problems and perform fundamental research in those fields leading to publications in top venues. Our algorithms and systems are used in a wide array of Google products such as Search, YouTube, AdWords, Play, Maps, and Social.

Team focus summaries

Large-Scale Clustering and Connected Components

Our team specializes in clustering at Google scale, efficiently implementing many different algorithms including hierarchical agglomerative clustering, correlation clustering, k-means clustering, DBSCAN, and connected components. Our methods scale to graphs with trillions of edges using multiple machines and can efficiently handle graphs of tens of billions of edges on a single multicore machine. The clustering library powers over a hundred different use-cases across Google.

Graph Neural Networks and Graph Embeddings

Our team specializes in large-scale learning on graph-structured data. We push the boundary on scalability, efficiency, and flexibility of our methods, informed by the complex heterogeneous systems abundant in our real-world industrial setting. In pursuit of scalability, we leverage both algorithmic improvements and novel hardware architectures. Our team develops and maintains TensorFlow-GNN, a library for training graph neural networks at Google scale.

Large-Scale balanced partitioning

Balanced Partitioning splits a large graph into roughly equal parts while minimizing cut size. The problem of “fairly” dividing a graph occurs in a number of contexts, such as assigning work in a distributed processing environment. Our techniques provided a 40% drop in multi-shard queries in Google Maps driving directions, saving a significant amount of CPU usage.

Large-Scale link modeling

Large-Scale similarity ranking

Our research in pairwise similarity ranking has produced a number of innovative methods, which we have published at top conferences such as WWW, ICML, and VLDB. We maintain a library of similarity algorithms including distributed Personalized PageRank, Egonet similarity, and others.

Public-private graph computation

Our research on novel models of graph computation addresses important issues of privacy in graph mining. Specifically, we present techniques to efficiently solve graph problems, including computing clustering, centrality scores and shortest path distances for each node, based on its personal view of the private data in the graph while preserving the privacy of each user.

Streaming and dynamic graph algorithms

We perform innovative research analyzing massive dynamic graphs. We have developed efficient algorithms for computing densest subgraph and triangle counting which operate even when subject to high velocity streaming updates.

Large-Scale centrality ranking

Google’s most famous algorithm, PageRank, is a method for computing importance scores for vertices of a directed graph. In addition to PageRank, we have scalable implementations of several other centrality scores, such as harmonic centrality.

Large-Scale graph building

The GraphBuilder library can convert data from a metric space (such as document text) into a similarity graph. GraphBuilder scales to massive datasets by applying fast locality sensitive hashing and neighborhood search.

Graph-based sampling

Distributed graph-based sampling has proved critical to various applications in active learning and data summarization, where the graph reveals signals about density and multi-hop connections. Combined with deep learning, we tackle provably hard problems and differentiable sampling helps GNN scalability too.

ML compiler optimization

We design and implement graph-based optimization techniques to improve the performance of ML compilers (e.g., XLA). For example, we replaced heuristic-based cost models with graph neural networks (GNNs), achieving significant training and serving speed-ups (see our external TpuGraphs benchmarks and large-scale GNN). We have also deployed model partitioning algorithms that split ML computation graphs across TPUs for pipeline parallelism, as well as designed novel methods to certify that these partitions are near-optimal.

