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.
Among the abundant methods for human mobility data mining, tensor factorization decomposition, like CANDECOMP PARAFAC (CP) @cite_9 and Tucker factorizations @cite_2 , gains particular interests for its distinct ability in modeling multi-aspect heterogeneous big data. Indeed, in city scenarios data samples are always involved with many aspects, such as time, space, human, urban contexts and so on, and therefore are very suitable for tensor factorization based data mining methods @cite_11 . Typical applications of tensor factorization could be classified into two categories. The first category is to reconstruct tensors for predicting unknown values in multi-aspect data sets, such as completing missing traffic data @cite_23 , inferring urban gas consumption @cite_31 , predicting travel time @cite_25 , recommending social tags @cite_21 , movies @cite_30 and sightseeing locations @cite_35 @cite_34 , and so on.
@cite_30 @cite_35 @cite_9 @cite_21 @cite_23 @cite_2 @cite_31 @cite_34 @cite_25 @cite_11
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In this paper, we propose a novel cross-space affinity learning algorithm over different spaces with heterogeneous structures. Unlike most of affinity learning algorithms on the homogeneous space, we construct a cross-space tensor model to learn the affinity measures on heterogeneous spaces subject to a set of order constraints from the training pool. We further enhance the model with a factorization form which greatly reduces the number of parameters of the model with a controlled complexity. Moreover, from the practical perspective, we show the proposed factorized cross-space tensor model can be efficiently optimized by a series of simple quadratic optimization problems in an iterative manner. The proposed cross-space affinity learning algorithm can be applied to many real-world problems, which involve multiple heterogeneous data objects defined over different spaces. In this paper, we apply it into the recommendation system to measure the affinity between users and the product items, where a higher affinity means a higher rating of the user on the product. For an empirical evaluation, a widely used benchmark movie recommendation data set-MovieLens-is used to compare the proposed algorithm with other state-of-the-art recommendation algorithms and we show that very competitive results can be obtained. With the increasing popularity of location tracking services such as GPS, more and more mobile data are being accumulated. Based on such data, a potentially useful service is to make timely and targeted recommendations for users on places where they might be interested to go and activities that they are likely to conduct. For example, a user arriving in Beijing might wonder where to visit and what she can do around the Forbidden City. A key challenge for such recommendation problems is that the data we have on each individual user might be very limited, while to make useful and accurate recommendations, we need extensive annotated location and activity information from user trace data. In this paper, we present a new approach, known as user-centered collaborative location and activity filtering (UCLAF), to pull many users' data together and apply collaborative filtering to find like-minded users and like-patterned activities at different locations. We model the user-location-activity relations with a tensor representation, and propose a regularized tensor and matrix decomposition solution which can better address the sparse data problem in mobile information retrieval. We empirically evaluate UCLAF using a real-world GPS dataset collected from 164 users over 2.5 years, and showed that our system can outperform several state-of-the-art solutions to the problem. This paper presents a standardized notation and terminology to be used for three- and multiway analyses, especially when these involve (variants of) the CANDECOMP PARAFAC model and the Tucker model. The notation also deals with basic aspects such as symbols for different kinds of products, and terminology for three- and higher-way data. The choices for terminology and symbols to be used have to some extent been based on earlier (informal) conventions. Simplicity and reduction of the possibility of confusion have also played a role in the choices made. Copyright (C) 2000 John Wiley & Sons, Ltd. Social tagging is the process by which many users add metadata in the form of keywords, to annotate and categorize items (songs, pictures, Web links, products, etc.). Social tagging systems (STSs) can provide three different types of recommendations: They can recommend 1) tags to users, based on what tags other users have used for the same items, 2) items to users, based on tags they have in common with other similar users, and 3) users with common social interest, based on common tags on similar items. However, users may have different interests for an item, and items may have multiple facets. In contrast to the current recommendation algorithms, our approach develops a unified framework to model the three types of entities that exist in a social tagging system: users, items, and tags. These data are modeled by a 3-order tensor, on which multiway latent semantic analysis and dimensionality reduction is performed using both the higher order singular value decomposition (HOSVD) method and the kernel-SVD smoothing technique. We perform experimental comparison of the proposed method against state-of-the-art recommendation algorithms with two real data sets (Last.fm and BibSonomy). Our results show significant improvements in terms of effectiveness measured through recall precision. The model for three-mode factor analysis is discussed in terms of newer applications of mathematical processes including a type of matrix process termed the Kronecker product and the definition of combination variables. Three methods of analysis to a type of extension of principal components analysis are discussed. Methods II and III are applicable to analysis of data collected for a large sample of individuals. An extension of the model is described in which allowance is made for unique variance for each combination variable when the data are collected for a large sample of individuals. Urban transportation is increasingly studied due to its complexity and economic importance. It is also a major component of urban energy use and pollution. The importance of this topic will only increase as urbanization continues around the world. A less researched aspect of transportation is the refueling behavior