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As online platforms are striving to get more users, a critical challenge is user churn, which is especially concerning for new users. In this paper, by taking the anonymous large-scale real-world data from Snapchat as an example, we develop \textit{ClusChurn}, a systematic two-step framework for interpretable new user clustering and churn prediction, based on the intuition that proper user clustering can help understand and predict user churn. Therefore, \textit{ClusChurn} firstly groups new users into interpretable typical clusters, based on their activities on the platform and ego-network structures. Then we design a novel deep learning pipeline based on LSTM and attention to accurately predict user churn with very limited initial behavior data, by leveraging the correlations among users' multi-dimensional activities and the underlying user types. \textit{ClusChurn} is also able to predict user types, which enables rapid reactions to different types of user churn. Extensive data analysis and experiments show that \textit{ClusChurn} provides valuable insight into user behaviors, and achieves state-of-the-art churn prediction performance. The whole framework is deployed as a data analysis pipeline, delivering real-time data analysis and prediction results to multiple relevant teams for business intelligence uses. It is also general enough to be readily adopted by any online systems with user behavior data., Comment: Published at KDD 2018

In this work, we propose to study the utility of different meta-graphs, as well as how to simultaneously leverage multiple meta-graphs for HIN embedding in an unsupervised manner. Motivated by prolific research on homogeneous networks, especially spectral graph theory, we firstly conduct a systematic empirical study on the spectrum and embedding quality of different meta-graphs on multiple HINs, which leads to an efficient method of meta-graph assessment. It also helps us to gain valuable insight into the higher-order organization of HINs and indicates a practical way of selecting useful embedding dimensions. Further, we explore the challenges of combining multiple meta-graphs to capture the multi-dimensional semantics in HIN through reasoning from mathematical geometry and arrive at an embedding compression method of autoencoder with $\ell_{2,1}$-loss, which finds the most informative meta-graphs and embeddings in an end-to-end unsupervised manner. Finally, empirical analysis suggests a unified workflow to close the gap between our meta-graph assessment and combination methods. To the best of our knowledge, this is the first research effort to provide rich theoretical and empirical analyses on the utility of meta-graphs and their combinations, especially regarding HIN embedding. Extensive experimental comparisons with various state-of-the-art neural network based embedding methods on multiple real-world HINs demonstrate the effectiveness and efficiency of our framework in finding useful meta-graphs and generating high-quality HIN embeddings., Comment: 10 pages, published at ICDM 2018

Classification is one of the most important problems in machine learning. To address label scarcity, semi-supervised learning (SSL) has been intensively studied over the past two decades, which mainly leverages data affinity modeled by networks. Label propagation (LP), however, as the most popular SSL technique, mostly only works on homogeneous networks with single-typed simple interactions. In this work, we focus on the more general and powerful heterogeneous networks, which accommodate multi-typed objects and links, and thus endure multi-typed complex interactions. Specifically, we propose \textit{neural embedding propagation} (NEP), which leverages distributed embeddings to represent objects and dynamically composed modular networks to model their complex interactions. While generalizing LP as a simple instance, NEP is far more powerful in its natural awareness of different types of objects and links, and the ability to automatically capture their important interaction patterns. Further, we develop a series of efficient training strategies for NEP, leading to its easy deployment on real-world heterogeneous networks with millions of objects. With extensive experiments on three datasets, we comprehensively demonstrate the effectiveness, efficiency, and robustness of NEP compared with state-of-the-art network embedding and SSL algorithms., Comment: 11 pages, published at ICDM 2019

Given a query, unlike traditional IR that finds relevant documents or entities, in this work, we focus on retrieving both entities and their connections for insightful knowledge summarization. For example, given a query "computer vision" on a CS literature corpus, rather than returning a list of relevant entities like "cnn", "imagenet" and "svm", we are interested in the connections among them, and furthermore, the evolution patterns of such connections along particular ordinal dimensions such as time. Particularly, we hope to provide structural knowledge relevant to the query, such as "svm" is related to "imagenet" but not "cnn". Moreover, we aim to model the changing trends of the connections, such as "cnn" becomes highly related to "imagenet" after 2010, which enables the tracking of knowledge evolutions. In this work, to facilitate such a novel insightful search system, we propose \textsc{SetEvolve}, which is a unified framework based on nonparanomal graphical models for evolutionary network construction from large text corpora. Systematic experiments on synthetic data and insightful case studies on real-world corpora demonstrate the utility of \textsc{SetEvolve}., Comment: published in CIKM 2019

