Graph Few-Shot Node Classification (GFSNC) has emerged as a promising approach to address the challenge of learning with limited labeled data in graph-structured networks.Despite the success of Graph Neural Networks (GNNs) in node classification tasks, their performance heavily depends on the availability of abundant labeled data, which is often impractical in real-world scenarios.To tackle this issue, GFSNC adopts the episodic meta-learning paradigm, where models are trained on a series of meta-tasks.However, existing methods face two critical limitations: (i) they focus on local distributions within individual meta-tasks, neglecting the global data distribution, and (ii) they optimize models to minimize intra-class distances without adequately addressing inter-class separability, leading to suboptimal performance.This paper presents TaskNS, a novel GFSNC framework that introduces task-negative samples into meta-training tasks to address these limitations.By incorporating samples from classes outside the current meta-task, our framework enables the model to gradually learn the global distribution of the graph data.Additionally, we design a novel loss function that enhances the model's ability to distinguish between different classes of query samples.This loss function not only ensures high intra-class compactness but also maximizes the inter-class separation by leveraging task-negative samples.To further enhance the quality of task-negative samples, we propose an ℎ-hop-neighbors-based sampling method that leverages the topological structure of a graph.It selects task-negative samples that are structurally close to query samples, ensuring that they are informative and challenging for the model to classify.Extensive experiments on four benchmark datasets demonstrate the effectiveness of TaskNS, achieving average improvements of 4.6% in accuracy (ACC) and 4.9% in F1-score over state-of-the-art methods.

Federated learning (FL) is a popular collaborative training paradigm in which data owners offer gradients instead of private data to model owners for model training to protect data privacy. However, it faces security threats from two sides: dishonest model owners may extract sensitive information about private data from gradients; meanwhile, adversaries may pretend to be data owners and poison the model by sending malicious gradients. We propose a novel FL protocol, PARSIFAL, to address privacy leakage and model poisoning threats. A poisoning detection module is designed based on a novel sketch structure. This module efficiently detects potential malicious gradients that are dissimilar to the majority of benign gradients. PARSIFAL also contains a robust aggregation module based on sign gradients to mitigate the influence of poisoning gradients on aggregation results. Meanwhile, all processes of our PARSIFAL are protected by privacy protocols, mainly based on secret sharing, to guarantee that malicious detection and aggregation processes will not leak sensitive information. Experimental results show that PARSIFAL improves poisoning defense performance by up to 28% compared with recent baselines.

Legal case retrieval aims to automatically scour comparable legal cases based on a given query, which is crucial for offering relevant precedents to support the judgment in intelligent legal systems. Due to similar goals, it is often associated with a similar case matching task. To address them, a daunting challenge is assessing the uniquely defined legal-rational similarity within the judicial domain, which distinctly deviates from the semantic similarities in general text retrieval. Past works either tagged domain-specific factors or incorporated reference laws to capture legal-rational information. However, their heavy reliance on expert or unrealistic assumptions restricts their practical applicability in real-world scenarios. In this article, we propose an end-to-end model named LCM-LAI to solve the above challenges. Through meticulous theoretical analysis, LCM-LAI employs a dependent multi-task learning framework to capture legal-rational information within legal cases by a law article prediction sub-task, without any additional assumptions in inference. In addition, LCM-LAI proposes an article-aware attention mechanism to evaluate the legal-rational similarity between across-case sentences based on the law distribution, which is more effective than semantic similarity. We perform a series of exhaustive experiments that include two different tasks that involving four real-world datasets. The results demonstrate that LCM-LAI achieves state-of-the-art performance.

Legal Judgment Prediction (LJP) aims to automatically predict a law case’s judgment results based on the text description of its facts. In practice, the confusing law articles (or charges) problem frequently occurs, reflecting that the law cases applicable to similar articles (or charges) tend to be misjudged. Although some recent works based on prior knowledge solve this issue well, they ignore that confusion also occurs between law articles with a high posterior semantic similarity due to the data imbalance problem instead of only between the prior highly similar ones, which is this work’s further finding. This article proposes an end-to-end model named D-LADAN to solve the above challenges. On the one hand, D-LADAN constructs a graph among law articles based on their text definition and proposes a graph distillation operator (GDO) to distinguish the ones with a high prior semantic similarity. On the other hand, D-LADAN presents a novel momentum-updated memory mechanism to dynamically sense the posterior similarity between law articles (or charges) and a weighted GDO to adaptively capture the distinctions for revising the inductive bias caused by the data imbalance problem. We perform extensive experiments to demonstrate that D-LADAN significantly outperforms state-of-the-art methods in accuracy and robustness.

