Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social-network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. Here, we describe the Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy-to-use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines, and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs in which nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and metadata on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic; they can be modified during the computation at low cost. SNAP is provided as an open-source library in C++ as well as a module in Python. We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms.

https://dl.acm.org/doi/pdf/10.1145/2898361

SNAP: A General-Purpose Network Analysis and Graph-Mining Library

Detecting and repairing dirty data is one of the perennial challenges in data analytics, and failure to do so can result in inaccurate analytics and unreliable decisions. Over the past few years, there has been a surge of interest from both industry and academia on data cleaning problems including new abstractions, interfaces, approaches for scalability, and statistical techniques. To better understand the new advances in the field, we will first present a taxonomy of the data cleaning literature in which we highlight the recent interest in techniques that use constraints, rules, or patterns to detect errors, which we call qualitative data cleaning. We will describe the state-of-the-art techniques and also highlight their limitations with a series of illustrative examples. While traditionally such approaches are distinct from quantitative approaches such as outlier detection, we also discuss recent work that casts such approaches into a statistical estimation framework including: using Machine Learning to improve the efficiency and accuracy of data cleaning and considering the effects of data cleaning on statistical analysis.

Data Cleaning: Overview and Emerging Challenges

Crowdsourcing has emerged as a novel problem-solving paradigm, which facilitates addressing problems that are hard for computers, e.g., entity resolution and sentiment analysis. However, due to the openness of crowdsourcing, workers may yield low-quality answers, and a redundancy-based method is widely employed, which first assigns each task to multiple workers and then infers the correct answer (called truth) for the task based on the answers of the assigned workers. A fundamental problem in this method is Truth Inference, which decides how to effectively infer the truth. Recently, the database community and data mining community independently study this problem and propose various algorithms. However, these algorithms are not compared extensively under the same framework and it is hard for practitioners to select appropriate algorithms. To alleviate this problem, we provide a detailed survey on 17 existing algorithms and perform a comprehensive evaluation using 5 real datasets. We make all codes and datasets public for future research. Through experiments we find that existing algorithms are not stable across different datasets and there is no algorithm that outperforms others consistently. We believe that the truth inference problem is not fully solved, and identify the limitations of existing algorithms and point out promising research directions.

/pdf/truth-inference-in-crowdsourcing-is-the-problem-solved-523kuaxe14.pdf

Truth inference in crowdsourcing: is the problem solved?

The Big Data era is upon us: data is being generated, collected and analyzed at an unprecedented scale, and data-driven decision making is sweeping through all aspects of society. Since the value of data explodes when it can be linked and fused with other data, addressing the big data integration (BDI) challenge is critical to realizing the promise of Big Data. BDI differs from traditional data integration in many dimensions: (i) the number of data sources, even for a single domain, has grown to be in the tens of thousands, (ii) many of the data sources are very dynamic, as a huge amount of newly collected data are continuously made available, (iii) the data sources are extremely heterogeneous in their structure, with considerable variety even for substantially similar entities, and (iv) the data sources are of widely differing qualities, with significant differences in the coverage, accuracy and timeliness of data provided. This seminar explores the progress that has been made by the data integration community on the topics of schema mapping, record linkage and data fusion in addressing these novel challenges faced by big data integration, and identifies a range of open problems for the community.

Big data integration

Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and manipulate large networks, only a limited number of tools are available for this task. 
Here, we describe Stanford Network Analysis Platform (SNAP), a general-purpose, high-performance system that provides easy to use, high-level operations for analysis and manipulation of large networks. We present SNAP functionality, describe its implementational details, and give performance benchmarks. SNAP has been developed for single big-memory machines and it balances the trade-off between maximum performance, compact in-memory graph representation, and the ability to handle dynamic graphs where nodes and edges are being added or removed over time. SNAP can process massive networks with hundreds of millions of nodes and billions of edges. SNAP offers over 140 different graph algorithms that can efficiently manipulate large graphs, calculate structural properties, generate regular and random graphs, and handle attributes and meta-data on nodes and edges. Besides being able to handle large graphs, an additional strength of SNAP is that networks and their attributes are fully dynamic, they can be modified during the computation at low cost. SNAP is provided as an open source library in C++ as well as a module in Python. 
We also describe the Stanford Large Network Dataset, a set of social and information real-world networks and datasets, which we make publicly available. The collection is a complementary resource to our SNAP software and is widely used for development and benchmarking of graph analytics algorithms.

