Trajectory time prediction and dataset publishing mechanism based on deep learning and differential privacy

Abstract

In order to solve the problems of inaccurate trajectory time prediction and poor privacy protection of dataset publishing mechanism, the study adds deep learning models into the trajectory time prediction model and designs the SLDeep model. Its performance is compared with LRD, STTM and DeepTTE models for experiments, and the results show that the SLDeep model. The lowest mean absolute error value was 116.357, indicating that it outperformed the other models. The study designed the Travelet publishing mechanism by incorporating differential privacy methods into the publishing mechanism, and compared it with Li’s and Hua’s publishing mechanisms for experiments. The results show that the mutual information index value of Travelet publishing mechanism is 0.06, which is better than Li’s and Hua’s publishing mechanisms. The experimental results show that the performance of the trajectory time prediction model incorporating deep learning and the dataset publishing mechanism incorporating differential privacy methods has been greatly improved, which can provide new ideas to obtain a more accurate and all-round trajectory big data management system.

Keywords

Deep learning differential privacy trajectory time prediction release mechanism

1 Introduction

With the development of society, trajectory time prediction has become more and more demanding [1]. However, the current prediction methods are not very accurate [2]. And with the rapid development of deep learning, it has been widely used in various models [3]. In order to enhance the accuracy of the trajectory time prediction model, the study applied deep learning to the trajectory time prediction model to obtain the SLDeep model. An effective method of trajectory analysis is trajectory classification, which regarding the implications a prediction model to categorize a new trajectory (or sub-trajectory) into a single-class or multi-class. Trajectory forecasting is a sequential prediction problem in which a forecasting model forecasts the future trajectories of all moving agents in a scene based on those agents’ prior trajectories and/or the context of the scene. In addition to this, today’s dataset publishing mechanisms suffer from poor privacy protection [4]. Differential privacy methods are widely used in privacy protection because of their strong ability to protect private information [5]. Therefore, the study incorporates the differential privacy approach into the dataset publishing mechanism and designs the Travelet publishing mechanism. The SLDeep model and the Travelet publishing mechanism are then combined to obtain a trajectory big data management system. The management system can query the information of the trajectory dataset and has a high-precision trip duration prediction function.

The main contribution of the paper is discussed as follows:

The deep learning model is incorporated into the trajectory time prediction model and SLDeep model to solve the problems of inaccurate trajectory time prediction and poor privacy protection of dataset publishing mechanism. Further, the paper designs the Travelet publishing mechanism by incorporating differential privacy methods into the publishing mechanism. Then, the performance of the study is combined with LRD, STTM and DeepTTE models.

The remaining of the paper is structured as follows: literature review of the study is discussed in Section 2; Section 3 discusses the research on a trajectory management system based on the union of deep learning and differential privacy; Section 4 indicates the analysis of experimental results of travel time prediction and protection mechanism of trajectory management system; finally, the conclusion of the study is discussed in Section 5.

2 Review of the literature

With the development of the times, deep learning methods are widely used in many fields due to their own advantages of strong processing power. A model for deep learning Long Short-Term Memory (LSTM) was utilized to analyze temporal data and forecast the exact trajectory. Clustering of comparable trajectory data is used to manage huge amounts of data, which helps to reduce the search space. Rui et al. used deep learning for autoencoder and its variants in order to solve the problem of insufficient performance of data-driven machine health monitoring system. It was found that the accuracy of the machine health monitoring system was improved after deep learning [6]. Shen et al. proposed a hybrid short-term forecasting method by combining an improved gravity model and a deep learning model to improve the performance of a short-term prediction system for metro traffic. The results showed that the method achieved a large improvement in model interpretability and predictability [7]. Deepak et al. proposed a deep learning method based on a multi-angle optimization model in order to solve the problem of projection and inaccurate alignment of complex 3D movements on a plane during the FER process. The results show that the method is effective and widely applicable in various metrics [8]. With the gradual rise of differential privacy and its increasing application to privacy preservation, Gohari P et al. propose to introduce a new mechanism to address the vulnerability of privacy leakage between network providers and agents, using differential privacy as the basic mathematical framework for this work. The results show that the mechanism has stronger privacy than the traditional mechanism [9]. Sun et al. proposed an optimization strategy based on differential privacy in order to address the problem that the existing mechanism of LDP is not comprehensive enough. Theoretical analysis and experimental results demonstrated that this scheme can improve the comprehensiveness problem of today’s LDP [10]. Ouyang et al. proposed a set-valued data collection based on the category hierarchy under the local differential privacy model in order to address the problem that local differential privacy models are prone to information loss in random responses and the privacy protection of set-valued data categories is easily ignored the results show that the method can not only preserve the information but also preserve the privacy of the data. The results show that the method not only preserves more information, but also protects the category private information in the set-valued data [11].