Computing set difference cardinalities is a critical task in database optimization, network management, and anomaly detection. Due to the limited computational and mem-ory resources, exactly calculating set difference cardinalities becomes impractical in real-world applications. To solve this issue, sketch methods such as Odd sketch, Tug-of-War sketch, and HyperLogLog sketch can be extended to provide approximate estimations of set difference cardinalities. They use a family of hash functions to compress all elements in a set into a compact data structure. Unfortunately, Odd sketch suffers from limited estimation range, while Tug-of-War sketch and HyperLogLog sketch unavoidably face the problems of large estimation errors and high computational costs. In this paper, we design a novel data structure of bit array GXBits to fast and accurately estimate set difference cardinalities in a large range. In GXBits, the prob-ability of each bit recording its corresponding elements follows a variant of geometric distributions and varies across different bits. We conduct extensive experiments on synthetic datasets and real-world datasets. Experimental results demonstrate that our method GXBits is more computationally and memory efficient, and significantly increases the estimation accuracy of existing methods by up to 221.3 times.

Key-value sequence data has become ubiquitous and naturally appears in a variety of real-world applications, ranging from the user-product purchasing sequences in e-commerce, to network packet sequences forwarded by routers in networking. Classifying these key-value sequences is important in many scenarios such as user profiling and malicious applications identification. In many time-sensitive scenarios, besides the requirement of classifying a key-value sequence accurately, it is also desired to classify a key-value sequence early, in order to respond fast. However, these two goals are conflicting in nature, and it is challenging to achieve them simultaneously. In this work, we formulate a novel tangled key-value sequence early classification problem, where a tangled key-value sequence is a mixture of several concurrent key-value sequences with different keys. The goal is to classify each individual key-value sequence sharing a same key both accurately and early. To address this problem, we propose a novel method, i.e., Key-Value sequence Early Co-classification (KVEC), which leverages both inner- and inter-correlations of items in a tangled key-value sequence through key correlation and value correlation to learn a better sequence representation. Meanwhile, a time-aware halting policy decides when to stop the ongoing key-value sequence and classify it based on current sequence representation. Experiments on both real-world and synthetic datasets demonstrate that our method outperforms the state-of-the-art baselines significantly. KVEC improves the prediction accuracy by up to 4.7 -17.5% under the same prediction earliness condition, and improves the harmonic mean of accuracy and earliness by up to 3.7 -14.0%.

Graph data are ubiquitous in real-world systems such as social networks and protein-protein interaction networks. In many applications, nodes usually are associated with real-value attributes, e.g., age, income, and wealth. Recently, industry and research communities have attracted attention to mining and learning attribute graphs. In this paper, we study the problem of calculating the general neighborhood cardinality of each node$v$in the graph, i.e., the sum of non-negative attribute values of the nodes in the$k$-hop neighborhood of a node$v$. The naive solution is to run a$k$-step breadth-first-search (BFS) algorithm starting from each node and storing all visited nodes' attributes. Clearly, the time complexity of this solution is$O\left(\vert V\vert d_{\max }^k\right)$, where$\vert V\vert$is the number of nodes and$d_{\max}$is the maximum node degree in the graph. In real-world networks such as Twitter,$d_{\max}$is over$3\times{1}0^{6}$. Therefore, it is infeasible to compute the neighborhood cardinality of nodes exactly in such massive networks even if we set$k=2$. To solve this problem, we propose efficient methods to compute the neighborhood cardinality of graphs with non-negative node attributes and binary node attributes, respectively. Extensive experiments on large real-world networks show the efficiency and effectiveness of our methods.

