A BiLSTM-attention-based point-of-interest recommendation algorithm

Aichuan Li; Fuzhi Liu

doi:10.1515/jisys-2023-0033

Artikel Open Access

A BiLSTM-attention-based point-of-interest recommendation algorithm

Aichuan Li und Fuzhi Liu

Veröffentlicht/Copyright: 21. Oktober 2023

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Aus der Zeitschrift Journal of Intelligent Systems Band 32 Heft 1

Abstract

Aiming at the problem that users’ check-in interest preferences in social networks have complex time dependences, which leads to inaccurate point-of-interest (POI) recommendations, a location-based POI recommendation model using deep learning for social network big data is proposed. First, the original data are fed into an embedding layer of the model for dense vector representation and to obtain the user’s check-in sequence (UCS) and space-time interval information. Then, the UCS and spatiotemporal interval information are sent into a bidirectional long-term memory model for detailed analysis, where the UCS and location sequence representation are updated using a self-attention mechanism. Finally, candidate POIs are compared with the user’s preferences, and a POI sequence with three consecutive recommended locations is generated. The experimental analysis shows that the model performs best when the Huber loss function is used and the number of training iterations is set to 200. In the Foursquare dataset, Recall@20 and NDCG@20 reach 0.418 and 0.143, and in the Gowalla dataset, the corresponding values are 0.387 and 0.148.

Keywords: location-based social networks; big data; deep learning; POI recommendation; embedding layer; bidirectional long short-term memory network; self-attention mechanism

1 Introduction

People use location-aware social media increasingly frequently as a result of the popularity of location-aware social media and the ongoing improvement of location technology and smart devices. Users can share their experiences using location, images, text, audio, and other data at any time and from any location. This, in turn, gives rise to location-based social networks (LBSNs), where users and locations are nodes, and the edges between nodes show the pertinent connections between users and other users, users and locations, and locations and other locations. One of the research hotspots in LBSNs is point-of-interest (POI) recommendation, because it can both help users find POIs rapidly and allow POI providers to quickly understand user preferences and improve service quality in a targeted manner.

Because of the development of information technology, several types of social network-based services have emerged and are widely used; LBSNs are the most popular of such applications [1]. Unlike traditional social networks, LBSN platforms allow users to share their real-time geographic locations by checking in. These locations are called POIs [2]. Users can connect the physical and virtual social network world through geographical coordinates, which can fully track their real-life spatial dynamics and activities. With the popularity of location-based information services, POI data are increasing exponentially. Users frequently spend a lot of time to reach locations they are interested in, which has led to the development of fast POI recommendation methods [3].

POI recommendation is based on estimating the user’s interest preferences based on their current location, social relationships, historical POIs visited, and their geographical location. Then, a score is predicted for each POI, and the POIs with the highest score are recommended to the user as those that the latter is most likely to be interested in the study of Islam et al. [4]. The user’s sequence pattern can reflect not only their mobility patterns but also their short-term dynamic interest preferences [5]. However, there are two problems with the POI recommendation. The first is that LBSN data are scarce, and the second is that users are limited by the scope of spatial activities, with access to only a few POIs in the city [6]. Some users will not share location data on the service platform following offline access to POIs for personal privacy protection [7]. On the other hand, due to the significant impact of geographical correlation, users are constrained by the scope of geospatial activities and tend to visit POIs that are adjacent in space, so their visits are usually concentrated in a few areas [8]. Therefore, combining factors such as geographical, content, and semantic impact is necessary to enrich contextual information and improve the reliability of POI recommendations.

To address the problem of current POI recommendation research, which cannot capture the high-level sequence transfer dependency of users from the complex check-in history effectively, as well as the difficulty in learning the complex dynamic preferences of users [8,9], a bidirectional long-term memory (BiLSTM)-attention-based POI sequence recommendation algorithm is proposed in this article. Overall, the main contributions of this article include two aspects:

Aiming at the problem of LBSN data sparsity, the proposed model uses the embedding method to map the original sparse data into a low-dimensional vector and perform a dense vector representation, so as to further discover the internal relationship between locations and users, better understand the different preferences of users more accurately, and improve predictions and scores.
Because existing POI recommendation models do not take into account the effective use of time and space interval information between users’ check-in locations, the proposed BiLSTM-attention model combines a spatiotemporal network and a self-attention mechanism (SAM). Specifically, the model combines the spatiotemporal interval information of user’s check-in information into the BiLSTM network and uses the SAM to assign weights to the check-in locations, further improving the accuracy of POI recommendation.

