Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data analytics characterized by diverse variety, large volume, and high velocity. We characterize these advances from the following four perspectives: general tensor completion algorithms, tensor completion with auxiliary information (variety), scalable tensor completion algorithms (volume), and dynamic tensor completion algorithms (velocity). Further, we identify several tensor completion applications on real-world data-driven problems and present some common experimental frameworks popularized in the literature along with several available software repositories. Our goal is to summarize these popular methods and introduce them to researchers and practitioners for promoting future research and applications. We conclude with a discussion of key challenges and promising research directions in this community for future exploration.

How can we efficiently recover missing values for very large-scale real-world datasets that are multi-dimensional even when the auxiliary information is regularized at certain mode? Tensor completion is a useful tool to recover a low-rank tensor that best approximates partially observed data and further predicts the unobserved data by this low-rank tensor, which has been successfully used for many applications such as location-based recommender systems, link prediction, targeted advertising, social media search, and event detection. Due to the curse of dimensionality, existing algorithms for tensor completion that integrate auxiliary information do not scale for tensors with billions of elements. In this paper, we propose DisTenC, a new distributed large-scale tensor completion algorithm that can be distributed on Spark. Our key insights are to (i) efficiently handle trace-based regularization terms; (ii) update factor matrices with caching; and (iii) optimize the update of the new tensor via residuals. In this way, we can tackle the high computational costs of traditional approaches and minimize intermediate data, leading to order-of-magnitude improvements in tensor completion. Experimental results demonstrate that DisTenC is capable of handling up to 10~1000X larger tensors than existing methods with much faster convergence rate, shows better linearity on machine scalability, and achieves up to an average improvement of 23.5% in accuracy in applications.

In the slot-filling paradigm, where a user can refer back to slots in the context during a conversation, the goal of the contextual understanding system is to resolve the referring expressions to the appropriate slots in the context. In large-scale multi-domain systems, this presents two challenges - scaling to a very large and potentially unbounded set of slot values, and dealing with diverse schemas. We present a neural network architecture that addresses the slot value scalability challenge by reformulating the contextual interpretation as a decision to carryover a slot from a set of possible candidates. To deal with heterogenous schemas, we introduce a simple data-driven method for trans- forming the candidate slots. Our experiments show that our approach can scale to multiple domains and provides competitive results over a strong baseline.

Tensor completion has become an effective computational tool in many real-world data-driven applications. Beyond traditional static setting, with the increasing popularity of high velocity streaming data, it requires efficient online processing without reconstructing the whole model from scratch. Existing work on streaming tensor completion is usually built upon the assumption that tensors only grow in one mode. Unfortunately, the assumption does not hold in many real-world situations in which tensors may grow in multiple modes, i.e., multi-aspect streaming tensors. Efficiently modeling and completing these incremental tensors without sacrificing its effectiveness remains a challenging task due to the uncertainty of tensor mode changes and complex data structure of multi-aspect streaming tensors. To bridge this gap, we propose a Multi-Aspect Streaming Tensor completion framework (MAST) based on CANDECOMP/PARAFAC (CP) decomposition to track the subspace of general incremental tensors for completion. In addition, we investigate a special situation where time is one mode of the tensors, and leverage its extra structure information to improve the general framework towards higher effectiveness. Experimental results on four datasets collected from various real-world applications demonstrate the effectiveness and efficiency of the proposed framework.

User interests and expertise are valuable but often hidden resources on social media. For example, Twitter Lists and LinkedIn's Skill Tags provide a partial perspective on what users are known for (by aggregating crowd tagging knowledge), but the vast majority of users are untagged; their interests and expertise are essentially hidden from important applications such as personalized recommendation, community detection, and expert mining. A natural approach to overcome these limitations is to intelligently learn user topical profiles by exploiting information from multiple, heterogeneous footprints: for instance, Twitter users who post similar hashtags may have similar interests, and YouTube users who upvote the same videos may have similar preferences. And yet identifying "similar" users by exploiting similarity in such a footprint space often provides conflicting evidence, leading to poor-quality user profiles. In this paper, we propose a unified model for learning user topical profiles that simultaneously considers multiple footprints. We show how these footprints can be embedded in a generalized optimization framework that takes into account pairwise relations among all footprints for robustly learning user profiles. Through extensive experiments, we find the proposed model is capable of learning high-quality user topical profiles, and leads to a 10-15% improvement in precision and mean average error versus a cross-triadic factorization state-of-the-art baseline.

In this paper, we explore the potential of geo-social media to construct location-based interest profiles to uncover the hidden relationships among disparate locations. Through an investigation of millions of geo-tagged Tweets, we construct a per-city interest model based on fourteen high-level categories (e.g., technology, art, sports). These interest models support the discovery of related locations that are connected based on these categorical perspectives (e.g., college towns or vacation spots) but perhaps not on the individual tweet level. We then connect these city-based interest models to underlying demographic data. By building multivariate multiple linear regression (MMLR) and neural network (NN) models we show how a location's interest profile may be estimated based purely on its demographics features.

Modeling, understanding, and predicting the spatio-temporal dynamics of online memes are important tasks, with ramifications on location-based services, social media search, targeted advertising and content delivery networks. However, the raw data revealing these dynamics are often incomplete and error-prone; for example, API limitations and data sampling policies can lead to an incomplete (and often biased) perspective on these dynamics. Hence, in this paper, we investigate new methods for uncovering the full (underlying) distribution through a novel spatio-temporal dynamics recovery framework which models the latent relationships among locations, memes, and times. By integrating these hidden relationships into a tensor-based recovery framework -- called AirCP -- we find that high-quality models of meme spread can be built with access to only a fraction of the full data. Experimental results on both synthetic and real-world Twitter hashtag data demonstrate the promising performance of the proposed framework: an average improvement of over 27% in recovering the spatio-temporal dynamics of hashtags versus five state-of-the-art alternatives.

We address the challenge of personalized recommendation of high quality content producers in social media. While some candidates are easily identifiable (say, by being "favorited" many times), there is a long-tail of potential candidates for whom we have little evidence. Through careful modeling of contextual factors like the geo-spatial, topical, and social preferences of users, we propose a tensor-based personalized expert recommendation framework that integrates these factors for revealing latent connections between homogeneous entities (e.g., users and users) and between heterogeneous entities (e.g., users and experts). Through extensive experiments over geo-tagged Twitter data, we find that the proposed framework can improve the quality of recommendation by over 30% in both precision and recall compared to the state-of-the-art.

URL sharing has become one of the most popular activities on many online social media platforms. Shared URLs are an avenue to interesting news articles, memes, photos, as well as low-quality content like spam, promotional ads, and phishing sites. While some URL sharing is organic, other sharing is strategically organized with a common purpose (e.g., aggressively promoting a website). In this paper, we investigate the individual-based and group-based user behavior of URL sharing in social media toward uncovering these organic versus organized user groups. Concretely, we pro- pose a four-phase approach to model, identify, characterize, and classify organic and organized groups who engage in URL sharing. The key motivating insights of this approach are (i) that patterns of individual-based behavioral signals embedded in URL posting activities can uncover groups whose members engage in similar behaviors; and (ii) that group-level behavioral signals can distinguish between organic and organized user groups. Through extensive experiments, we find that levels of organized behavior vary by URL type and that the proposed approach achieves good performance -- an F-measure of 0.836 and Area Under the Curve of 0.921.