Graph few-shot learning (GFSL) has achieved great success in node classification tasks with rare labels. However, graph few-shot classification (GFSC) models often encounter the problem of classifying test samples with unobserved (or unknown) classes due to the rareness of labels. We formulate this problem as out-of-distribution (OOD) sample detection in inductive graph few-shot learning. This paper presents SMUG, a novel GFSL framework that can detect unobserved classes. Since we have no ground-truth OOD samples in a practical training dataset, it is challenging for the GFSC model to retrieve knowledge about unknown classes from labeled samples. To address this difficulty, we propose a sand mixing scheme to introduce observed classes as artificial OOD samples into meta-tasks. We also develop two unsupervised OOD discriminators to identify OOD samples. Thus, we can assess the performance of OOD discriminators since we know the true classes of these artificial OOD samples. Subsequently, we design a novel training procedure to optimize the encoder based on the performance of the OOD discriminators and the GFSC model. It not only enables the GFSL model to distinguish OOD samples but also promotes the classification accuracy of normal samples. We conduct extensive experiments to evaluate the effectiveness of SMUG based on four benchmark datasets. Experimental results demonstrate that SMUG achieves superior performance over state-of-the-art approaches in OOD detection and node classification. The source code of this paper is available at https://github.com/Memepp/SMUG.

Kernel density estimation is a useful method for estimating the probability distribution of data. It is a challenge to achieve efficient kernel density estimation, especially for large-scale and high-dimension stream data. We proposerotation kernel, a novel kernel function for density estimation. The rotation kernel density can be fast estimated by a data structure namedRotation Kernel Density Sketch(RKDS). RKDS is a time- and memory-efficient method for kernel density estimation, even over data streams and distributed systems. RKDS is applicable for estimating density at specific points and also for representing data distribution. We provide theoretical analysis for rotation kernel and RKDS. Furthermore, we apply RKDS to outlier detection, concept drift detection, and personalized federated learning. Experiments show that our method improves time efficiency by up to$3\times 10^{3}$times compared with baselines. RKDS also provides comparable detecting precision and better delay on outlier detection and concept drift detection tasks.

Calculating the number of distinct values (i.e., NDV) in a column of a big table is costly yet fundamental to a variety of database applications such as data compression and profiling. To reduce the high time and space cost, a number of sketch methods (e.g., HyperLogLog) have been proposed, which estimate the NDV from a constructed compact data summary of distinct values. However, these methods fail or are costly to manage fully-dynamic scenarios where data is often inserted into and deleted from the table. To solve this issue, we propose a novel sketch method,Half-Xor. Our Half-Xor sketch consists of a compact bit matrix and a small counter array, and it needs to set a few bits and update a counter when handling a data insertion/deletion. Compared with the state-of-the-art mergeable method, our experimental results demonstrate that our method Half-Xor is up to 6.6 times more accurate under the same memory usage and reduces the memory usage by up to 16 times to achieve the same estimation accuracy.

Counting the number of distinct elements distributed over multiple data holders is a fundamental problem with many real-world applications ranging from crowd counting to network monitoring. Although a number of space and computationally efficient sketch methods (e.g., the Flajolet-Martin sketch and the HyperLogLog sketch) for cardinality estimation have been proposed to solve the above problem, these sketch methods are insecure when considering privacy concerns related to the use of each data holder's personal dataset. Despite a recently proposed protocol that successfully implements the well-known Flajolet-Martin (FM) sketch on a secret-sharing based multiparty computation (MPC) framework for solving the problem of private distributed cardinality estimation (PDCE), we observe that this MPC-FM protocol is not differentially private. In addition, the MPC-FM protocol is computationally expensive, which limits its applications to data holders with limited computation resources. To address the above issues, in this paper we propose a novel protocol DP-DICE, which is computationally efficient and differentially private for solving the problem of PDCE. Experimental results show that our DP-DICE achieves orders of magnitude speedup and reduces the estimation error by several times in comparison with state-of-the-arts under the same security requirements.

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a non-negative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element$i$in proportion to its positive weight$v_{i}$, the Gumbel-Max Trick first computes a Gumbel random variable$g_{i}$for each positive weight element$i$, and then samples the element$i$with the largest value of$g_{i}+\ln v_{i}$. Recently, applications including similarity estimation and weighted cardinality estimation require to generate$k$independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large$k$(e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm,FastGM, which reduces the time complexity from$O(kn^+)$to$O(k \ln k + n^+)$, where$n^+$is the number of positive elements in the vector of interest. FastGM stops the procedure of Gumbel random variables computing for many elements, especially for those with small weights. We perform experiments on a variety of real-world datasets and the experimental results demonstrate that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy or incurring additional expenses.