The remaining part of this article is arranged as follows: First, in Section 2, related works on POI recommendation systems are studied. Then, in Section 3, the proposed BiLSTM-attention is introduced in detail. In Section 4, a comprehensive experimental comparison is conducted on the proposed model. Finally, Section 5 summarizes this article and discusses future work.

2 Related research

To improve the prediction performance of POI recommendation models, many scholars have proposed different prediction methods for different situations.

Researchers in traditional POI recommendation systems mostly analyze users’ location preferences using collaborative filtering. The main process is to analyze the check-in location of users, find similar users using a similarity measure, and then make recommendations based on the check-in location of similar users [10,11]. For example, Liu et al. [12] proposed a POI group recommendation method based on collaborative filtering with intragroup divergence to calculate the degree of user preference for categories. First, a group feature preference model is established to obtain the similarity between groups and other users’ feature preferences using check-in locations, where the intra-group variation of the POI is measured using the POI preferences of group members and their friends. Then, the preference scores of the group for each location are calculated using collaborative filtering methods and intra-group differences, and the top-ranked locations are the recommendation results for the group. Experiments were conducted on two LBSN datasets, and the experimental results in terms of precision and recall show that the method outperformed other methods. However, the collaborative filtering-based approach only utilizes the interaction information of users and items and cannot utilize their inherent features and contexts.

To address the current shortcomings of machine learning-based methods in POI recommendation tasks, many recommendation methods based on deep learning have gradually been proposed by scholars. A spatiotemporal long- and short-term memory (ST-LSTM) network was initially proposed by Huang et al. [13]. ST-LSTM can simulate spatiotemporal information more effectively by feeding spatiotemporal contextual information to the LSTM network at each step. For the subsequent POI recommendation, they also created an attention-based spatiotemporal LSTM (ATST-LSTM) network, which can use spatiotemporal contextual information to selectively focus on historical check-in records that are pertinent to the check-in sequence using the attention mechanism. They also performed a detailed performance evaluation utilizing real very large datasets from Gowalla and Brightkite, two well-known LBSNs. The experimental findings reveal that the proposed ATST-LSTM network outperformed the next two leading POI recommendation techniques on three widely used evaluation metrics. Wang et al. [14] proposed a deep learning-based LBSN for POI recommendation while maintaining privacy. First, embedding is used to quantify user information, friend relationships, POI information, etc., to obtain the internal relationship of location. Then, the user’s history and current POI check-in sequence set are used as the input to a long- and short-term attention mechanism to better capture the user’s long and short-term preferences. Finally, the social network information and semantic information are fitted in different input layers, and the temporal and geographic location information of users’ historical behaviors are used to recommend the next POI for users. The Gowalla and Brightkite datasets are used to demonstrate the proposed approach, and the results showed that the method outperforms other comparable methods for different sparsities, location sequence lengths, and embedding lengths. The recommended method tended to stabilize at an accuracy of 0.27 after 500 iterations and achieved inference times of less than 130 ms, which is better than the other deep learning methods of the comparison. Safavi and Jalali [15] proposed a novel convolutional neural network-based POI recommendation pipeline, RecPOID, which can accurately recommend the top k POI sequences and consider only the effect of the user’s most similar friends’ patterns instead of all their friends. Experimental results show that considering the most similar friends improves the accuracy of recommendations, and consequently, RecPOID outperforms state-of-the-art methods. While the above study led to improved recommendation effects, due to the underlying assumptions of the RNN, any adjacent check-in behaviors in the check-in sequence would be considered as interdependent, which can easily generate false dependencies and affect the recommendation results.

Many studies have demonstrated the excellent performance of neural network models in POI recommendation prediction tasks. To further improve its feature extraction capability in such tasks, researchers have focused on the adoption of attention mechanisms to neural networks. A novel exploration-utilization model that simultaneously exploits unique user preferences and explores new POIs in the global spatiotemporal preference (STP) neighborhood was proposed by Lim et al. [16]. The model allowed users to selectively learn from other users using the STP user-dimensional graph attention network (STP-udgat). Additionally, random walks were suggested as a disguised self-focus alternative to utilize the STP graph’s structure and discover fresh higher-order POI neighbors while exploring. Experimental results on six real datasets showed that this model performs much better than the industry standard and cutting-edge approaches. However, although the recommendation effect has been improved, the user’s check-in sequence (UCS) data do not take fully into account time and space interval information, which can provide key clues about the user’s next action and lead to better recommendations.