Various methods have also emerged in trajectory time prediction. The team of Rong et al. proposed a data-driven non-parametric Bayesian model based on Gaussian process to describe the uncertainty of lateral motion in order to solve the uncertainty problem of ship trajectory prediction, and the prediction model was tested by AIS data. The results showed that the method has high prediction accuracy and meets the requirements of real-time applications [12]. Gomez-Gonzalez et al. proposed a deep conditional generative model for trajectory prediction in order to address the problem that real-time robotic systems cannot predict accurately in the long term, and the encoder and decoder networks used stochastic gradient variational Bayesian training was performed. The results showed that the model provided more accurate long-term predictions with lower latency [13]. Zhao et al. proposed a new spatio-temporal attention model that jointly investigated spatio-temporal affinity in order to address the problem of temporal influence in human trajectory prediction. The results showed that the model outperformed other similar prediction methods in terms of accuracy on the same dataset [14]. Various methods have also been used in dataset publishing. Parra-Arnau J et al. proposed a generalization of classical microaggregation to address the problem of reduced utility of differential privacy-preserving data, and experimental evidence suggests that this method can provide not only higher utility but also higher privacy compared to traditional micro aggregation [15]. He et al. proposed differential privacy considering a general random noise addition mechanism in order to guarantee different privacy in differential privacy, and then applied the resulting results to the privacy analysis of privacy-preserving consensus algorithms. A privacy-preserving consensus algorithm allows all of the directed network’s agents to subsequently attain the weighted average of their initial states while maintaining the confidentiality of each agent’s initial state. The results show that the method is not only consistent with the literature, but also provides an efficient method for estimating privacy parameters [16].

The above research illustrates that deep learning models and differential privacy methods have been used in a variety of fields and there are various approaches in trajectory time prediction and dataset publishing, but there is a lack of research that combines deep learning with trajectory time prediction and differential privacy for dataset publishing mechanisms. The study therefore applies deep learning models to trajectory time prediction, differential privacy methods to dataset publishing mechanisms, and combines trajectory time prediction and data publishing mechanisms to design a trajectory prediction system.

3 Research on a trajectory management system based on the union of deep learning and differential privacy

3.1 Research on deep learning based trajectory time prediction model

There are many factors involved in trip trajectory time prediction, not only related to weather and road conditions, but also to the driver’s own state [17]. Traditional prediction methods are generally based on traffic theory, and the core of the method is the description of the whole process through physical models and the detection of vehicle speed through detectors. However, the traditional method ignores the existence of interactions between different road sections, which is not conducive to overall time prediction, and also lacks consideration of the driver’s state and the vehicle itself, and the prediction results are often far from the true value. With the popularity of deep learning, deep learning is increasingly being used in the field of journey track time due to its ability to handle large amounts of data [18]. The study proposes a deep learning model to solve the prediction problem of trip track time by normalizing the samples and inputting them into SLDeep for training, then capturing the features of the track samples using bi-directional long and short-term memory networks and convolutional networks, and using the captured features to predict the trip time. The expression for the GPS data p_i is defined as Equation (1). $pi = (i d_{i}, y_{n_{i}}, lo n_{i}, la t_{i}, t_{i})$ (1)

In Equation (1), id_i is the taxi number, y_{n
_i} is used to indicate if there are passengers in the taxi, lon_i indicates the GPS longitude value, lat_i indicates the GPS latitude value, and t_i indicates the GPS time. Multiple consecutive GPS data are put together to form the trajectory T, and the expression for the trajectory T is shown in Equation (2). $T = (p_{1}, p_{2}, \dots, p_{i})$ (2)

The expression for the trajectory data set D, D from the existing trajectory set is shown in Equation (3). $D = {T_{i}, o_{i}, d_{i}}_{i = 1}^{N}$ (3)

In Equation (3), T_i is the i track, o_i is the departure time and d_i is the arrival time, so the expression for the journey time s_i is shown in Equation (4). $s_{i} = d_{i} - o_{i}$ (4)