Featured publications

Preview abstract Graphs are a powerful tool for representing and analyzing complex relationships in real-world applications such as social networks, recommender systems, and computational finance. Reasoning on graphs is essential for drawing inferences about the relationships between entities in a complex system, and to identify hidden patterns and trends. Despite the remarkable progress in automated reasoning with natural text, reasoning on graphs with large language models (LLMs) remains an understudied problem. In this work, we perform the first comprehensive study of encoding graph-structured data as text for consumption by LLMs. We show that LLM performance on graph reasoning tasks varies on three fundamental levels: (1) the graph encoding method, (2) the nature of the graph task itself, and (3) interestingly, the very structure of the graph considered. These novel results provide valuable insight on strategies for encoding graphs as text. Using these insights we illustrate how the correct choice of encoders can boost performance on graph reasoning tasks inside LLMs by 4.8% to 61.8%, depending on the task. View details
Measuring Re-identification Risk
Travis Dick
Adel Javanmard
Josh Karlin
Andres Munoz Medina
Gabriel Henrique Nunes
Peilin Zhong
SIGMOD (2023)
Preview abstract Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on hypothesis testing, formally bounds the probability that an attacker may be able to obtain the identity of a user from their representation. As an application, we show how our framework is general enough to model important real-world applications such as the Chrome's Topics API for interest-based advertising. We complement our theoretical bounds by showing provably good attack algorithms for re-identification that we use to estimate the re-identification risk in the Topics API. We believe this work provides a rigorous and interpretable notion of re-identification risk and a framework to measure it that can be used to inform real-world applications. View details
Preview abstract We study the differentially private (DP) $k$-means and $k$-median clustering problems of $n$ points in $d$-dimensional Euclidean space in the massively parallel computation (MPC) model. We provide two near-optimal algorithms where the near-optimality is in three aspects: they both achieve (1). $O(1)$ parallel computation rounds, (2). near-linear in $n$ and polynomial in $k$ total computational work (i.e., near-linear running time in the sequential setting), (3). $O(1)$ relative approximation and $\text{poly}(k, d)$ additive error, where $\Omega(1)$ relative approximation is provably necessary even for any polynomial-time non-private algorithm, and $\Omega(k)$ additive error is a provable lower bound for any polynomial-time DP $k$-means/median algorithm. Our two algorithms provide a tradeoff between the relative approximation and the additive error: the first has $O(1)$ relative approximation and $\sim (k^{2.5} + k^{1.01} \sqrt{d})$ additive error, and the second one achieves $(1+\gamma)$ relative approximation to the optimal non-private algorithm for an arbitrary small constant $\gamma>0$ and with $\text{poly}(k, d)$ additive error for a larger polynomial dependence on $k$ and $d$. To achieve our result, we develop a general framework which partitions the data and reduces the DP clustering problem for the entire dataset to the DP clustering problem for each part. To control the blow-up of the additive error introduced by each part, we develop a novel charging argument which might be of independent interest. View details
Optimal Distributed Submodular Optimization via Sketching
Hossein Esfandiari
Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2018), pp. 1138-1147
Preview abstract As an important special case of submodular optimization problems, coverage problems are a central problem in optimization with a wide range of applications in data mining and machine learning. As we need to handle larger and larger data sets, there is a clear need to develop distributed solutions to these problems. While several results have been developed for distributed coverage maximizations, all the existing method have notable limitations, e.g., they all achieve either suboptimal approximation guarantees or suboptimal space and memory complexities. Moreover, most previous results for submodular maximization either explicitly or implicitly assume that one has a value oracle access to the submodular function. Such a value oracle for coverage functions has the following form: given a subfamily of (input) subsets, determine the size of the union of the subsets in this subfamily. View details
Preview abstract Representative Selection (RS) is the problem of finding a small subset of exemplars from a dataset that is representative of the dataset. In this paper, we study RS for attributed graphs, and focus on finding representative nodes that optimize the accuracy of a model trained on the selected representatives. Theoretically, we establish a new hardness result for RS (in the absence of a graph structure) by proving that a particular, highly practical variant of it (RS for Learning) is hard to approximate in polynomial time within any reasonable factor, which implies a significant potential gap between the optimum solution of widely-used surrogate functions and the actual accuracy of the model. We then study the setting where a (homophilous) graph structure is available, or can be constructed, between the data points. We show that with an appropriate modeling approach, the presence of such a structure can turn a hard RS (for learning) problem into one that can be effectively solved. To this end, we develop RS-GNN, a representation learning-based RS model based on Graph Neural Networks. Empirically, we demonstrate the effectiveness of RS-GNN on problems with predefined graph structures as well as problems with graphs induced from node feature similarities, by showing that RS-GNN achieves significant improvements over established baselines on a suite of eight benchmarks. View details
Preview abstract We introduceTeraHAC, a (1+epsilon)-approximate hierarchical agglomerative clustering (HAC) algorithm whichs cales to trillion-edge graphs. Our algorithm is based on a new approach to computing (1+epsilon)-approximate HAC, which is a novel combination of the nearest-neighbor chain algorithm and the notion of (1+epsilon)-approximate HAC. Our approach allows us to partition the graph among multiple machines and make significant progress in computing the clustering within each partition before any communication with other partitions is needed.We evaluate TeraHAC on a number of real-world and synthetic graphs of up to 8 trillion edges. We show that TeraHAC requires over 100x fewer rounds compared to previously known approaches for computing HAC. It is up to 8.3x faster than SCC, the state-of-the-art distributed algorithm for hierarchical clustering, while achieving 1.16x higher quality. In fact, TeraHAC essentially retains the quality of the celebrated HAC algorithm while significantly improving the running time. View details