In recent years, excellent POI recommendation prediction methods have emerged. However, current POI recommendation methods lack the ability to capture user, item, and contextual features, and they are prone to overdependence. In view of this, a BiLSTM-attention-based POI sequence recommendation algorithm is proposed, which uses the embedding layer’s output vector representation, followed by a BiLSTM network model for spatiotemporal feature learning. Then, an attention mechanism is used for weight assignment, finally outputting the user-matching candidate POIs in the form of a POI sequence containing three consecutive positions. The results show that the model has advantages in POI recommendation prediction.

3 POI recommendation algorithm based on deep learning

3.1 BiLSTM-attention POI recommended model

In this article, the POI sequence recommendation system model is formulated through the integration of a spatiotemporal network and an SAM. The input is user’s historical check-in sequence data P ˜ i = [ U i , P i , T i ] and current location data P i , where U i and T i are the user and time data. The model structure is shown in Figure 1.

Figure 1

Architecture of the BiLSTM-attention POI recommendation model.

First, the original data are entered into the model in vectorized form, and the UCS and space–time interval information are obtained. Then, the UCS, time interval, and space interval information are passed through the BiLSTM model, and the SAM is used for the check-in sequence location to obtain the updated representation of the UCS [20]. Finally, candidate POIs are matched to the user, and a POI sequence containing three consecutive locations is generated.

3.2 Embedding

The main function of the embedding is to express the original data using a dense vector, so as to facilitate data processing, further discovery of the internal relationship between locations and users, and a more accurate understanding of the different preferences of users to improve predictions and scores. The embedding structure is shown in Figure 2.

Figure 2

Architecture of the embedding.

The user’s data, location, and other raw data are inputed into the embedding layer for conversion to a dense vectorized representation, where the user’s and location’s feature vector dimensions are d × m and d × n , which represent the d -dimensional vector of m users and the d -dimensional vector of n locations, respectively. When predicting the score, the transposition of the feature vector is used for multiplication, so that the dimensions of the multiplied matrix become m × n , and d represents the hidden vector dimension. The activation function is tanh.

3.3 BiLSTM

When expressing Chinese text, the meaning of a sentence is not only related to the above but also closely related to the following. Although LSTM can learn the above information well, it cannot learn the future information. Therefore, a BiLSTM model is used for analysis, whose structure is shown in Figure 3.

Figure 3

Structure of the BiLSTM model.

Each timing module of the forward and reverse LSTM network in the BiLSTM model contains an input and an output gate and a memory unit [17]. At any time, there will be two hidden layer outputs of two LSTMs with forward and backward, and their states are shown as follows:

(1) h → t = LSTM ( x t , h → t − 1 ) h ← t = LSTM ( x t , h ← t − 1 ) h t = ω t h → t + ϖ t h ← t + b t .

The direction of the arrow to the right indicates the positive direction and to the left indicates the negative direction; x t represents the input; ω t , v t , and b t represent the forward and reverse output weight matrices and the offset at time t. The contextual information of the text learned from the BiLSTM model can solve the polysemy of a word in the social network text effectively, thus improving the accuracy of POI recommendations.

3.4 Attention model

Due to the successful application of SAMs in language modeling, the most advanced POI recommendation models use this powerful method to achieve the best performance [18]. In traditional recommendation systems, the idea of self-attention-based modeling methods is widely used. Its biggest contribution is that the sequence information can be weighted and combined into the query vector. Because the current query vector incorporates different attention to all visible vectors, self-attention represents their previous significance by calculating the similarity between the query vector and all vectors, which is also in line with the modeling methods of many real-world modeling methods [19,20].

The attention mechanism is simply input x , and the output y is obtained after giving different degrees of attention to each part of x , which in this case refers to the different contribution weights of different parts of x to y. The analysis process of the SAM is shown in Figure 4.

Figure 4

Analysis process of SAM.