Trajectory time prediction model is able to predict the travel time s_i from the trajectory T_i and the departure time o_i by the process described above. Machine learning methods have fewer feature dimensions that can be used effectively when training data, so the study constructs a richer feature dimension for the model. This can be divided into temporal, spatial and additional information feature dimensions. The temporal feature dimension refers to the strong correlation between the travel time to be predicted and the temporal information, specifically that the predicted travel time has a periodicity and that this periodicity can be reflected in a certain point in time. The study performs feature extraction of time points of the day for predicting travel times. Feature extraction is a class of dimensionality reduction techniques that creates a new collection of features from the original feature set. The new characteristics are less in number than the original ones in order to decrease dimensionality. Dimensioning is the process of determining the area or volume of an object. It is a way of determining capacity for products storage, handling, transportation, and billing. The other feature dimension, spatial features, indicates that the predicted journey time is also more relevant to the spatial information of the travel trajectory, which includes factors such as road width, gradient, latitude and longitude. The study extracts information on the distance between p_i and p_i+1 and the total distance travelled in the trajectory sample T as spatial features. The additional information feature dimension covers additional information such as driver’s physical condition and vehicle driving condition. The study focuses on the taxi number id_i and whether there are passengers riding y_{n
_i} as its additional information features. By extracting the feature information in the three dimensions, a sample data of (N, L, n) can be obtained, which is shown in Fig. 1.

The left part of Fig. 1 shows that the sample data contains N trajectory samples, each of which has L GPS data, and each of which has n dimensional features. The larger the feature dimension n, the higher the accuracy of the prediction model. The model used for deep learning is the SLDeep model, and its overall model structure is shown in Fig. 2.

Fig. 1

Feature information extraction.

Fig. 2

Overall structure of SLDeep model.

As shown in Fig. 2, SLDeep is mainly composed of attribute component, feature component and output component, where the feature component is further divided into local feature component and sequence feature component. The GPS data of the taxi is processed by the feature component to obtain (N, L, n), which is the first sample to enter the attribute component module, where it is processed separately according to the dispersion of the values of different dimensions, and the processed results are combined and input to the sequence feature component and the local feature component for training. A bidirectional LSTM, often known as a biLSTM, is a sequence processing model that combines two LSTMs, one of which receives input in the forward direction and the other in the backward direction. Max Pooling is a pooling procedure that computes the maximum value for regions in a feature map and utilizes it to construct a down sampled (pooled) feature map. It is frequently used following a convolutional layer. The captured results are combined and the final output is obtained through a fully concatenated block at y_i. In the attribute component, the temporal and additional information features cannot be learned directly by the model, so they need to be mapped to reduce the dimensionality of the data, while the spatial information features need to be normalized to reduce their numerical span. Normalization is a data standardization method used in pre-processing. In other words, having many data sources inside the same range. The network may encounter issues if the data is not normalized before training, which will make training extremely difficult and slow down learning. The mapped temporal and additional information features and the normalized spatial information features are combined into a new input tensor. The input tensor is then fed into the temporal and local feature components. The main model used in the sequential features is the common bidirectional long- and short-term memory network structure, as shown in Fig. 3.

Fig. 3

Bidirectional long-term and short-term memory network structure.

As shown in Fig. 3, the main structure of the bi-directional long and short term memory network structure is the forward long and short term memory network as well as the backward long and short term memory network. The two directions of the long and short term memory network deal with the hidden states simultaneously, allowing for easier discovery of temporal features. In the local features module, a convolutional neural network is used to identify local features in the input sample data. After the pooling layer of the convolutional network, only the most important features are left, and the information in the trajectory is convolved using convolutional kernels of different heights to better obtain the local relevance in the local features. The pooling layers’ objective is to reduce the dimensions of the hidden layer by integrating the outputs of neuron clusters from the previous layer into a single neuron in the subsequent layer. Average pooling and max pooling are two typical pooling algorithms that summarize a feature’s average availability and most active presence, respectively. Due to pooling’s independent application to each channel, the number of input channels and output channels are equal. Pooling has the advantage that it has no parameters need to be learned. The output temporal features as well as the output values of the local features module are integrated through a fully connected layer to output the final values. In order to test the performance of the SLDeep model, common evaluation metrics are the mean absolute error, the coefficient of resolvability and the root mean square error. The mean absolute error (MAE) is calculated by adding the absolute difference between each observation’s estimated and actual values throughout the whole array, then dividing the result by the array’s total number of observations. The expression for the mean absolute error is shown in Equation (5).

