POI recommendation finds significant importance in various reallife applications, especially when meeting with locationbased services, e.g., checkins social networks. In this paper, we propose to solve POI recommendation through a novel model of dynamic tensor, which is among the first triumphs of its kind. In order to carry out timely recommendation, we predict POI by utilizing a completion algorithm based on fast lowrank tensor. Particularly, the dynamic tensor structure is complemented by the fast lowrank tensor completion algorithm so as to achieve prediction with better performance, where the parameter optimization is achieved by a pigeoninspired heuristic algorithm. In short, our POI recommendation via the dynamic tensor method can take advantage of the intrinsic characteristics of checkins data due to the multimode features such as current categories, subsequent categories, and temporal information as well as seasons variations are all integrated into the model. Extensive experiment results not only validate the superiority of our proposed method but also imply the application prospect in largescale and realtime POI recommendation environment.
The mobile recommendation system has played an indispensable role in people’s daily life. For instance, people naturally put up mobile phone to find the restaurants to eat, stores to go, and amusement parks to spare the time. With the proliferation of global positioning system (GPS), locationbased social networking services (LBSNs), e.g., Foursquare, Facebook Places, Google Places, and so on, tighten the relationships among people. Through these platforms, people can easily access the information of popular points of interest (POI) which might well cater to their preferences. Therefore, comprehensive analysis of POIs via online checkins data can make recommendation more accurate and suitable for people’s need.
Accurate and prompt recommendation is the key component of an ideal POI recommender system. For example, when a user just leaves the train station at summer night, hotels and restaurants, rather than bars and nightspots, should be recommended due to the common sense that searching for places to settle down is the priority even though he or she is a king or queen of nightclub. The situation can be briefly described in Figure
Sketch of POI recommendation problem.
Credible POI recommendation heavily relies on user checkins data. In order to meet the realtime nature of the task, conventional methods usually resort to matrix factorization to solve the sparsity of userPOI matrices [
Intuitively, if a model handles data with higher dimensions, it can mine more information and the prediction result can accordingly become more accurate and reliable [
Consequently, there are many methods based on tensor factorization put forward to improve the performance. Cheng et al. first added the successive timestamp in the POI recommendation. They put forward the next personalized POI recommendation problem; a checkin tensor is constructed and factorizing personalized Markov chain (FBMC) is harnessed [
Despite the superiority of TAFBMC, there are at least two shortcomings:
Consequently, a clear gap between existing research and potential application can be identified.
In this article, we investigate to close the gap by developing a more accurate approach, namely, Prido (POI recommendation via dynamic tensor), which makes full advantage of multimode checkins data so as to improve the performance of POI recommendation. Specifically, in accordance with the successful application of tensor in the field of recommendation, we conceive a dynamic tensor model for POI recommendation. On top of it, we also develop a heuristic tensor completion method, which is on the basis of lowrank tensor completion approach. In contrast to existing approaches, Prido considers more features—current category mode, next category mode, month mode, and temporal mode—of checkins data, and leverages more advanced tensor completion algorithm with effective optimization strategy, for higher accuracy and efficiency. As to empirical assessment, we conduct extensive experiments on realworld data and compare the proposed method with a number of stateoftheart methods. The empirical results prove that Prido remarkably improves the overall performance in comparison to the competitors.
We propose to model POI recommendation with a dynamic tensor structure to exploit all available feature aspects, which is, to our best knowledge, among the first attempts
A 4dimension tensor is constructed to capture users’ preference between two successive categories in different seasons and different hours
The category information is recommended by leveraging a fast lowrank tensor completion method, equipped with pigeoninspired algorithm to optimize the parameters and
The proposed method is validated on realworld checkins datasets and demonstrated to offer remarkable improvement over alternatives as far as efficiency and accuracy are concerned
As a special form of item recommendation, POI recommendation, which converts the online checkins data into physical behavior suggestions, helps both academic and industrial development. Thus, a large number of methods are devoted to dealing with POI recommendation task.
Collaborative filtering (CF) was used to handle the POI recommendations problem in [
Recently, people pay more attention to the expansion of factors so as to enhance the explanatory power of the model. Based on Bayesian network, Park et al. introduced user profile to evaluate the matching between user profiles and restaurant profiles and output recommendation results in accordance to the matching scores [