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based on sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first high-performance linear algebra-based graph framework on NVIDIA GPUs that is open-source. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model., Comment: 50 pages, 14 figures, 14 tables, to appear in ACM Transactions on Mathematical Software

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions., Comment: A long version of EvoNet (WSDM 2021)

Deep neural networks (DNNs) have been widely applied to various applications, including image classification, text generation, audio recognition, and graph data analysis. However, recent studies have shown that DNNs are vulnerable to adversarial attacks. Though there are several works about adversarial attack and defense strategies on domains such as images and natural language processing, it is still difficult to directly transfer the learned knowledge to graph data due to its representation structure. Given the importance of graph analysis, an increasing number of studies over the past few years have attempted to analyze the robustness of machine learning models on graph data. Nevertheless, existing research considering adversarial behaviors on graph data often focuses on specific types of attacks with certain assumptions. In addition, each work proposes its own mathematical formulation, which makes the comparison among different methods difficult. Therefore, this review is intended to provide an overall landscape of more than 100 papers on adversarial attack and defense strategies for graph data, and establish a unified formulation encompassing most graph adversarial learning models. Moreover, we also compare different graph attacks and defenses along with their contributions and limitations, as well as summarize the evaluation metrics, datasets and future trends. We hope this survey can help fill the gap in the literature and facilitate further development of this promising new field., Comment: Published on IEEE TKDE. For more open-source and up-to-date information, please check our Github repository: https://github.com/YingtongDou/graph-adversarial-learning-literature

Heterogeneous information networks (HINs) with rich semantics are ubiquitous in real-world applications. For a given HIN, many reasonable clustering results with distinct semantic meaning can simultaneously exist. User-guided clustering is hence of great practical value for HINs where users provide labels to a small portion of nodes. To cater to a broad spectrum of user guidance evidenced by different expected clustering results, carefully exploiting the signals residing in the data is potentially useful. Meanwhile, as one type of complex networks, HINs often encapsulate higher-order interactions that reflect the interlocked nature among nodes and edges. Network motifs, sometimes referred to as meta-graphs, have been used as tools to capture such higher-order interactions and reveal the many different semantics. We therefore approach the problem of user-guided clustering in HINs with network motifs. In this process, we identify the utility and importance of directly modeling higher-order interactions without collapsing them to pairwise interactions. To achieve this, we comprehensively transcribe the higher-order interaction signals to a series of tensors via motifs and propose the MoCHIN model based on joint non-negative tensor factorization. This approach applies to arbitrarily many, arbitrary forms of HIN motifs. An inference algorithm with speed-up methods is also proposed to tackle the challenge that tensor size grows exponentially as the number of nodes in a motif increases. We validate the effectiveness of the proposed method on two real-world datasets and three tasks, and MoCHIN outperforms all baselines in three evaluation tasks under three different metrics. Additional experiments demonstrated the utility of motifs and the benefit of directly modeling higher-order information especially when user guidance is limited., Comment: 24 pages including additional supplementary materials. In Proceedings of the 2019 European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, W\"urzburg, Germany, 2019

We implement exact triangle counting in graphs on the GPU using three different methodologies: subgraph matching to a triangle pattern; programmable graph analytics, with a set-intersection approach; and a matrix formulation based on sparse matrix-matrix multiplies. All three deliver best-of-class performance over CPU implementations and over comparable GPU implementations, with the graph-analytic approach achieving the best performance due to its ability to exploit efficient filtering steps to remove unnecessary work and its high-performance set-intersection core., Comment: 7 pages, 6 figures and 2 tables