$MAE = \frac{\sum_{i = 1}^{n} | y_{i} - {\overset{⌢}{y}}_{l} |}{n}$ (5)

In Equation (5), MAE denotes the mean absolute error and ${\overset{⌢}{y}}_{l}$ denotes the predicted travel time. The expression for the root means square error is shown in (6). $RMSE = \sqrt{\frac{\sum_{i = 1}^{n} | y_{i} - {\overset{⌢}{y}}_{l} |}{n}}$ (6)

The standard deviation of the prediction errors is represented by the Root Mean Square Error (RMSE). The distance between the data points and the regression line is measured by residuals, and the spread of these residuals is measured by RMSE. In Equation (6), RMSE represents the root mean square error and $y_{l}^{⌢}$ represents the predicted travel time. An effective method for determining whether an equation is a member of a theory or not, given any random formula in the theory’s signature is called “Decidability” theory. The expression for the decidability factor is shown in Equation (7). $R^{2} = 1 - \frac{\sum_{i = 1}^{n} (y_{i} - {\overset{⌢}{y}}_{l})}{\sum_{i = 1}^{n} (y_{i} - {\overset{⌢}{y}}_{i})}$ (7)

In Equation (7), ${\overset{⌢}{y}}_{i}$ represents the true mean travel time and R² represents the coefficient of determinability, the magnitude of which reflects the reliability of the variables in the model, with values closer to 1 indicating better model performance.

3.2 Mechanism for publishing trajectory datasets based on differential privacy

Early trajectory data publishing mechanisms were built on the basis of indistinguishable privacy models, and it is difficult to design an effective trajectory privacy protection model through the limitations of indistinguishable privacy models [19]. As a result, the privacy protection of early trajectory data publishing mechanisms was insufficient. In order to increase the privacy protection of trajectory data release mechanisms, some studies have proposed differential privacy methods, and the biggest advantage of differential privacy methods is that they address the shortcoming that early privacy protection methods must have the knowledge possessed by the attacker of privacy. The implementation of differential privacy generally requires the use of the Laplacian mechanism, which focuses on placing the noise obtained from the Laplacian distribution onto location coordinates [20]. Since the Laplace noise is infinite, the noise obtained from it can also have an impact on the privacy of the data, leading to a privacy-preserving approach to differential privacy that needs further optimization. In order to increase the performance of differential privacy protection, the study proposed a trajectory data publishing mechanism called Travelet, which includes a differential privacy trajectory generalization algorithm and a differential privacy trajectory data publishing algorithm, where the process of trajectory coordinate generalization is shown in Fig. 4. Publication of trajectory data that assures differentially-private output while preserving high value and scalability. The dimension of publishing trajectory data is high. The number of dimensions in the data is increased since trajectories could include a lengthy string of doublets. As a result of the constraint of large dimensionality, releasing trajectory data often produces poor utility output. Further, the targeted privacy protection cannot be fully realized using trajectory data publication approaches based on differential privacy.

Fig. 4

Trajectory coordinate generalization process.

As can be seen from Fig. 4, the release mechanism generalizes all trajectory coordinates at each timestamp on the trajectory in the first step. The number of trajectories in the generalized trajectory is counted and the difference between the number of real trajectories and the number of trajectories required is made up by randomly generating generalized trajectories using an exponential mechanism to filter out the generalization scheme with the highest probability. In the second step of the release mechanism, the matrix M is transformed using Haar wavelet variations and noise is added to it to reconstruct M into M¡¯. The Haar wavelet is a collection of resampled “square-shaped” functions that collectively make up a wavelet family or basis. Like Fourier analysis, wavelet analysis provides for the representation of a target function across an interval in terms of an arbitrary function. The Haar transform is the most basic of the wavelet transformations. This transform combines a function with multiple shifts and stretches against the Haar wavelet. To justify the final result, the reconstructed count matrix M¡¯ is constrained for consistency, and the publishing mechanism publishes the consistent constrained matrix M¡¯¡¯ together with the generalized trajectory. The GPS coordinate data l_i is defined as one consisting of longitude coordinate data lon_i and latitude coordinate data lat_i. The expression is shown in Equation (8).