Attention is mainly divided into three stages:

Stage 1: Calculate the similarity sim of query value q and key value e . The attention score function score ( ⋅ ) is as follows:

(2) score ( q , e ) = sim ( q , e ) .

The proposed method calculates similarity based on location attention, so score ( ⋅ ) is expressed as:

(3) score ( a , b ) = soft max ( r a ) .

Stage 2: Normalize the similarity and obtain the contribution weight α i j of each part:

(4) α i j = soft max ( score ( q i , e j ) ) = exp ( score ( q i , e j ) ) ∑ n = 1 N exp ( score ( q i , e n ) ) .

Stage 3: Calculate the weighted sum to obtain the attention value c i :

(5) c i = ∑ j = 1 n α i j z j ,

where z j is the quantity of each part of the information.

Due to the attention mechanism, different POIs or comment information in the sequence can be given different attention to different parts of vectors through the similarity calculation, which is a weighted vector summation [21,22]. In this way, the sequence rules of POIs can be captured effectively through the self-attention model, and the fusion function of the POI vector and the comment information vector can be realized through co-attention. In addition, the effect of weighted aggregation of different feature vectors can also be realized through the attention mechanism and is mainly reflected in the fusion of different influencing factors into a single vector [23,24].

4 Experimental results and analysis

4.1 Experimental setting and data

The hardware configuration and software environment of the experimental setup of the proposed model are shown in Tables 1 and 2.

Table 1

Server hardware configuration

Hardware parameters	Configuration
RAM	128G
CPU	Intel(R) Xeon(R) CPU E5-2650 v4 @ 2.20 GHz
GPU	NVIDIA TITAN V

Table 2

Experimental software environment

Software environment	Configuration
OS	Ubuntu 16.04.5 LTS
Python	3.6.12
Pytorch-GPU	1.1.0
CUDA	9.0
Cudnn	7.5.1
Matplotlib	3.3.4

The proposed model is trained and tested on real Foursquare and Gowalla check-in datasets. Foursquare has a long-term check-in dataset of users in New York City, whereas Gowalla is a social check-in application user behavior record. Locations that featured less than ten times in the datasets are removed, and the UCSs are arranged in increasing order of check-in time. The continuous timestamps are divided into 7 × 24 = 168 dimensions to represent the users’ check-in behavior in 1 day or 1 week, which is used to reflect periodicity. During training, the first G items of the UCSs are used as the check-in data, while the last three items of G are used as the POI sequence, which contains three consecutive recommended places to visit. The details of the datasets are shown in Table 3.

Table 3

Basic information of dataset

	Foursquare	Gowalla
User	1,083	13,137
Location	8,386	32,510
Check-in	143,362	1,375,418

4.2 Evaluation index

To better and clearly evaluate the recommendation ability of the model, two general evaluation criteria are used to measure the performance of the BiLSTM-attention model and the comparative experimental model. The mathematical expression of the recall rate is

(6) Recall@ K = TP TP + FN ,

where TP (true positive) indicates that the actual type is consistent with the predicted result, and both are positive; FN (false negative) indicates that the actual type is positive, while the predicted result is negative. K ’s value was set to 1/5/10/20.

The normalized discounted cumulative gain (NDCG) is used to evaluate the accuracy of the sorting results, whose main factor considered is the ranking position. A higher ranking of the real tag in the predicted ranking list results in a better prediction effect and consequently a better evaluation result. The mathematical expression of NDCG is as follows:

(7) CG@ K = ∑ i k ϑ ( i ) ,

(8) DCG @ K = ∑ i = 0 k 2 ϑ ( i ) − 1 log 2 ( i + 1 ) ,

(9) NDCG @ K = DCG @ K IDCG ,

where the cumulative gain (CG) represents the correlation degree of the prediction results and is the sum of the correlation scores of the prediction results but does not consider the location factor; J ( i ) represents the correlation of the i th position; DCG represents the discounted cumulative gain (), which is the CG result divided by the discount value and makes the top ranking to have a greater impact on the result, while the lower ranking has a smaller impact; IDCG is the maximum cumulative loss gain under ideal conditions; K ’s value was set to 1/5/10/20.