Graph Neural Networks (GNNs) have been success-fully applied to a variety of graph analysis tasks. Some recent studies have demonstrated that decoupling neighbor aggregation and feature transformation helps to scale GNNs to large graphs. However, very large graphs, with billions of nodes and millions of features, are still beyond the capacity of most existing GNNs. In addition, when we are only interested in a small number of nodes (called target nodes) in a large graph, it is inefficient to use the existing GNNs to infer the labels of these few target nodes. The reason is that they need to propagate and aggregate either node features or predicted labels over the whole graph, which incurs high additional costs relative to the few target nodes. To solve the above challenges, in this paper we propose a novel scalable and effective GNN framework COSAL. In COSAL, we substitute the expensive aggregation with an efficient proximate node selection mechanism, which picks out the most important$K$nodes for each target node according to the graph topology. We further propose a fine-grained neighbor importance quantification strategy to enhance the expressive power of COSAL. Empirical results demonstrate that our COSAL achieves superior performance in accuracy, training speed, and partial inference efficiency. Remarkably, in terms of node classification accuracy, our model COSAL outperforms baselines by significant margins of 2.22%, 2.23%, and 3.95% on large graph datasets Amazon2M, MAG-Scholar-C, and ogbn-papers100M, respectively.11Code available at https://github.com/joyce-x/COSAL.

Many real-world datasets are given in the stream of entity-identifier pairs, and measuring data distribution on these datasets is fundamental for applications such as privacy protection. In this paper, we study the problem of computing the cumulative distribution for different cardinalities (i.e., the number of distinct entities owning the same identifier). However, previous sketch-based methods cost large memory space especially when there are a large number of identifiers, and sampling-based methods require much time for cardinality estimation. A recent work KHyperLogLog combines both sketch and sampling methods but it is wasteful to separately build a HyperLogLog sketch of large size for identifiers with small cardinalities. To address these challenges, we propose a memory-efficient method EV-HLL, which designs a shared structure to store all sampled identifiers and their entities and utilizes additional sketches to track value updates during the sampling procedure. Meanwhile, EV-HLL provides real-time unbiased estimations according to value changes whenever a new entity-identifier pair arrives. We evaluate the performance of EV-HLL and other state-of-the-arts on real-world available datasets. Experimental results demonstrate that comparing to other methods, EV-HLL effectively reduces their memory usage with the same estimation accuracy and has higher accuracy with the same memory usage.

Bipartite graphs widely exist in real-world scenarios and model binary relations like host-website, author-paper, and user-product. In bipartite graphs, a butterfly (i.e.,$2\times 2$bi-clique) is the smallest non-trivial cohesive structure and plays an important role in applications such as anomaly detection. Considerable efforts focus on counting butterflies in static bipartite graphs. However, they suffer from high time and space complexity when the bipartite graph of interest is given as a stream of edges. Although there are methods for approximately counting butterflies from bipartite graph streams, they suffer from either low accuracy or high time complexity. Therefore, it is still a challenge to accurately estimate butterfly counts from bipartite graph streams in a short time. To address this issue, we develop novel algorithms by exploiting the bipartite nature, which subtly integrates sampling and sketching techniques. We provide accurate estimators for butterfly counts and derive simple yet exact formulas for bounding their errors. We also conduct extensive experiments on a variety of real-world large bipartite graphs. Experimental results demonstrate that our algorithms are up to 20.0 times more accurate and up to 286.3 times faster than state-of-the-art methods under the same memory usage.