$l_{i} = (lo n_{i}, la t_{i})$ (8)

Multiple coordinates can form the trajectory set T and the trajectory T is expressed as shown in Equation (9). $T = {o_{1}, \dots, o_{i}}$ (9) The expression for o_i in Equation (9) is shown in Equation (10). $o_{i} = (l_{i}, t_{i})$ (10)

In Equation (10), l_i is the GPS coordinates and t_i represents the timestamp. In the first step of the Travelet publishing mechanism the coordinates at each timestamp on each trajectory are generalized using the trajectory generalization algorithm. This is done by setting the set of trajectory coordinates for the same timestamp t_i in the dataset T to T (t_i) and the set of candidate generalization schemes represented by τ. Then for each generalization scheme p in τ corresponds to a utility function u, and the utility function expression is shown in Equation (11). $u (D, p) = \frac{MeanDist (\tilde{p})}{MeanDist (p)}$ (11) The expression MeanDist (p) in Equation (11) is shown in Equation (12).

$\begin{matrix} MeanDist (p) = \frac{1}{g | D_{{LS}_{p}^{k}} |} \sum_{k = 1}^{g} \sum_{T_{i} \in D_{{LS}_{p}^{k}}} \\ Dis tan ce (T_{i}, {\tilde{T}}_{i}) \end{matrix}$ (12)

In Equation (12), ${LS}_{p}^{k}$ denotes the set of GPS coordinates in the generalization scheme p divided into clusters, k $D_{{LS}_{p}^{k}}$ denotes the set of trajectories with GPS coordinates, T_i denotes the ith trajectory in $D_{{LS}_{p}^{k}}$ and ${\tilde{T}}_{i}$ denotes the average trajectory of $D_{{LS}_{p}^{k}}$ .

For each generalisation scheme p in τ, MeanDist (p) is larger than $MeanDist (\tilde{p})$ . The study uses an exponential mechanism to calculate the probability for each generalisation scheme. The calculation formula is shown in Equation (13). $\frac{exp (\frac{ɛ_{1}}{2 Δ u} u (D, p))}{\sum_{p \in τ} exp (\frac{ɛ_{1}}{2 Δ u} u (D, p))}$ (13)

Therefore, the k-means clustering algorithm is chosen as the generalization scheme to divide T (t_i) into clusters of g and replace the origin with the cluster centre to generate different generalized trajectories. In the second step of the Travelet publishing mechanism, the trajectory publishing algorithm is used, mainly to ensure the privacy of the coefficient matrix C by adding appropriate noise to it. The wavelet coefficient matrix C is added to the noise to obtain the reconstruction matrix M′, for which the scale parameter should be set to $\frac{b}{W (c i)}$ , where W (c_i) = 2^l and l are the heights of c_i in the wavelet coefficients. Define W to be a set of functions that take the matrix as input and output, let W be the weight function of the function f belonging to F, and define F to be the minimum value that can satisfy Equation (14) for the generalized sensitivity Δf of W. $\sum_{f \in F} (W (f) \cdot | f (M) - f (M^{'}) |) ⩽ Δ f \cdot {∥ M - M^{'} ∥}_{1}$ (14)

With such a weight function setting, the generalized sensitivity of the 1D wavelet transform Δf is 1 + log ₂m. Define F as the set of weight functions W having the generalized sensitivity Δf. Let A be the algorithm with input M and output set {f (M)+ laplace (f) |f ∈ F }, where laplace (f) is the Laplace noise with the scale parameter set to $\frac{b}{W (c i)}$ . The algorithm A satisfies ɛ₂ - differential privacy, where $ɛ_{2} = \frac{2 Δ f}{b}$ . The noise is then added to the wavelet coefficients and the expression for the added noise is shown in (15). $Laplace (\frac{2 * (1 + {log}_{2} m)}{ɛ * W (c_{i})})$ (15)

After the first step of trajectory generalization, there are necessarily multiple trajectories in the dataset that generate a generalized trajectory. The reduced number of trajectories due to trajectory generalization is made up in the second step by selecting trajectories from the generalized trajectory space. In order to test the performance of the Travelet publishing mechanism, two random variables of mutual information are introduced as indicators. The expression for the mutual information of the two random variables X and Y is shown in Equation (16). $MI (X, Y) = \sum_{y \in Y} \sum_{x \in X} p (x, y) log \frac{p (x, y)}{p (x) p (y)}$ (16)

In Equation (16), MI (X, Y) represents the mutual information of the random variables X and Y. The study combines privacy protection and trajectory time prediction to design a trajectory big data management system. The system can query the information of the trajectory dataset and has a high accuracy trip duration prediction function. The specific architecture of the system is shown in Fig. 5.