4.3 Implementation details and training strategy

The loss function, which reflects the deviation degree of the predicted value from the actual one, is an important characteristic feature of the neural network. The closer the loss value is to 0, the better the effect of neural network fitting data, and the better the learning result. The loss function is also a required parameter for model compilation using the Keras framework, as it will affect the performance of the BiLSTM-attention. When determining the loss function, the L2, L1, and Huber loss functions are selected for comparative experiments. The mean absolute error (MAE) and mean square error (MSE) of the results are shown in Figure 5.

Figure 5

MAE and MSE values of different loss functions: (a) MAE and (b) MSE.

Figure 5 shows that, with training, the MAE and MSE values of the three loss functions decrease smoothly and show relatively stable performance. The MAE value of the L1 loss function is the lowest, about 0.70, while for MSE, the Huber loss function had the lowest value, about 1.15. Moreover, the Huber function converges relatively fast, at about the 35th Epoch. Given its effect, efficiency, and characteristics, the Huber function was the final selection for the system loss function.

The training efficiency of the BiLSTM-attention model is affected by the number of iterations, so its convergence was evaluated on the Foursquare and Gowalla datasets. The results are shown in Figure 6.

Figure 6

The effect of iteration number on the performance of the recommendation model.

Figure 6 shows that, after 200 iterations, Recall@10 of the BiLSTM-attention model becomes relatively stable. Similarly, after 150 iterations on the Gowalla dataset, the BiLSTM-attention model reaches a stable value. Therefore, the number of iterations was set to 200 in the experiment to ensure the convergence of the proposed recommendation model.

4.4 Experimental comparison

4.4.1 Comparison of POI at different length sites

First, POI recommendation sequences with lengths of 1, 2, and 3 consecutive locations were considered. The results of the proposed model’s POI recommendation sequences of different lengths for the evaluation index Recall@K on the Foursquare dataset and Gowalla dataset are shown in Figure 7.

Figure 7

Recall rate of POI results on different datasets: (a) Foursquare and (b) Gowalla.

Figure 7 shows that, when recommending sequences of multiple POIs to users, Recall@K will decrease to some extent. The sequence factor is the key in the POI sequence recommendation; as the recommended POI sequence contains places that the user may visit in sequence in the future, the sequence should be correct. Therefore, the recall rate of the three-location POI sequence recommended to users will decrease compared to sequences with fewer locations. Different K values have different results on POI sequence recommendation. In the Foursquare and Gowalla datasets, as the value of K increases, the proportion of original positive samples considered before recommending K items for users also increases, and the recall rate will also increase accordingly. The proposed method finally recommends a POI sequence containing three locations for users.

4.4.2 Distribution reference of users and POI on different datasets

Both datasets were composed of user check-in records, and each record contained a check-in timestamp, longitude and latitude coordinates of the POI, the POI type, and other information. The distribution of users and POIs in Foursquare and Gowalla datasets is shown in Figure 8.

Figure 8

Distribution of users and POIs on different datasets. (a) Distribution of users on Foursquare, (b) distribution of POIs on Foursquare, (c) distribution of users on Gowalla, (d) distribution of POIs on Gowalla.

From Figure 8, the number of users’ check-ins and visits to POIs roughly follows a power-law distribution. That is, only a small number of users have many check-ins, while most users have few check-ins for the same POI rules. Therefore, in order to filter the noise in the dataset and alleviate the sparsity of the data, users with fewer than 10 check-ins and POIs with fewer than 10 visits were removed from the dataset.

4.4.3 Performance comparison of the model under different check-in numbers

In order to further analyze the POI recommendation model, the users in the dataset were divided according to the number of check-ins, they registered into five groups, namely those with <20 check-ins, those with [20, 50), those with [50, 100), and those with ≥100 check-ins. The performance of four models ([12,13,16] and the proposed model) on different user groups is shown in Figure 9.

Figure 9

Performance comparison of the model for user groups with different check-in numbers. (a) Recall@10(Foursquare), (b) NDCG@10(Foursquare), (c) Recall@10(Gowalla), and (d) NDCG@10(Gowalla).

Figure 9 shows that the Gowalla dataset is more dense, and users are more evenly distributed in different groups. In contrast, the Foursquare dataset users are sparse, as they are mainly concentrated in the first two groups, that is, the number of users with <50 check-ins account for about three-quarters of the total number of users. As the number of check-ins increases, the performance of the four models shows a downward trend, but the proposed model has the best performance in all five user groups. This shows that the proposed model has good adaptability for users with different check-in frequencies.