of drivers. In this paper, we propose a step toward real-time sensing of refueling behavior and citywide petrol consumption. We use reported trajectories from a fleet of GPS-equipped taxicabs to detect gas station visits, measure the time spent, and estimate overall demand. For times and stations with sparse data, we use collaborative filtering to estimate conditions. Our system provides real-time estimates of gas stations' waiting times, from which recommendations could be made, an indicator of overall gas usage, from which macro-scale economic decisions could be made, and a geographic view of the efficiency of gas station placement. With the increasing popularity of location-based services, we have accumulated a lot of location data on the Web. In this paper, we are interested in answering two popular location-related queries in our daily life: (1) if we want to do something such as sightseeing or dining in a large city like Beijing, where should we go? (2) If we want to visit a place such as the Bird@?s Nest in Beijing Olympic park, what can we do there? We develop a mobile recommendation system to answer these queries. In our system, we first model the users@? location and activity histories as a user-location-activity rating tensor. Because each user has limited data, the resulting rating tensor is essentially very sparse. This makes our recommendation task difficult. In order to address this data sparsity problem, we propose three algorithms based on collaborative filtering. The first algorithm merges all the users@? data together, and uses a collective matrix factorization model to provide general recommendation (, 2010 [3]). The second algorithm treats each user differently and uses a collective tensor and matrix factorization model to provide personalized recommendation (, 2010 [4]). The third algorithm is a new algorithm which further improves our previous two algorithms by using a ranking-based collective tensor and matrix factorization model. Instead of trying to predict the missing entry values as accurately as possible, it focuses on directly optimizing the ranking loss w.r.t. user preferences on the locations and activities. Therefore, it is more consistent with our ultimate goal of ranking locations activities for recommendations. For these three algorithms, we also exploit some additional information, such as user-user similarities, location features, activity-activity correlations and user-location preferences, to help the CF tasks. We extensively evaluate our algorithms using a real-world GPS dataset collected by 119 users over 2.5 years. We show that all our three algorithms can consistently outperform the competing baselines, and our newly proposed third algorithm can also outperform our other two previous algorithms. In this paper, we propose a citywide and real-time model for estimating the travel time of any path (represented as a sequence of connected road segments) in real time in a city, based on the GPS trajectories of vehicles received in current time slots and over a period of history as well as map data sources. Though this is a strategically important task in many traffic monitoring and routing systems, the problem has not been well solved yet given the following three challenges. The first is the data sparsity problem, i.e., many road segments may not be traveled by any GPS-equipped vehicles in present time slot. In most cases, we cannot find a trajectory exactly traversing a query path either. Second, for the fragment of a path with trajectories, they are multiple ways of using (or combining) the trajectories to estimate the corresponding travel time. Finding an optimal combination is a challenging problem, subject to a tradeoff between the length of a path and the number of trajectories traversing the path (i.e., support). Third, we need to instantly answer users' queries which may occur in any part of a given city. This calls for an efficient, scalable and effective solution that can enable a citywide and real-time travel time estimation. To address these challenges, we model different drivers' travel times on different road segments in different time slots with a three dimension tensor. Combined with geospatial, temporal and historical contexts learned from trajectories and map data, we fill in the tensor's missing values through a context-aware tensor decomposition approach. We then devise and prove an object function to model the aforementioned tradeoff, with which we find the most optimal concatenation of trajectories for an estimate through a dynamic programming solution. In addition, we propose using frequent trajectory patterns (mined from historical trajectories) to scale down the candidates of concatenation and a suffix-tree-based index to manage the trajectories received in the present time slot. We evaluate our method based on extensive experiments, using GPS trajectories generated by more than 32,000 taxis over a period of two months. The results demonstrate the effectiveness, efficiency and scalability of our method beyond baseline approaches. Urbanization's rapid progress has modernized many people's lives but also engendered big issues, such as traffic congestion, energy consumption, and pollution. Urban computing aims to tackle these issues by using the data that has been generated in cities (e.g., traffic flow, human mobility, and geographical data). Urban computing connects urban sensing, data management, data analytics, and service providing into a recurrent process for an unobtrusive and continuous improvement of people's lives, city operation systems, and the environment. Urban computing is an interdisciplinary field where computer sciences meet conventional city-related fields, like transportation, civil engineering, environment, economy, ecology, and sociology in the context of urban spaces. This article first introduces the concept of urban computing, discussing its general framework and key challenges from the perspective of computer sciences. Second, we classify the applications of urban computing into seven categories, consisting of urban planning, transportation, the environment, energy, social, economy, and public safety and security, presenting representative scenarios in each category. Third, we summarize the typical technologies that are needed in urban computing into four folds, which are about urban sensing, urban data management, knowledge fusion across heterogeneous data, and urban data visualization. Finally, we give an outlook on the future of urban computing, suggesting a few research topics that are somehow missing in the community.