Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

Recommender systems are an important part of the information and e-commerce ecosystem. They represent a powerful method for enabling users to filter through large information and product spaces. Nearly two decades of research on collaborative filtering have led to a varied set of algorithms and a rich collection of tools for evaluating their performance. Research in the field is moving in the direction of a richer understanding of how recommender technology may be embedded in specific domains. The differing personalities exhibited by different recommender algorithms show that recommendation is not a one-size-fits-all problem. Specific tasks, information needs, and item domains represent unique problems for recommenders, and design and evaluation of recommenders needs to be done based on the user tasks to be supported. Effective deployments must begin with careful analysis of prospective users and their goals. Based on this analysis, system designers have a host of options for the choice of algorithm and for its embedding in the surrounding user experience. This paper discusses a~wide variety of the choices available and their implications, aiming to provide both practicioners and researchers with an introduction to the important issues underlying recommenders and current best practices for addressing these issues.

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Collaborative Filtering Recommender Systems

Influence Maximization (IM), which selects a set of $k$ users (called seed set) from a social network to maximize the expected number of influenced users (called influence spread), is a key algorithmic problem in social influence analysis. Due to its immense application potential and enormous technical challenges, IM has been extensively studied in the past decade. In this paper, we survey and synthesize a wide spectrum of existing studies on IM from an algorithmic perspective , with a special focus on the following key aspects: (1) a review of well-accepted diffusion models that capture the information diffusion process and build the foundation of the IM problem, (2) a fine-grained taxonomy to classify existing IM algorithms based on their design objectives, (3) a rigorous theoretical comparison of existing IM algorithms, and (4) a comprehensive study on the applications of IM techniques in combining with novel context features of social networks such as topic, location, and time. Based on this analysis, we then outline the key challenges and research directions to expand the boundary of IM research.

https://ink.library.smu.edu.sg/cgi/viewcontent.cgi?article=4983&context=sis_research

Influence Maximization on Social Graphs: A Survey

We introduce HoloClean, a framework for holistic data repairing driven by probabilistic inference. HoloClean unifies qualitative data repairing, which relies on integrity constraints or external data sources, with quantitative data repairing methods, which leverage statistical properties of the input data. Given an inconsistent dataset as input, HoloClean automatically generates a probabilistic program that performs data repairing. Inspired by recent theoretical advances in probabilistic inference, we introduce a series of optimizations which ensure that inference over HoloClean's probabilistic model scales to instances with millions of tuples. We show that HoloClean finds data repairs with an average precision of ∼ 90% and an average recall of above ∼ 76% across a diverse array of datasets exhibiting different types of errors. This yields an average F1 improvement of more than 2× against state-of-the-art methods.

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HoloClean: holistic data repairs with probabilistic inference

Research on social networks has exploded over the last decade. To a large extent, this has been fueled by the spectacular growth of social media and online social networking sites, which continue growing at a very fast pace, as well as by the increasing availability of very large social network datasets for purposes of research. A rich body of this research has been devoted to the analysis of the propagation of information, influence, innovations, infections, practices and customs through networks. Can we build models to explain the way these propagations occur? How can we validate our models against any available real datasets consisting of a social network and propagation traces that occurred in the past? These are just some questions studied by researchers in this area. Information propagation models find applications in viral marketing, outbreak detection, finding key blog posts to read in order to catch important stories, finding leaders or trendsetters, information feed ranking, etc. A number of algorithmic problems arising in these applications have been abstracted and studied extensively by researchers under the garb of influence maximization. This book starts with a detailed description of well-established diffusion models, including the independent cascade model and the linear threshold model, that have been successful at explaining propagation phenomena. We describe their properties as well as numerous extensions to them, introducing aspects such as competition, budget, and time-criticality, among many others. We delve deep into the key problem of influence maximization, which selects key individuals to activate in order to influence a large fraction of a network. Influence maximization in classic diffusion models including both the independent cascade and the linear threshold models is computationally intractable, more precisely #P-hard, and we describe several approximation algorithms and scalable heuristics that have been proposed in the literature. Finally, we also deal with key issues that need to be tackled in order to turn this research into practice, such as learning the strength with which individuals in a network influence each other, as well as the practical aspects of this research including the availability of datasets and software tools for facilitating research. We conclude with a discussion of various research problems that remain open, both from a technical perspective and from the viewpoint of transferring the results of research into industry strength applications. Table of Contents: Acknowledgments / Introduction / Stochastic Diffusion Models / Influence Maximization / Extensions to Diffusion Modeling and Influence Maximization / Learning Propagation Models / Data and Software for Information/Influence: Propagation Research / Conclusion and Challenges / Bibliography / Authors' Biographies / Index