Fig. 5

Specific architecture of track big data management system.

From Fig. 5, the system is divided into an interaction layer, a service layer and a data management layer from top to bottom. The main function of the interaction layer is to provide an interactive screen for administrators and users. The main function of the interaction layer is to provide an interactive screen for administrators and users. The main function of the data management layer is to store information about generalized trajectories and accesses.

4 Analysis of experimental results of travel time prediction and protection mechanism of trajectory management system

4.1 SLDeep model training results and performance comparison

The deep learning SLDeep model was trained in two training sets, and the change curves of the loss function values of the two training and validation sets with increasing training times are shown in Fig. 6.

Fig. 6

Sldeep model loss curve.

As can be seen from Fig. 6, the LOSS curves of the SLDeep model trended downwards until they stabilised in both datasets, and when the number of training sessions reached 30, the LOSS curves of the model stabilised and the LOSS values of the training set were lower than those of the validation set. To test and compare the performance of the SLDeep model, the root mean square error, the coefficient of resolvability and the mean absolute error of the SLDeep model were compared with the LRD model, the STTM model and the DeepTTE model on the Shanghai and Beijing travel time data sets, and the results are shown in Fig. 7. Limited risk distributor (LRD) models are frequently used by global distribution corporations to promote their goods in a certain area or jurisdiction. A common supply chain structure, this strategy is driven mostly by corporate tax optimization. The goal of Shot Text Topic Modeling (STTP) is to determine concepts or clusters within a corpus of texts without necessarily understanding what the subjects exist. Topic models can help users to organize and analyze enormous quantities of unstructured text bodies. And, a multi-task learning component is provided on the DeepTT, to estimate the trip time of both the overall path and each local path simultaneously during the training phase. DeepTTE is made up of three parts: the attribute component, the spatio-temporal learning component, and the multi-task learning component.

Fig. 7

Performance comparison of four models.

As can be seen from Fig. 7, the results of the four forecasting models on the Beijing and Shanghai datasets are generally not significantly different. Among the four forecasting models, the SLDeep forecasting model has the smallest root mean square error and the highest mean absolute error, and the highest decidability coefficient, indicating that its forecasting performance is better than that of the LRD model, STTM model and DeepTTE model. The SLDeep prediction model has the highest coefficient of determination of 0.781 in the Beijing dataset, the lowest mean absolute error of 116.357 in the Shanghai dataset, and the lowest root mean square error of 355.369 in the Shanghai dataset, which indicates the feasibility and superior performance of the SLDeep prediction model used in the study. To investigate the effect of training set size on the performance of SLDeep prediction models. In the Beijing dataset, the training set sizes of 50,000, 80,000 and 110,000 trajectory sample sets were used for comparison experiments, and SLDeep, STTM, and the DeepTTE prediction model is used to predict three different sizes of samples respectively, and the mean absolute error is used as the prediction accuracy metric; in the Shanghai dataset, the trajectory sample sets with training set sizes of 100,000, 200,000 and 300,000 are used for comparison experiments, and the SLDeep, STTM and DeepTTE prediction models are used to predict these three different sizes of samples respectively, and the mean absolute error as the prediction accuracy index. The specific results are shown in Fig. 8.

Fig. 8

Mae curves of three prediction models in data sets of different sizes.

As can be seen in Fig. 8, the average absolute error curves of the three prediction models trend downwards as the number of samples in the training set increases, both in the Beijing dataset and in the Shanghai dataset. This result indicates that as the sample size increases, the higher the prediction accuracy of the model, the better the results. Looking at the magnitude of the average absolute error values of the three prediction models, it can be found that in both datasets, the absolute error values of the SLDeep prediction model are smaller than those of the STTM prediction model and the DeepTTE prediction model, and the SLDeep prediction model has the smallest average absolute error of 111.32 in the Beijing dataset of size 110,000. This result again shows that the SLDeep prediction model outperforms both the STTM prediction model and the DeepTTE prediction model. Taken together, these results conclude that the SLDeep prediction model does outperform other prediction models and the larger the data set, the better the prediction performance of the model in model prediction.