Despite the boom of neural networks and their successful applications in many fields, there is little progress in the POI recommendation domain, for the heterogeneity nature of checkins data, where the transformation of input may increase the complexity of the model. Among various neural networks, recurrent neural networks (RNN) have been proved to outperform other methods in modeling sequential data of arbitrary length with its recurrent calculation of hidden representation [
Over the recent years, tensor, the highdimensional expansion matrix, is proved to have prominent advantage when compared with other methods in terms of explaining data with multimode [
In this section, the dynamic tensor model is elaborated, followed by the introduction of the tensor completion algorithm for personalized tensor, followed by the pigeoninspired parameter optimization procedure.
The fundamental knowledge of tensor is detailed at first, and the dynamic tensor model designed for personalized recommendation is then presented.
Tensor is a highdimensional data representation, the expression of which can be 1mode (vector) and 2mode (matrix). A tensor with
The reverse of matriculation is represented by
Specifically, the primary task of tensor unfolding is dimension reduction, turning it into a matrix. Instead of sampling eigenvalues simply from one order after another, tensor unfolding samples them from different orders in an alternating way to realize the transmission and the blending among eigenvalues from different orders in a tensor. For example, unfolding a tensor of
The product of two tensors with the same size
With regard to any
The Frobenius norm of a tensor is denoted by
Tensor stream is represented by a series of tensors, denoted by
Sketch of tensor stream.
Sketch of dynamic tensor blocks.
Since the Foursquare datasets possess temporal traits, evidently the adjacent historical data are crucial for improving overall performance. As a result, the prediction of category recommendation can be transformed into tensor structure completion task.
Our goal is to offer specific user POI recommendations during the selected time period, on the basis of the existing data. Considering that the category dataset merely contains checkins data, by comparing FBMC [
The soundness was proved in [
A tensor with 4way is utilized to construct the category data, including current categories, next categories, months, and time periods. The whole structure accordingly is converted to
Sketch of 4dimensions tensor.
Furthermore, we elaborate the dynamic tensor as follows. Existing category dataset with missing data constitutes
In the forecasting phase, the dynamic tensor updates itself by refreshing
After predicting the missing data, the current category data integrity will be improved; the number and the length of utilized data will also get enhanced.
In a nutshell, the overall algorithm concerning the structure of dynamic tensor completion is encapsulated in Algorithm
initialize
Firstly, we input the existing sets
Thus far, we have not explained the intrinsic characteristics of PIO and FALRTC, which will be covered in the following subsections.
A tensor completion algorithm to realize fast dynamic tensor completion is proposed so as to cope with POI recommendation task.
Current heuristic methods such as Tucker decomposition [
As far as Tucker decomposition is concerned, tensor
These methods require data structure transformation. But as this process goes, the error gradually accumulates because of the accompanied inevitable distortion of the original dataset.
Unlike traditional methods, we focus on dynamic tensor completion, in which low computational costs, fast convergence, and high accuracy are required. Consequently, the fast lowrank tensor completion algorithm, namely, FALRTC [
In order to improve convergence speed and tackle the tensor trance norm minimization problem, FALRTC is put forward.
With regard to POI recommendation,
The convergence rate can be reduced to
The optimization algorithm applied to each dynamic completion parameter optimization is developed in this section.
We mainly utilize the pigeoninspired optimization (PIO) to optimize the parameters of the dynamic tensor completion method and pinpoint the patterns of each step. As introduced in [
In the first stage, pigeons can briefly picture the topographic map in the head by means of magnetic sense. They take the height of the sun as compass to modify flight path. After approaching the destination, the dependence on the sun decreases.
In the second stage, when approaching the destination, the pigeons take more attention on the landmark. When spotting the familiar building, they will fly straightly to the goal. Otherwise, they will follow leaders that are familiar with the landmark.
Similarly, in the beginning, PIO sets initial location
In the second stage, with landmark operator utilized, pigeons compare the operator with destination. If marching well, the pigeons fly straightly to the goal. After each iteration, half of the pigeons which are far away from the destination might be weeded out.
The whole twostage operation is depicted in Algorithm
initialize
Calculate the velocity of each pigeon
Update the location of each pigeon
Calculate landmark
Update
Calculate the location
With PIO applied to optimize the parameters of each step in dynamic tensor, each block owns more explanatory and typical power for the specific sampling month interval. For example, when the model is utilized to recommend the July location category, the parameters trained by PIO in the block from Feb to July evidently outperform the one from Jan to Jun.
In this section, the experimental results are reported, followed by indepth analysis.
We utilized Foursquare,
We utilized the checkins data in New York and Los Angeles from January 2010 to June 2011, which contain the information of users, locations, categories, and tips. The statistics of the data are depicted in Table
The data statistics.
City  User  Location  Category  Tip 