Many real-world datasets are given in the format of data streams, and processing these data streams is fundamental for many applications such as anomaly detection. In this paper, we study the problem of computing item frequencies, finding topk hot items, and detecting heavy changes. However, the widelyused sketches cost large memory usage and their performance is easily affected by the unbalanced distribution of data streams. To solve this issue, a novel method Cold Filter (CF) is proposed to split cold items and hot items, and use a separate structure to record the frequencies of hot items. Typically, CF has a small filter range and is only effective for filtering cold items with small frequencies. For some real-world applications, however, the cold items' frequencies may also be greater than hundreds or even tens of thousands. To solve the above challenges, we exploit the “LogLog” structure and develop a memory-efficient method LogLog Filter (LLF) to accurately estimate the above three metrics. LLF builds a register array where each register approximately counts the sum of item frequencies hashed into it. Our method remarkably enlarges the filter range of CF with fewer bits and only requires 4 bits to filter cold items with frequencies up to 224. We conduct extensive experiments on real-world and synthetic datasets, and the experimental results demonstrate the efficiency and effectiveness of our method.

Kernel density estimation method is a powerful tool and is widely used in many important real-world applications such as anomaly detection and statistical learning. Unfortunately, current kernel methods suffer from high computational or space costs when dealing with large-scale, high-dimensional datasets, especially when the datasets of interest are given in a stream fashion. Although there are sketch methods designed for kernel density estimation over data streams, they still suffer from high computational costs. To address this problem, in this paper, we propose a novel Rotation Kernel. The Rotation Kernel is based on a Rotation Hash method and is much faster to compute. To achieve memory-efficient kernel density estimation over data streams, we design a method, RKD-Sketch, which compresses high dimensional data streams into a small array of integer counters. We conduct extensive experiments on both synthetic and real-world datasets, and experimental results demonstrate that our RKD-Sketch saves up to 216 times computational resources and up to 104 times space resources than state-of-the-arts. Furthermore, we apply our Rotation Kernel in active learning. Results show that our method achieves up to 256 times speedup and saves up to 13 times space to achieve the same accuracy as the baseline methods.

Submodular optimization lies at the core of many data mining and machine learning applications such as data summarization and subset selection. For data streams where elements arrive one at a time, streaming submodular optimization (SSO) algorithms are desired. Existing SSO solutions are mainly designed for insertion-only streams where elements in the stream all participate in the analysis, or sliding-window streams where only the most recent data participates in the analysis. SSO for insertion-only streams does not sufficiently emphasize recent data. SSO for sliding-window streams abruptly forgets all past data. In this work, we propose a new SSO problem, i.e., temporal biased streaming submodular optimization (TBSSO), which embraces the special settings of all previous studies. TBSSO leverages a temporal bias function to force each element in the stream to participate in the analysis with a probability decreasing over time and hence elements in the stream are forgotten gradually. We design novel streaming algorithms to solve the TBSSO problem with provable approximation guarantees. Experiments show that our algorithm can find high quality solutions and improve the efficiency to about one order of magnitude faster than the baseline method.

As an efficient tool for approximate similarity computation and search, Locality Sensitive Hashing (LSH) has been widely used in many research areas including databases, data mining, information retrieval, and machine learning. Classical LSH methods typically require to perform hundreds or even thousands of hashing operations when computing the LSH sketch for each input item (e.g., a set or a vector); however, this complexity is still too expensive and even impractical for applications requiring processing data in real-time. To address this issue, several fast methods such as OPH and BCWS have been proposed to efficiently compute the LSH sketches; however, these methods may generate many sketches with empty bins, which may introduce large errors for similarity estimation and also limit their usage for fast similarity search. To solve this issue, we propose a novel densification method, i.e., BiDens. Compared with existing densification methods, our BiDens is more efficient to fill a sketch's empty bins with values of its non-empty bins in either the forward or backward directions. Furthermore, it also densifies empty bins to satisfy the densification principle (i.e., the LSH property). Theoretical analysis and experimental results on similarity estimation, fast similarity search, and kernel linearization using real-world datasets demonstrate that our BiDens is up to 106 times faster than state-of-the-art methods while achieving the same or even better accuracy.