We factor Beamer's push-pull, also known as direction-optimized breadth-first-search (DOBFS) into 3 separable optimizations, and analyze them for generalizability, asymptotic speedup, and contribution to overall speedup. We demonstrate that masking is critical for high performance and can be generalized to all graph algorithms where the sparsity pattern of the output is known a priori. We show that these graph algorithm optimizations, which together constitute DOBFS, can be neatly and separably described using linear algebra and can be expressed in the GraphBLAS linear-algebra-based framework. We provide experimental evidence that with these optimizations, a DOBFS expressed in a linear-algebra-based graph framework attains competitive performance with state-of-the-art graph frameworks on the GPU and on a multi-threaded CPU, achieving 101 GTEPS on a Scale 22 RMAT graph., Comment: 11 pages, 7 figures, International Conference on Parallel Processing (ICPP) 2018

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion. While previous SpMM work concentrates on thread-level parallelism, we additionally focus on latency hiding with instruction-level parallelism and load-balancing. We show, both theoretically and experimentally, that the proposed SpMM is a better fit for the GPU than previous approaches. We identify a key memory access pattern that allows efficient access into both input and output matrices that is crucial to getting excellent performance on SpMM. By combining these two ingredients---(i) merge-based load-balancing and (ii) row-major coalesced memory access---we demonstrate a 4.1x peak speedup and a 31.7% geomean speedup over state-of-the-art SpMM implementations on real-world datasets., Comment: 16 pages, 7 figures, International European Conference on Parallel and Distributed Computing (Euro-Par) 2018

Multi-view networks are broadly present in real-world applications. In the meantime, network embedding has emerged as an effective representation learning approach for networked data. Therefore, we are motivated to study the problem of multi-view network embedding with a focus on the optimization objectives that are specific and important in embedding this type of network. In our practice of embedding real-world multi-view networks, we explicitly identify two such objectives, which we refer to as preservation and collaboration. The in-depth analysis of these two objectives is discussed throughout this paper. In addition, the mvn2vec algorithms are proposed to (i) study how varied extent of preservation and collaboration can impact embedding learning and (ii) explore the feasibility of achieving better embedding quality by modeling them simultaneously. With experiments on a series of synthetic datasets, a large-scale internal Snapchat dataset, and two public datasets, we confirm the validity and importance of preservation and collaboration as two objectives for multi-view network embedding. These experiments further demonstrate that better embedding can be obtained by simultaneously modeling the two objectives, while not over-complicating the model or requiring additional supervision. The code and the processed datasets are available at http://yushi2.web.engr.illinois.edu/.

Graph clustering (or community detection) has long drawn enormous attention from the research on web mining and information networks. Recent literature on this topic has reached a consensus that node contents and link structures should be integrated for reliable graph clustering, especially in an unsupervised setting. However, existing methods based on shallow models often suffer from content noise and sparsity. In this work, we propose to utilize deep embedding for graph clustering, motivated by the well-recognized power of neural networks in learning intrinsic content representations. Upon that, we capture the dynamic nature of networks through the principle of influence propagation and calculate the dynamic network embedding. Network clusters are then detected based on the stable state of such an embedding. Unlike most existing embedding methods that are task-agnostic, we simultaneously solve for the underlying node representations and the optimal clustering assignments in an end-to-end manner. To provide more insight, we theoretically analyze our interpretation of network clusters and find its underlying connections with two widely applied approaches for network modeling. Extensive experimental results on six real-world datasets including both social networks and citation networks demonstrate the superiority of our proposed model over the state-of-the-art.

On social networks, while nodes bear rich attributes, we often lack the `semantics' of why each link is formed-- and thus we are missing the `road signs' to navigate and organize the complex social universe. How to identify relationship semantics without labels? Founded on the prevalent homophily principle, we propose the novel problem of Attribute-based Relationship Profiling (ARP), to profile the closeness w.r.t. the underlying relationships (e.g., schoolmate) between users based on their similarity in the corresponding attributes (e.g., education) and, as output, learn a set of social affinity graphs, where each link is weighted by its probabilities of carrying the relationships. As requirements, ARP should be systematic and complete to profile every link for every relationship-- our challenges lie in effectively modeling homophily. We propose a novel reverse smoothness principle by observing that the similarity-closeness duality of homophily is consistent with the well-known smoothness assumption in graph-based semi-supervised learning-- only the direction of inference is reversed. To realize smoothness over noisy social graphs, we further propose a novel holistic closeness modeling approach to capture `high-order' smoothness by extending closeness from edges to paths. Extensive experiments on three real-world datasets demonstrate the efficacy of ARP.