SNAP: A General Purpose Network Analysis and Graph Mining Library

We propose a new algorithm, FAST-PPR, for computing personalized PageRank: given start node s and target node t in a directed graph, and given a threshold δ, it computes the Personalized PageRank π_s(t) from s to t, guaranteeing that the relative error is small as long πs(t) > δ. Existing algorithms for this problem have a running-time of Ω(1/δ in comparison, FAST-PPR has a provable average running-time guarantee of O(√d/δ) (where d is the average in-degree of the graph). This is a significant improvement, since δ is often O(1/n) (where n is the number of nodes) for applications. We also complement the algorithm with an Ω(1/√δ) lower bound for PageRank estimation, showing that the dependence on δ cannot be improved.We perform a detailed empirical study on numerous massive graphs, showing that FAST-PPR dramatically outperforms existing algorithms. For example, on the 2010 Twitter graph with 1.5 billion edges, for target nodes sampled by popularity, FAST-PPR has a 20 factor speedup over the state of the art. Furthermore, an enhanced version of FAST-PPR has a 160 factor speedup on the Twitter graph, and is at least 20 times faster on all our candidate graphs.

https://dl.acm.org/doi/pdf/10.1145/2623330.2623745

FAST-PPR: scaling personalized pagerank estimation for large graphs

We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on networks including social networks, user-item networks, and the web. Past work has proposed using Monte Carlo or using linear algebra to estimate scores from a single source to every target, making them inefficient for a single pair. Our contribution is a new bidirectional algorithm which combines linear algebra and Monte Carlo to achieve significant speed improvements. On a diverse set of six graphs, our algorithm is 70x faster than past state-of-the-art algorithms. We also present theoretical analysis: while past algorithms require $\Omega(n)$ time to estimate a random walk score of typical size $\frac{1}{n}$ on an $n$-node graph to a given constant accuracy, our algorithm requires only $O(\sqrt{m})$ expected time for an average target, where $m$ is the number of edges, and is provably accurate. 
In addition to our core bidirectional estimator for personalized PageRank, we present an alternative algorithm for undirected graphs, a generalization to arbitrary walk lengths and Markov Chains, an algorithm for personalized search ranking, and an algorithm for sampling random paths from a given source to a given set of targets. We expect our bidirectional methods can be extended in other ways and will be useful subroutines in other graph analysis problems.

pdf/efficient-algorithms-for-personalized-pagerank-4re91ipn89.pdf

Efficient Algorithms for Personalized PageRank

We develop a new bidirectional algorithm for estimating Markov chain multi-step transition probabilities: given a Markov chain, we want to estimate the probability of hitting a given target state in l steps after starting from a given source distribution. Given the target state t, we use a (reverse) local power iteration to construct an 'expanded target distribution', which has the same mean as the quantity we want to estimate, but a smaller variance - this can then be sampled efficiently by a Monte Carlo algorithm. Our method extends to any Markov chain on a discrete (finite or countable) state-space, and can be extended to compute functions of multi-step transition probabilities such as PageRank, graph diffusions, hitting/return times, etc. Our main result is that in 'sparse' Markov Chains - wherein the number of transitions between states is comparable to the number of states -the running time of our algorithm for a uniform-random target node is order-wise smaller than Monte Carlo and power iteration based algorithms; in particular, our method can estimate a probability p using only O(1/√p) running time.

/pdf/fast-bidirectional-probability-estimation-in-markov-models-iml4dtqnh6.pdf

Fast bidirectional probability estimation in Markov models

We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average-case sense, for a uniformly random choice of target node. Crucially, we show how the reversibility of random walks on undirected networks can be exploited to convert average-case to worst-case guarantees. While past bidirectional methods combine forward random walks with reverse local pushes, our algorithm combines forward local pushes with reverse random walks. We also discuss how to modify our methods to estimate random-walk probabilities for any length distribution, thereby obtaining fast algorithms for estimating general graph diffusions, including the heat kernel, on undirected networks.

Bidirectional PageRank Estimation: From Average-Case to Worst-Case

This paper summarizes substantive new results derived by a student team (the first three authors) under the direction of the fourth author at the 2008 session of the KSU REU "Brainstorming and Barnstorming". The main results show that the construction of the inner automorphism group of a quandle gives rise to a functor from the category of quandles and surjective quandle homomorphisms to the category of groups, characterize quotient maps of quandles which do not change the group of inner automorphims, and characterize those normal subgroups of the inner automorphism group which arise as kernels of homomorphisms induced by quandle surjections.

On quotients of quandles

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