Given a set S, Membership Querying (MQ) answers whether a query element $q\in S$. It is a fundamental task in areas like database systems and computer networks. In this paper, we consider a more general problem, Multi-Set Multi-Membership Querying (MS-MMQ). Given n sets $S_0,łdots,S_n-1 $, MS-MMQ answers which sets contain element q. A direct way to address MS-MMQ is to build an MQ structure (e.g., Bloom Filter) for each set. However, the query and space complexities grow linearly with n and become prohibitive for a large n. To address this challenge, we propose a novel Circular Shift and Coalesce (CSC) framework to efficiently achieve approximate MS-MMQ. Instead of building an MQ data structure for each set, the CSC index encodes all n sets into a compact sketch and retrieves only a few bytes in the sketch for a query, which achieves high memory-efficiency and boosts the query speed by several times. CSC is compatible with mainstream data structures for Approximate MQ. We conduct experiments on real-world datasets and results demonstrate that our framework is up to 91.2 times faster and up to 48.9 times more accurate than state-of-the-art methods.

The sheer scale of big data causes the information overload issue and there is an urgent need for tools that can draw valuable insights from massive data. This paper investigates the core items tracking (CIT) problem where the goal is to continuously track representative items, called core items, in a data stream so to best represent/summarize the stream. In order to simultaneously satisfy the recency and continuity requirements, we consider CIT over probabilistic-decaying streams where items in the stream are forgotten gradually in a probabilistic manner. We first introduce an algorithm, called PNDCIT, to find core items in a special kind of probabilistic non-decaying streams. Furthermore, using PNDCIT as a building block, we design two novel algorithms, namely PDCIT and PDCIT+, to maintain core items over probabilistic-decaying streams with constant approximation ratios. Finally, extensive experiments on real data demonstrate that PDCIT+ achieves a speedup of up to one order of magnitude over a batch algorithm while providing solutions with comparable quality.

The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element i (or a Gumbel-Max variable i) in proportion to its positive weight vi, the Gumbel-Max Trick first computes a Gumbel random variable gi for each positive weight element i, and then samples the element i with the largest value of gi + ln vi. Recently, applications including similarity estimation and graph embedding require to generate k independent Gumbel-Max variables from high dimensional vectors. However, it is computationally expensive for a large k (e.g., hundreds or even thousands) when using the traditional Gumbel-Max Trick. To solve this problem, we propose a novel algorithm, FastGM, that reduces the time complexity from O(kn+) to O(kln k + n+), where n+ is the number of positive elements in the vector of interest. Instead of computing k independent Gumbel random variables directly, we find that there exists a technique to generate these variables in descending order. Using this technique, our method FastGM computes variables gi + ln vi for all positive elements i in descending order. As a result, FastGM significantly reduces the computation time because we can stop the procedure of Gumbel random variables computing for many elements especially for those with small weights. Experiments on a variety of real-world datasets show that FastGM is orders of magnitude faster than state-of-the-art methods without sacrificing accuracy and incurring additional expenses.

“Unbiasedness,” which is an important property to ensure that users’ ratings indeed reflect their true evaluations of products, is vital both in shaping consumer purchase decisions and providing reliable recommendations in online rating systems. Recent experimental studies showed that distortions from historical ratings would ruin the unbiasedness of subsequent ratings. How to “discover” historical distortions in each single rating (or at the micro-level), and perform the “debiasing operations” are our main objective. Using 42M real customer ratings, we first show that users either “assimilate” or “contrast” to historical ratings under different scenarios, which can be further explained by a well-known psychological argument: the “Assimilate-Contrast” theory. This motivates us to propose the Historical Influence Aware Latent Factor Model (HIALF), the “first” model for real rating systems to capture and mitigate historical distortions in each single rating. HIALF allows us to study the influence patterns of historical ratings from a modelling perspective, which perfectly matches the assimilation and contrast effects observed in experiments. Moreover, HIALF achieves significant improvements in predicting subsequent ratings and characterizing relationships in ratings. It also contributes to better recommendations, wiser consumer purchase decisions, and deeper understanding of historical distortions in both honest rating and misbehaving rating settings.