The models of Liu et al. [12] and Huang et al. [13] use collaborative filtering and LSTM for POI recommendation, respectively. Because it is difficult for these models to take fully into account interest preferences, and thus the overall recall@10 and NDCG@10 are small. However, the model of Lim et al. [16] uses an attention mechanism for POI recommendation, which has good feature extraction performance but does not work well with the spatiotemporal features of the data. The proposed model, which combines a BiLSTM and an attention mechanism, can capture multi-dimensional preferences to fully use the check-in history and obtain the best recommendation results for groups of users with different numbers of registered check-ins.

4.4.4 Performance comparison on different datasets

To verify the performance of the proposed model, it was compared with the models proposed in previous studies [12,13,16]. The performance of the four models as a function of the training rounds on the Foursquare and Gowalla datasets is shown in Figure 10.

Figure 10

Comparison of model performance as a function of the number of training epochs. (a) Recall@20(Foursquare), (b) NDCG@20(Foursquare), (c) Recall@20(Gowalla), and (d) NDCG@20(Gowalla).

Figure 10 shows that as the number of training epochs increases to about 35, the performance of the four models converges relatively smoothly. Since the proposed BiLSTM-attention POI model integrates the spatiotemporal interval information between check-in data into the BiLSTM network and uses the SAM to assign weights to check-in locations, it can fully consider the geographical characteristics of the POIs, thus ensuring the accuracy of its recommendation effect. The Recall@20 and NDCG@20 values of the proposed model were about 0.418 and 0.143 on the Foursquare and 0.387 and 0.148 on the Gowalla datasets, respectively. In the study of Liu et al. [12], the feature utilization of the POI recommendation algorithm based on collaborative filtering is limited, as the model only uses the interaction information between users and items and does not take into account the features of users, items, and context. Similarly, in the study of Huang et al. [13], due to the underlying assumption of RNN, any adjacent check-in behaviors in the check-in sequence will be considered interdependent, which can easily lead to the generation of false dependencies and affect the recommendation results. In the study of Lim et al. [16], although the predictive effect of the attention-based POI recommendation model has been improved to some extent, the spatiotemporal interval information in the UCS data is considered fully.

5 Conclusions

A BiLSTM-attention-based POI sequence recommendation algorithm is proposed to address the problem of low accuracy of existing POI recommendation algorithms. The effectiveness of this method is validated experimentally, and the following conclusions can be drawn:

The spatiotemporal characteristics of the data are obtained using embedding, which solves the data sparsity problem and improves the high-quality data for later analysis. The recommendation performance of the model is best when the Huber loss function is used, and 200 training iterations are performed.
The proposed model integrates a BiLSTM network and an attention mechanism to fully extract the time series features of the data and capture the global connections, which greatly improves the recommendation performance.

However, the proposed model still has some limitations:

The model complexity is high.
There is a risk of user privacy leakage.

In future research work, the complexity of deep learning algorithms can be further reduced, fault tolerance can be improved, and more reliable deep learning models can be developed. In addition, the enriched user data, under the premise of protecting user privacy, is used to improve the practicality of POI recommendation models. In addition to the above improvement strategies, there are other very good methods that can be borrowed, such as the novel particle swarm-cuckoo search optimization algorithm proposed in the study of Jawad et al. [25].

Funding information: This work was supported by the NSFC Youth Science Fund Project (No. 32201655) and Heilongjiang Agricultural Reclamation Administration’s Project (No. HKKY190201-02).
Author contributions: Aichuan Li: Conceptualization, Funding acquisitio, Project administration, Writing – original draft; Fuzhi Liu: Resources, Software, Supervision, Validation, Visualization, Writing – review & editing.
Conflict of interest: The authors declare that they have no conflicts of interest to report regarding the present study.
Data availability statement: The data used to support the findings of this study are included within the article.

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Received: 2023-03-07

Revised: 2023-07-20

Accepted: 2023-08-28

Published Online: 2023-10-21

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

https://doi.org/10.1515/jisys-2023-0033

Schlagwörter für diesen Artikel

location-based social networks; big data; deep learning; POI recommendation; embedding layer; bidirectional long short-term memory network; self-attention mechanism

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BY 4.0