Detecting communities has long been popular in the research on networks. It is usually modeled as an unsupervised clustering problem on graphs, based on heuristic assumptions about community characteristics, such as edge density and node homogeneity. In this work, we doubt the universality of these widely adopted assumptions and compare human labeled communities with machine predicted ones obtained via various mainstream algorithms. Based on supportive results, we argue that communities are defined by various social patterns and unsupervised learning based on heuristics is incapable of capturing all of them. Therefore, we propose to inject supervision into community detection through Community Oriented Network Embedding (CONE), which leverages limited ground-truth communities as examples to learn an embedding model aware of the social patterns underlying them. Specifically, a deep architecture is developed by combining recurrent neural networks with random-walks on graphs towards capturing social patterns directed by ground-truth communities. Generic clustering algorithms on the embeddings of other nodes produced by the learned model then effectively reveals more communities that share similar social patterns with the ground-truth ones., Comment: 10 pages, accepted by IJCNN 2018

For large-scale graph analytics on the GPU, the irregularity of data access and control flow, and the complexity of programming GPUs, have presented two significant challenges to developing a programmable high-performance graph library. "Gunrock", our graph-processing system designed specifically for the GPU, uses a high-level, bulk-synchronous, data-centric abstraction focused on operations on a vertex or edge frontier. Gunrock achieves a balance between performance and expressiveness by coupling high performance GPU computing primitives and optimization strategies with a high-level programming model that allows programmers to quickly develop new graph primitives with small code size and minimal GPU programming knowledge. We characterize the performance of various optimization strategies and evaluate Gunrock's overall performance on different GPU architectures on a wide range of graph primitives that span from traversal-based algorithms and ranking algorithms, to triangle counting and bipartite-graph-based algorithms. The results show that on a single GPU, Gunrock has on average at least an order of magnitude speedup over Boost and PowerGraph, comparable performance to the fastest GPU hardwired primitives and CPU shared-memory graph libraries such as Ligra and Galois, and better performance than any other GPU high-level graph library., Comment: 52 pages, invited paper to ACM Transactions on Parallel Computing (TOPC), an extended version of PPoPP'16 paper "Gunrock: A High-Performance Graph Processing Library on the GPU"

The GraphBLAS standard (GraphBlas.org) is being developed to bring the potential of matrix based graph algorithms to the broadest possible audience. Mathematically the Graph- BLAS defines a core set of matrix-based graph operations that can be used to implement a wide class of graph algorithms in a wide range of programming environments. This paper provides an introduction to the mathematics of the GraphBLAS. Graphs represent connections between vertices with edges. Matrices can represent a wide range of graphs using adjacency matrices or incidence matrices. Adjacency matrices are often easier to analyze while incidence matrices are often better for representing data. Fortunately, the two are easily connected by matrix mul- tiplication. A key feature of matrix mathematics is that a very small number of matrix operations can be used to manipulate a very wide range of graphs. This composability of small number of operations is the foundation of the GraphBLAS. A standard such as the GraphBLAS can only be effective if it has low performance overhead. Performance measurements of prototype GraphBLAS implementations indicate that the overhead is low., Comment: 9 pages; 11 figures; accepted to IEEE High Performance Extreme Computing (HPEC) conference 2016. arXiv admin note: text overlap with arXiv:1504.01039

We present a single-node, multi-GPU programmable graph processing library that allows programmers to easily extend single-GPU graph algorithms to achieve scalable performance on large graphs with billions of edges. Directly using the single-GPU implementations, our design only requires programmers to specify a few algorithm-dependent concerns, hiding most multi-GPU related implementation details. We analyze the theoretical and practical limits to scalability in the context of varying graph primitives and datasets. We describe several optimizations, such as direction optimizing traversal, and a just-enough memory allocation scheme, for better performance and smaller memory consumption. Compared to previous work, we achieve best-of-class performance across operations and datasets, including excellent strong and weak scalability on most primitives as we increase the number of GPUs in the system., Comment: 12 pages. Final version submitted to IPDPS 2017