Identifying influential nodes that can jointly trigger the maximum influence spread in networks is a fundamental problem in many applications such as viral marketing, online advertising, and disease control. Most existing studies assume that social influence is static and they fail to capture the dynamics of influence in reality. In this work, we address the dynamic influence challenge by designing efficient streaming methods that can identify influential nodes from highly dynamic node interaction streams. We first propose a general time-decaying dynamic interaction network (TDN) model to model node interaction streams with the ability to smoothly discard outdated data. Based on the TDN model, we design three algorithms, i.e., SieveADN, BasicReduction and HistApprox. SieveADN identifies influential nodes from a special kind of TDNs with efficiency. BasicReduction uses SieveADN as a basic building block to identify influential nodes from general TDNs. HistApprox significantly improves the efficiency of BasicReduction. More importantly, we theoretically show that all three algorithms enjoy constant factor approximation guarantees. Experiments conducted on various real interaction datasets demonstrate that our approach finds near-optimal solutions with speed at least 5 to 15 times faster than baseline methods.

Recently exploring locally connected subgraphs (also known as motifs or graphlets) of complex networks attracts a lot of attention. Previous work made the strong assumption that the graph topology of interest is known in advance. In practice, sometimes researchers have to deal with the situation where the graph topology is unknown because it is expensive to collect and store all topological information. Hence, typically what is available to researchers is only a snapshot of the graph, i.e., a subgraph of the graph. Crawling methods such as breadth first sampling can be used to generate the snapshot. However, these methods fail to sample a streaming graph represented as a high speed stream of edges. Therefore, graph mining applications such as network traffic monitoring usually use random edge sampling (i.e., sample each edge with a fixed probability) to collect edges and generate a sampled graph, which we call a “ RESampled graph”. Clearly, a RESampled graph's motif statistics may be quite different from those of the original graph. To resolve this, we propose a framework Minfer, which takes the given RESampled graph and accurately infers the underlying graph's motif statistics. Experiments using large scale datasets show the accuracy and efficiency of our method.

Despite recent efforts in counting 3-node and 4-node graphlets, little attention has been paid to characterizing 5-node graphlets. In this paper, we develop a computationally efficient sampling method to estimate 5-node graphlet counts. We not only provide a fast sampling method and unbiased estimators of graphlet counts, but also derive simple yet exact formulas for the variances of the estimators which are of great value in practice-the variances can be used to bound the estimates' errors and determine the smallest necessary sampling budget for a desired accuracy. We conduct experiments on a variety of real-world datasets, and the results show that our method is several orders of magnitude faster than the state-of-the-art methods with the same accuracy.

Counting 3-, 4-, and 5-node graphlets in graphs is important for graph mining applications such as discovering abnormal/ evolution patterns in social and biology networks. In addition, it is recently widely used for computing similarities between graphs and graph classification applications such as protein function prediction and malware detection. However, it is challenging to compute these graphlet counts for a large graph or a large set of graphs due to the combinatorial nature of the problem. Despite recent efforts in counting 3-node and 4-node graphlets, little attention has been paid to characterizing 5-node graphlets. In this paper, we develop a computationally efficient sampling method to estimate 5-node graphlet counts. We not only provide a fast sampling method and unbiased estimators of graphlet counts, but also derive simple yet exact formulas for the variances of the estimators which are of great value in practice-the variances can be used to bound the estimates' errors and determine the smallest necessary sampling budget for a desired accuracy. We conduct experiments on a variety of real-world datasets, and the results show that our method is several orders of magnitude faster than the state-of-the-art methods with the same accuracy.

The unbiasedness of online product ratings, an important property to ensure that users' ratings indeed reflect their true evaluations to products, is vital both in shaping consumer purchase decisions and providing reliable recommendations. Recent experimental studies showed that distortions from historical ratings would ruin the unbiasedness of subsequent ratings. How to "discover" the distortions from historical ratings in each single rating (or at the micro-level), and perform the "debiasing operations" in real rating systems are the main objectives of this work.

Characterizing motif (i.e., locally connected sub-graph patterns) statistics is important for understanding complex networks such as online social networks and communication networks. Previous work made the strong assumption that the graph topology of interest is known in advance. In practice, sometimes researchers have to deal with the situation where the graph topology is unknown because it is expensive to collect and store all topological and meta information. Hence, typically what is available to researchers is only a snapshot of the graph, i.e., a subgraph of the graph. Crawling methods such as breadth first sampling can be used to generate the snapshot. However, these methods fail to sample a streaming graph represented as a high speed stream of edges. Therefore, graph mining applications such as network traffic monitoring use random edge sampling (i.e., sample each edge with a fixed probability) to collect edges and generate a sampled graph, which we called a “RESampled graph”. Clearly, a RESampled graph's motif statistics may be quite different from those of the underlying original graph. To resolve this, we propose a framework and implement a system called Minfer, which takes the given RESampled graph and accurately infers the underlying graph's motif statistics. We also apply Fisher information to bound the errors of our estimates. Experiments using large scale datasets show the accuracy and efficiency of our method.