Information and Influence Propagation in Social Networks

Recently, there has been significant interest in the study of the community search problem in social and information networks: given one or more query nodes, find densely connected communities containing the query nodes. However, most existing studies do not address the "free rider" issue, that is, nodes far away from query nodes and irrelevant to them are included in the detected community. Some state-of-the-art models have attempted to address this issue, but not only are their formulated problems NP-hard, they do not admit any approximations without restrictive assumptions, which may not always hold in practice.In this paper, given an undirected graph G and a set of query nodes Q, we study community search using the k-truss based community model. We formulate our problem of finding a closest truss community (CTC), as finding a connected k-truss subgraph with the largest k that contains Q, and has the minimum diameter among such subgraphs. We prove this problem is NP-hard. Furthermore, it is NP-hard to approximate the problem within a factor (2-e), for any e > 0. However, we develop a greedy algorithmic framework, which first finds a CTC containing Q, and then iteratively removes the furthest nodes from Q, from the graph. The method achieves 2-approximation to the optimal solution. To further improve the efficiency, we make use of a compact truss index and develop efficient algorithms for k-truss identification and maintenance as nodes get eliminated. In addition, using bulk deletion optimization and local exploration strategies, we propose two more efficient algorithms. One of them trades some approximation quality for efficiency while the other is a very efficient heuristic. Extensive experiments on 6 real-world networks show the effectiveness and efficiency of our community model and search algorithms.

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Approximate closest community search in networks

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation" strategy. The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines on four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

/pdf/from-competition-to-complementarity-comparative-influence-134h6yzf9e.pdf

From competition to complementarity: comparative influence diffusion and maximization

Classical recommender systems provide users with a list of recommendations where each recommendation consists of a single item, e.g., a book or DVD. However, several applications can benefit from a system capable of recommending packages of items, in the form of sets. Sample applications include travel planning with a limited budget (price or time) and twitter users wanting to select worthwhile tweeters to follow given that they can deal with only a bounded number of tweets. In these contexts, there is a need for a system that can recommend top-k packages for the user to choose from.Motivated by these applications, we consider composite recommendations, where each recommendation comprises a set of items. Each item has both a value (rating) and a cost associated with it, and the user specifies a maximum total cost (budget) for any recommended set of items. Our composite recommender system has access to one or more component recommender system, focusing on different domains, as well as to information sources which can provide the cost associated with each item. Because the problem of generating the top recommendation (package) is NP-complete, we devise several approximation algorithms for generating top-k packages as recommendations. We analyze their efficiency as well as approximation quality. Finally, using two real and two synthetic data sets, we subject our algorithms to thorough experimentation and empirical analysis. Our findings attest to the efficiency and quality of our approximation algorithms for top-k packages compared to exact algorithms.

/pdf/breaking-out-of-the-box-of-recommendations-from-items-to-4tjdsqc2zl.pdf

Breaking out of the box of recommendations: from items to packages

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation". The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines in four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.

From Competition to Complementarity: Comparative Influence Diffusion and Maximization

Influence maximization is the problem of finding a set of influential users in a social network such that the expected spread of influence under a certain propagation model is maximized. Much of the previous work has neglected the important distinction between social influence and actual product adoption. However, as recognized in the management science literature, an individual who gets influenced by social acquaintances may not necessarily adopt a product (or technology), due, e.g., to monetary concerns. In this work, we distinguish between influence and adoption by explicitly modeling the states of being influenced and of adopting a product. We extend the classical Linear Threshold (LT) model to incorporate prices and valuations, and factor them into users' decision-making process of adopting a product. We show that the expected profit function under our proposed model maintains submodularity under certain conditions, but no longer exhibits monotonicity, unlike the expected influence spread function. To maximize the expected profit under our extended LT model, we employ an unbudgeted greedy framework to propose three profit maximization algorithms. The results of our detailed experimental study on three real-world datasets demonstrate that of the three algorithms, \textsf{PAGE}, which assigns prices dynamically based on the profit potential of each candidate seed, has the best performance both in the expected profit achieved and in running time.

Laks V. S. Lakshmanan

Papers

Approximate closest community search in networks

From competition to complementarity: comparative influence diffusion and maximization

Breaking out of the box of recommendations: from items to packages

From Competition to Complementarity: Comparative Influence Diffusion and Maximization

Profit Maximization over Social Networks