Massively Parallel Computation via Remote Memory Access
Hossein Esfandiari
Laxman Dhulipala
Soheil Behnezhad
Warren Schudy
SPAA 2019
Preview abstract We introduce the Adaptive Massively Parallel Computation (AMPC) model, which is an extension of the widely popular Massively Parallel Computation (MPC) model. At a high level, the AMPC model strengthens the MPC model by storing all messages sent within a round in a distributed data store. In the following round all machines are provided with random read access to the data store, subject to the same constraints on the total amount of communication as in the MPC model. Our model is inspired by the previous empirical studies of distributed graph algorithms using MapReduce and a distributed hash table service. This extension allows us to give new graph algorithms with much lower round complexities compared to the best known solutions in the MPC model. In particular, in the AMPC model we show how to solve maximal independent set in O(1) rounds, and connectivity/minimum spanning tree in O(log log_{m/n} n) rounds, which is an exponential improvement upon the best known algorithms in the MPC model with sublinear space per machine. Our results imply that the 2-Cycle conjecture, the most popular hardness conjecture in the MPC model, does not hold in the AMPC model. View details
Affinity Clustering: Hierarchical Clustering at Scale
Soheil Behnezhad
Mahsa Derakhshan
MohammadTaghi Hajiaghayi
Raimondas Kiveris
NIPS 2017, pp. 6867-6877
Preview abstract Graph clustering is a fundamental task in many data-mining and machine-learning pipelines. In particular, identifying good hierarchical clustering structure is at the same time a fundamental and challenging problem for several applications. In many applications, the amount of data to analyze is increasing at an astonishing rate each day. Hence there is a need for new solutions to efficiently compute effective hierarchical clusterings on such huge data. In this paper, we propose algorithms to address this problem. First, we analyze minimum spanning tree-based clustering algorithms and their corresponding hierarchical clusterings. In particular we consider classic single-linkage clustering based on Kruskal's algorithm and a variation of Boruvka algorithm that we call affinity clustering and prove new interesting properties of these clusterings via the concept of certificates. Then we present new algorithms in the MapReduce model and their efficient real world implementations via Distributed Hash Tables (DHTs). Our MapReduce algorithms indeed improve upon the previous MapReduce algorithms for finding a minimum spanning tree in graphs as well. Finally we show experimentally that our algorithms are scalable for huge data and competitive with state-of-the-art algorithms. In particular we show that Affinity Clustering is in practice superior to several state-of-the-art clustering algorithms. View details
Distributed Balanced Partitioning via Linear Embedding
Ninth ACM International Conference on Web Search and Data Mining (WSDM), ACM (2016), pp. 387-396
Preview abstract Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems: in some cases, a big graph is chopped into pieces that fit on one machine to be processed independently before stitching the results together, leading to certain suboptimality from the interaction among different pieces. In other cases, links between different parts may show up in the running time and/or network communications cost, hence the desire to have small cut size. We study a distributed balanced partitioning problem where the goal is to partition the vertices of a given graph into k pieces, minimizing the total cut size. Our algorithm is composed of a few steps that are easily implementable in distributed computation frameworks, e.g., MapReduce. The algorithm first embeds nodes of the graph onto a line, and then processes nodes in a distributed manner guided by the linear embedding order. We examine various ways to find the first embedding, e.g., via a hierarchical clustering or Hilbert curves. Then we apply four different techniques such as local swaps, minimum cuts on partition boundaries, as well as contraction and dynamic programming. Our empirical study compares the above techniques with each other, and to previous work in distributed algorithms, e.g., a label propagation method [34], FENNEL [32] and Spinner [23]. We report our results both on a private map graph and several public social networks, and show that our results beat previous distributed algorithms: we notice, e.g., 15-25% reduction in cut size over [34]. We also observe that our algorithms allow for scalable distributed implementation for any number of partitions. Finally, we apply our techniques for the Google Maps Driving Directions to minimize the number of multi-shard queries with the goal of saving in CPU usage. During live experiments, we observe an ≈ 40% drop in the number of multi-shard queries when comparing our method with a standard geography-based method. View details
Preview abstract As a fundamental tool in modeling and analyzing social, and information networks, large-scale graph mining is an important component of any tool set for big data analysis. Processing graphs with hundreds of billions of edges is only possible via developing distributed algorithms under distributed graph mining frameworks such as MapReduce, Pregel, Gigraph, and alike. For these distributed algorithms to work well in practice, we need to take into account several metrics such as the number of rounds of computation and the communication complexity of each round. For example, given the popularity and ease-of-use of MapReduce framework, developing practical algorithms with good theoretical guarantees for basic graph algorithms is a problem of great importance. In this tutorial, we first discuss how to design and implement algorithms based on traditional MapReduce architecture. In this regard, we discuss various basic graph theoretic problems such as computing connected components, maximum matching, MST, counting triangle and overlapping or balanced clustering. We discuss a computation model for MapReduce and describe the sampling, filtering, local random walk, and core-set techniques to develop efficient algorithms in this framework. At the end, we explore the possibility of employing other distributed graph processing frameworks. In particular, we study the effect of augmenting MapReduce with a distributed hash table (DHT) service and also discuss the use of a new graph processing framework called ASYMP based on asynchronous message-passing method. In particular, we will show that using ASyMP, one can improve the CPU usage, and achieve significantly improved running time. View details
Grale: Designing Networks for Graph Learning
Alexandru Moșoi
Sam Ruth
Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Association for Computing Machinery (2020), 2523–2532
Preview abstract 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. View details

Highlighted work

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