Random walk-based graph sampling methods have become increasingly popular and important for characterizing large-scale complex networks. While powerful, they are known to exhibit problems when the graph is loosely connected, which slows down the convergence of a random walk and can result in poor estimation accuracy. In this work, we observe that many graphs under study, called target graphs, usually do not exist in isolation. In many situations, a target graph is often related to an auxiliary graph and an affiliation graph, and the target graph becomes better connected when viewed from these three graphs as a whole, or what we called a hybrid social-affiliation network. This viewpoint brings extra benefits to the graph sampling framework, e.g., when directly sampling a target graph is difficult or inefficient, we can efficiently sample it with the assistance of auxiliary and affiliation graphs. We propose three sampling methods on such a hybrid social-affiliation network to estimate target graph characteristics, and conduct extensive experiments on both synthetic and real datasets, to demonstrate the effectiveness of these new sampling methods.

Characterizing user pair relationships is important for applications such as friend recommendation and interest targeting in online social networks (OSNs). Due to the large-scale nature of such networks, it is infeasible to enumerate all user pairs and thus sampling is used. In this article, we show that it is a great challenge for OSN service providers to characterize user pair relationships, even when they possess the complete graph topology. The reason is that when sampling techniques (i.e., uniform vertex sampling (UVS) and random walk (RW)) are naively applied, they can introduce large biases, particularly for estimating similarity distribution of user pairs with constraints like existence of mutual neighbors, which is important for applications such as identifying network homophily. Estimating statistics of user pairs is more challenging in the absence of the complete topology information, as an unbiased sampling technique like UVS is usually not allowed and exploring the OSN graph topology is expensive. To address these challenges, we present unbiased sampling methods to characterize user pair properties based on UVS and RW techniques. We carry out an evaluation of our methods to show their accuracy and efficiency. Finally, we apply our methods to three OSNs—Foursquare, Douban, and Xiami—and discover that significant homophily is present in these networks.

Exploring statistics of locally connected subgraph patterns (also known as network motifs) has helped researchers better understand the structure and function of biological and Online Social Networks (OSNs). Nowadays, the massive size of some critical networks—often stored in already overloaded relational databases—effectively limits the rate at which nodes and edges can be explored, making it a challenge to accurately discover subgraph statistics. In this work, we propose sampling methods to accurately estimate subgraph statistics from as few queried nodes as possible. We present sampling algorithms that efficiently and accurately estimate subgraph properties of massive networks. Our algorithms require no precomputation or complete network topology information. At the same time, we provide theoretical guarantees of convergence. We perform experiments using widely known datasets and show that, for the same accuracy, our algorithms require an order of magnitude less queries (samples) than the current state-of-the-art algorithms.

Characterizing user pair relationships is important for applications such as friend recommendation and interest targeting in online social networks (OSNs). Due to the large scale nature of such networks, it is infeasible to enumerate all user pairs and so sampling is used. In this paper, we show that it is a great challenge even for OSN service providers to characterize user pair relationships even when they possess the complete graph topology. The reason is that when sampling techniques (i.e., uniform vertex sampling (UVS) and random walk (RW)) are naively applied, they can introduce large biases, in particular, for estimating similarity distribution of user pairs with constraints such as existence of mutual neighbors, which is important for applications such as identifying network homophily. Estimating statistics of user pairs is more challenging in the absence of the complete topology information, since an unbiased sampling technique such as UVS is usually not allowed, and exploring the OSN graph topology is expensive. To address these challenges, we present asymptotically unbiased sampling methods to characterize user pair properties based on UVS and RW techniques respectively. We carry out an evaluation of our methods to show their accuracy and efficiency. Finally, we apply our methods to two Chinese OSNs, Doudan and Xiami, and discover significant homophily is present in these two networks.