Recent years have witnessed the world-wide emergence of mega-metropolises with incredibly huge populations. Understanding residents mobility patterns, or urban dynamics, thus becomes crucial for building modern smart cities. In this paper, we propose a Neighbor-Regularized and context-aware Non-negative Tensor Factorization model (NR-cNTF) to discover interpretable urban dynamics from urban heterogeneous data. Different from many existing studies concerned with prediction tasks via tensor completion, NR-cNTF focuses on gaining urban managerial insights from spatial, temporal, and spatio-temporal patterns. This is enabled by high-quality Tucker factorizations regularized by both POI-based urban contexts and geographically neighboring relations. NR-cNTF is also capable of unveiling long-term evolutions of urban dynamics via a pipeline initialization approach. We apply NR-cNTF to a real-life data set containing rich taxi GPS trajectories and POI records of Beijing. The results indicate: 1) NR-cNTF accurately captures four kinds of city rhythms and seventeen spatial communities; 2) the rapid development of Beijing, epitomized by the CBD area, indeed intensifies the job-housing imbalance; 3) the southern areas with recent government investments have shown more healthy development tendency. Finally, NR-cNTF is compared with some baselines on traffic prediction, which further justifies the importance of urban contexts awareness and neighboring regulations.
In recent years, more and more works focused on mining explainable latent factors from multi-aspect urban data sets, which form the second category of applications. The focal point here is to use tensor factorization to discover latent lower-dimensional factors from higher-dimensional multi-aspect data sets. For instance, Metafac @cite_20 used CP factorizations to extract latent community structures from various social networks, and @cite_27 proposed a multi-view data clustering and partitioning method based on Tucker factorization. Our study in this paper also falls in this category, with some most related works as follows.
@cite_27 @cite_20
2147512299 2945404669 2158781217 2949531434
CANDECOMP PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance. In recent years, the rapid growth in technology has increased the opportunity for longitudinal human behavioral studies. Rich multimodal data, from wearables like Fitbit, online social networks, mobile phones etc. can be collected in natural environments. Uncovering the underlying low-dimensional structure of noisy multi-way data in an unsupervised setting is a challenging problem. Tensor factorization has been successful in extracting the interconnected low-dimensional descriptions of multi-way data. In this paper, we apply non-negative tensor factorization on a real-word wearable sensor data, StudentLife, to find latent temporal factors and group of similar individuals. Meta data is available for the semester schedule, as well as the individuals' performance and personality. We demonstrate that non-negative tensor factorization can successfully discover clusters of individuals who exhibit higher academic performance, as well as those who frequently engage in leisure activities. The recovered latent temporal patterns associated with these groups are validated against ground truth data to demonstrate the accuracy of our framework. Tensor factorization has become a popular method for learning from multi-relational data. In this context, the rank of the factorization is an important parameter that determines runtime as well as generalization ability. To identify conditions under which factorization is an efficient approach for learning from relational data, we derive upper and lower bounds on the rank required to recover adjacency tensors. Based on our findings, we propose a novel additive tensor factorization model to learn from latent and observable patterns on multi-relational data and present a scalable algorithm for computing the factorization. We show experimentally both that the proposed additive model does improve the predictive performance over pure latent variable methods and that it also reduces the required rank — and therefore runtime and memory complexity — significantly. Tensor CANDECOMP PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are unique to tensors. We develop novel methods for randomized computation of tensor contractions via FFTs, without explicitly forming the tensors. Such tensor contractions are encountered in decomposition methods such as tensor power iterations and alternating least squares. We also design novel colliding hashes for symmetric tensors to further save time in computing the sketches. We then combine these sketching ideas with existing whitening and tensor power iterative techniques to obtain the fastest algorithm on both sparse and dense tensors. The quality of approximation under our method does not depend on properties such as sparsity, uniformity of elements, etc. We apply the method for topic modeling and obtain competitive results.