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.
Despite of the wide existence of related works mentioned above, our study in this paper has its own uniqueness. Unlike the previous works, we focus on understanding urban dynamics from multiple aspects, including spatial, temporal, as well as spatio-temporal interactions, with still a pursue to long-term evolution patterns. The results indeed bring some important managerial insights and suggestions to city development of Beijing. The proposed NR-cNTF model takes Tucker factorization as a basic framework, which compared with CP and matrix factorization based models @cite_14 @cite_0 @cite_36 @cite_40 has better interpretability for adopting a core tensor to model relations among latent factors. Compared with the existing Tucker factorization based methods @cite_4 @cite_23 @cite_11 , NR-cNTF incorporates urban contexts and neighboring regulation, which improve both the accuracy and interpretability of Tucker factorization greatly. Moreover, we proposed a pipeline initialization approach to analyze the evolution of urban dynamics across several years, which is simple yet practical.
@cite_14 @cite_4 @cite_36 @cite_0 @cite_40 @cite_23 @cite_11
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The traffic networks reflect the pulse and structure of a city and shows some dynamic characteristic. Previous research in mining structure from networks mostly focus on static networks and fail to exploit the temporal patterns. In this paper, we aim to solve the problem of discovering the urban spatio-temporal structure from time-evolving traffic networks. We model the time-evolving traffic networks into a 3-order tensor, each element of which indicates the volume of traffic from i-th origin area to j-th destination area in k-th time domain. Considering traffic data and urban contextual knowledge together, we propose a regularized Non-negative Tucker Decomposition (rNTD) method, which discovers the spatial clusters, temporal patterns and relations among them simultaneously. Abundant experiments are conducted in a large dataset collected from Beijing. Results show that our method outperforms the baseline method. Spatial and temporal contextual information plays a key role for analyzing user behaviors, and is helpful for predicting where he or she will go next. With the growing ability of collecting information, more and more temporal and spatial contextual information is collected in systems, and the location prediction problem becomes crucial and feasible. Some works have been proposed to address this problem, but they all have their limitations. Factorizing Personalized Markov Chain (FPMC) is constructed based on a strong independence assumption among different factors, which limits its performance. Tensor Factorization (TF) faces the cold start problem in predicting future actions. Recurrent Neural Networks (RNN) model shows promising performance comparing with PFMC and TF, but all these methods have problem in modeling continuous time interval and geographical distance. In this paper, we extend RNN and propose a novel method called Spatial Temporal Recurrent Neural Networks (ST-RNN). ST-RNN can model local temporal and spatial contexts in each layer with time-specific transition matrices for different time intervals and distance-specific transition matrices for different geographical distances. Experimental results show that the proposed ST-RNN model yields significant improvements over the competitive compared methods on two typical datasets, i.e., Global Terrorism Database (GTD) and Gowalla dataset. Abstract Visual tracking algorithms based on structured output support vector machine (SOSVM) have demonstrated excellent performance. However, sampling methods and optimization strategies of SOSVM undesirably increase the computational overloads, which hinder real-time application of these algorithms. Moreover, due to the lack of high-dimensional features and dense training samples, SOSVM-based algorithms are unstable to deal with various challenging scenarios, such as occlusions and scale variations. Recently, visual tracking algorithms based on discriminative correlation filters (DCF), especially the combination of DCF and features from deep convolutional neural networks (CNN), have been successfully applied to visual tracking, and attains surprisingly good performance on recent benchmarks. The success is mainly attributed to two aspects: the circular correlation properties of DCF and the powerful representation capabilities of CNN features. Nevertheless, compared with SOSVM, DCF-based algorithms are restricted to simple ridge regression which has a weaker discriminative ability. In this paper, a novel circular and structural operator tracker (CSOT) is proposed for high performance visual tracking, it not only possesses the powerful discriminative capability of SOSVM but also efficiently inherits the superior computational efficiency of DCF. Based on the proposed circular and structural operators, a set of primal confidence score maps can be obtained by circular correlating feature maps with their corresponding structural correlation filters. Furthermore, an implicit interpolation is applied to convert the multi-resolution feature maps to the continuous domain and make all primal confidence score maps have the same spatial resolution. Then, we exploit an efficient ensemble post-processor based on relative entropy, which can coalesce primal confidence score maps and create an optimal confidence score map for more accurate localization. The target is localized on the peak of the optimal confidence score map. Besides, we introduce a collaborative optimization strategy to update circular and structural operators by iteratively training structural correlation filters, which significantly reduces computational complexity and improves robustness. Experimental results demonstrate that our approach achieves state-of-the-art performance in mean AUC scores of 71.5 and 69.4 on the OTB2013 and OTB2015 benchmarks respectively, and obtains a third-best expected average overlap (EAO) score of 29.8 on the VOT2017 benchmark. Simple structure and other common principles of factor rotation do not in general provide strong grounds for attributing explanatory significance to the factors which they select. In contrast, it is shown that an extension of Cattell's principle of rotation to Proportional Profiles (PP) offers a basis for determining explanatory factors for three-way or higher order multi-mode data. Conceptual models are developed for two basic patterns of multi-mode data variation, systemand object-variation, and PP analysis is found to apply in the system-variation case. Although PP was originally formulated as a principle of rotation to be used with classic two-way factor analysis, it is shown to embody a latent three-mode factor model, which is here made explicit and generalized frown two to N "parallel occasions". As originally formulated, PP rotation was restricted to orthogonal factors. The generalized PP model is demonstrated to give unique "correct" solutions with oblique, non-simple structure, and even non-linear factor structures. A series of tests, conducted with synthetic data of known factor composition, demonstrate the capabilities of linear and non-linear versions of the model, provide data on the minimal necessary conditions of uniqueness, and reveal the properties of the analysis procedures when these minimal conditions are not fulfilled. In addition, a mathematical proof is presented for the uniqueness of the solution given certain conditions on the data. Three-mode PP factor analysis is applied to a three-way set of real data consisting of the fundamental and first three formant frequencies of 11 persons saying 8 vowels. A unique solution is extracted, consisting of three factors which are highly meaningful and consistent with prior knowledge and theory concerning vowel quality. The relationships between the three-mode PP model and Tucker's multi-modal model, McDonald's non-linear model and Carroll and Chang's multi-dimensional scaling model are explored.