4.2 Performance testing of the Travelet publishing mechanism

The study compares the Travelet publishing mechanism with the similar Li’s publishing mechanism and Hua’s publishing mechanism on the Shanghai trajectory dataset to evaluate the performance of the Travelet publishing mechanism in terms of the degree of privacy protection and usability. The study evaluates the privacy loss of the publishing mechanism by the mutual information formula between two matrices of the true count matrix M and M″. The results of the mutual information of different ɛ publishing mechanisms on the Shanghai trajectory dataset are shown in Fig. 9.

Fig. 9

Privacy loss on Shanghai track dataset.

As can be seen in Fig. 9, the values of the mutual information indicator for the Travelet publishing mechanism are lower than those of Li’s publishing mechanism and Hua’s publishing mechanism for the four different privacy budgets ɛ in the Shanghai trajectory dataset. The lower the mutual information indicator, the lower the correlation between the variables, i.e. the higher the privacy security. This result indicates that the Travelet publishing mechanism has the highest privacy security of the three publishing mechanisms. Comparing the four sets of curves in Fig. 9, it is found that as the privacy budget ɛ increases, the value of the mutual information indicator increases for the Travelet, Li’s and Hua’s release mechanisms. This result also verifies that the larger the privacy budget ɛ the lower the level of privacy protection. In addition to the above results, it can be observed from the graph that the value of the mutual information metric for the three different publishing mechanisms increases as the number of k-means clusters g increases. As g increases, the number of clusters together decreases, the trajectory accuracy loss decreases, and the usability of the publishing mechanism increases. In order to investigate the extent to which the addition of noise affects the usability of the release mechanism, the study uses the mean absolute error as a measure of the noise added to the trajectory technique. The smaller the mean absolute error value, the higher the usability of the publishing mechanism. A comparison of the mean absolute error values between the Travelet publishing mechanism for trajectory data and Li’s publishing mechanism for real and noise added counts under different g and privacy budgets ɛ is shown in Fig. 10.

Fig. 10

Availability comparison under different privacy budgets.

Looking at Fig. 10, it can be concluded that the two trajectory data publishing mechanisms, Travelet Publishing and Li’s Publishing, do not differ significantly in the absolute error values of the evaluations when the privacy budget ɛ is large. This indicates that the usability of the two publishing mechanisms is very close when the privacy budget ɛ is large. However, when the privacy budget ɛ is 0.1 and 0.2, the average absolute error of Travelet’s publishing mechanism is 0.83 and 0.68, which is significantly higher than the average absolute error of Li’s publishing mechanism of 0.48 and 0.45. As the privacy budget ɛ increases, the average absolute error of Travelet’s publishing mechanism tends to decrease, and when the privacy budget is 0.8, the mean absolute error of the Travelet publishing mechanism is 0.38, which is lower than the mean absolute error of Li’s publishing mechanism of 0.40. In addition, it can be observed that the larger the number of k-means clusters g, the smaller the mean absolute error of the publishing mechanism, indicating that the usability of the publishing mechanism increases with the increase of g. Finally, by looking at the mean absolute error curves of the two publishing mechanisms under the privacy budget ɛ, it can be observed that as the privacy budget ɛ increases, the mean absolute error decreases, i.e., the usability increases.

5 Conclusion

In order to solve the problem of lack of security and accuracy in today’s large system of trajectory data, the study added deep learning model to the trajectory time prediction model to obtain a new prediction model SLDeep. The SLDeep model outperforms the LRD, STTM and DeepTTE models in all three evaluation criteria, indicating that its performance is far better than the other models. The study proposes a new Travelet publishing mechanism by incorporating differential privacy methods into the publishing mechanism, and the performance of the Travelet publishing mechanism is tested against the other two publishing mechanisms. The results show that the Travelet release mechanism has a mutual information index value of 0.06 and a mean absolute error value of 0.40, both of which are better than the comparison release mechanism, and this result indicates that the privacy of the Travelet release mechanism is better. Although the research design travel time prediction model has better performance, the model mainly relies on deep learning to obtain information without considering realistic road network information, and how to combine reality and learning content is the future research direction.

Conflict of interest disclosure

The authors declare that there is no conflict of interest.

Footnotes

Acknowledgments

This project funded by the General Project of Universities in Yunnan of topic “Research on Feature Learning Methods Based on Deep Computing in Big Data Environment” (no. 201801CF00022), and National Natural Science Foundation of China of topic “Research on Automatic Annotation Technology of Yi Speech Data Based on Poverty Alleviation Log” (no. 62066023), and Key Laboratory of Data Governance and Intelligent Decision in Universities of Yunnan.

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