New York  2,581  206,416  249  166,530 
Los Angeles  1,604  215,614  249  109,526 
Our target is to recommend a suitable category to the user in need, and a list of TopN recommended categories is provided. Once the user selects at least one item in the suggested list, the recommendation will be reckoned as successful. Specifically, if our recommended categories intersect with users’ real TopN lists, the prediction is deemed to be correct:
We experimentally compare our tensor completionbased method with matrix factorization models MF, PMF, and FBMC and tensor factorization models CD, TD TAFBMC, and TADFMPC, and the details are shown in Table
Models for comparison.
Model  Scale  Description 

Matrix factorization (MF) 

MF is widely used in CF and usually set as baseline. 
Probabilistic matrix factorization (PMF) 

PMF is a conventional model in recommendation domain. 
Factorized personalized Markov chain (FBMC) 

FBMC formalizes the user’s preference as a personalized Markov chain. 
Tucker decomposition (TD) 

TD transforms the highdimension tensor into a core tensor with a relative matrix in each dimension. 
Canonical polyadic decomposition (CD) 

CD transforms the highdimension tensor into a multiple equation of linear complexity. 
Timeaware FBMC (TAFBMC) 

TAFBMC equips the time factor with the FBMC. 
Timeaware decay FBMC (TADFMPC) 

TADFMPC adds decay of the probability over time in TAFBMC. 
Static prido (sPrido) 

sPrido removes the dynamic tensor structure from Prido. 
All experiments were implemented in MATLAB 2013a, and all tests were performed on a PC with Intel Core 2 2.67 GHz and 4 GB RAM. Tables
Result comparison in New York.
Matrix factorization  Tensor factorization  

Metrics  MF  PMF  FBMC  CD  TD  TAFBMC  TADFMPC  sPrido  Prido 

0.0016  0.0060  0.0310  0.0767  0.0921  0.0747  0.1230  0.1022  0.1310 

0.0197  0.0283  0.1063  0.2221  0.2642  0.2298  0.2996  0.2454  0.3201 

0.0444  0.0571  0.1700  0.3249  0.3863  0.3397  0.4136  0.3768  0.4234 

0.0822  0.1160  0.2699  0.4829  0.5357  0.4801  0.5615  0.5387  0.5911 

0.2744  0.2843  0.4893  0.7195  0.7552  0.7130  0.7699  0.7488  0.7824 

0.5053  0.5127  0.7280  0.8887  0.9040  0.8812  0.8965  0.8876  0.9010 
Result comparison in Los Angeles.
Matrix factorization  Tensor factorization  

Metrics  MF  PMF  FBMC  CD  TD  TAFBMC  TADFMPC  sPrido  Prido 

0.0433  0.0057  0.0477  0.0677  0.0964  0.0928  0.1519  0.1252  0.1672 

0.1142  0.0336  0.1351  0.2270  0.2695  0.2580  0.3250  0.2742  0.3425 

0.1734  0.0666  0.1992  0.3216  0.3957  0.3610  0.4382  0.3923  0.4594 

0.2863  0.1305  0.3023  0.4920  0.5477  0.4974  0.5756  0.5523  0.6092 

0.4486  0.2949  0.5088  0.7242  0.7588  0.7262  0.7753  0.7598  0.7973 

0.5834  0.5389  0.7412  0.8920  0.9027  0.8839  0.8971  0.8856  0.8993 
As Tables
Sketch of category prediction. (a) New York. (b) Los Angeles.
Overall speaking, the various traditional matrix factorization models perform relatively worse compared with tensor factorization models. In terms of accuracy, even the best method utilizing matrix factorization (FBMC) achieves half the value of the worst one harnessing tensor factorization (TAFBMC). The reason can be attributed to the fact that the matrix is 2dimension tensor in essence, which means at least two dimension information cannot be involved in the structure, and no matter which factorization methods is utilized, missing dimensions inevitably will restrict the latent accuracy. Thus, the further development of POI recommendation has to rely on tensor factorization.
As for the comparisons among tensor factorizationbased methods, CD and TD, as the earliest solutions, their practical arithmetical operations cost much more running time and they also perform badly in the finegrained prediction task. Although TD obtains the best performance in
Moreover, sPrido outperforms TAFBMC by approximately 3%, which reveals that our 4dimensions tensor structure is effective. Despite the fact that the user factor matters in personalized recommendation, people prefer to do popular things and consequently, the introduction of users’ checkins data is more reasonable than separate analysis. With the month dimension added, the influence of different seasons can be expressed in the model. Nevertheless, TADFMPC defeats sPrido across all metrics since static structure cannot expose the weight of diverse time, in which the premier data have the same influence as recent data for recommendation. To tackle this issue, TADFMPC adopts three different types of decay of the probability over the time factor. Nevertheless, this method neglects the variety of different seasons. Due to the adjacency of seasons, the user’s behavior in autumn is similar to summer, whereas it has little correlation with spring. Therefore, the checkins data in different seasons should not be simply reflected in the same equation. Based on the consideration, we propose Prido, in which adjacent seasons data are put into one dynamic tensor block. As can be seen from the table, Prido improves the result by 2% when compared with TADFMPC.
In this paper, a novel dynamic heuristic tensor completion approach on the basis of fast lowrank tensor completion algorithm is proposed to solve the POI recommendation task. Fast lowrank tensor completion (FALRTC) is leveraged as a supplement to the original dynamic tensor structure, so as to improve the performance prediction. Prido is able to capture the inner features of checkins data due to the multimode characteristics such as current categories, next categories, and temporal information as well as seasons variations are all integrated in the model. Experiment results not only validate the superiority of our proposed method but also suggest that there is potential application opportunity as for POI recommendation environment in a large and dynamic scope.
The data used to support this study are available at
The authors declare that they have no conflicts of interest.
This work was partially supported by NSFC under Grant nos. 61872446, 71690233, and 71331008.