Can We Enhance the Quality of Mobile Crowdsensing Data Without Ground Truth?

Numerous studies have been dedicated to the establishment of data quality-based MCS systems [37, 39, 38, 40, 36]. An effective approach is to design incentive and task assignment mechanisms that induce MUs to submit high-quality data. For example, Jin et al. [37] designed an incentive mechanism based on reverse combinatorial auctions, aiming to encourage the participation of MUs and maximize social welfare. Xiao et al. [38] used a multi-armed bandit algorithm to select MUs with good performance to ensure data quality. Gu et al. [39] adopted a Stackelberg leader-follower game framework in MCS systems to design a task assignment mechanism that is able to choose MUs with high potential through multiagent reinforcement learning. However, these methods assume prior data quality knowledge, which does not always hold in practice. Therefore, some methods have added pre-exploration stages to MCS systems to estimate the capabilities of MUs [40]. For example, Zhang et al. [11] and Gao et al. [12] used the data sensed in the pre-exploration stages as baselines for evaluating the sensing errors of MUs, which could represent their abilities. Although these methods can more accurately evaluate the quality of the sensing data, the overhead of the resulting MCS platform is greatly increased.

Many studies have focused on evaluating the quality of the data collected within MCS systems [41, 35]. Zhang et al. [11] and Jin et al. [37] compared sensing data with the corresponding ground truth to calculate the induced sensing errors and to evaluate the quality of the data. On the basis of these results, Gao et al. [12] decomposed the sensing errors into deviations and variances to represent the sensing abilities and stabilities of MUs. However, these methods assume that the ground truth is known to the sensing platform, which is impractical in MCS systems. Therefore, many studies have been conducted on ground truth estimation, resulting in three types of methods: data aggregation methods [8, 9, 10, 12, 11], prediction-based methods [15, 13, 16, 17, 14, 18, 19, 20, 21], and TD methods [22, 23, 24, 25, 26, 27, 29, 30, 31].

Data aggregation methods. Zhang et al. [11] applied a weighted averaging method to estimate the ground truth of the sensing data. However, this method requires sufficient sensing data to obtain accurate estimates, which is difficult to achieve in scenarios with sparse data. To address data sparsity, Meng et al. [8] introduced a method for estimating the quality of the sensing data via a sparse data matrix. Specifically, they constructed a data matrix from submitted data and then filled in the missing data via Bayesian probabilistic matrix factorization. Building on this contribution, Yang et al. [9] deployed a small number of unmanned aerial vehicles to collect trustworthy data for constructing the sparse baseline data matrix. However, these methods focus only on the spatial correlations among data and overlook the temporal aspect, which limits their effectiveness.

Prediction-based methods. Min et al. [15] utilized the spatio-temporal correlations among traffic data and achieved improved prediction performance with their proposed dynamic space-time autoregressive integrated moving average (STARIMA) model. Furthermore, Yao et al. [16] applied a Transformer framework for traffic prediction and proposed a novel multi-view spatio-temporal graph network. This model combines attention and convolution mechanisms in its traffic pattern analysis strategy to comprehensively determine the spatio-temporal characteristics. On the basis of this approach, Gu et al. [17] proposed a Transformer model with global and local spatio-temporal modules to analyze the strong dynamics and spatio-temporal dependencies that are inherent in cellular traffic data. However, the predictions yielded by these methods may be inaccurate when bursty values are present in the sensing data, which limits the performance of prediction-based methods in MCS systems.

TD methods. TD methods are considered efficient for estimating the ground truth from unreliable data [22, 23, 24, 25] and are thus suitable for MCS systems. For example, Cheng et al. [26] presented a framework that combines TD with zero-knowledge proof in an MCS system to improve the accuracy of the ground truth produced for sensing data while preserving user privacy. Yin et al. [27] leveraged TD to evaluate the trustworthiness of web-based information sources and identify incorrect and fake data. However, these traditional TD methods typically produce unsatisfactory results in practical applications because of the possibility of sparse sensing data being present in MCS systems.

In summary, most existing methods can handle only specific scenarios. Inspired by these works, we have found that prediction-based methods and TD methods can effectively complement each other. Therefore, we propose leveraging the principles of prediction-based methods and reputation-based TD methods while fully utilizing the spatio-temporal correlations among data to implement our PRBTD method, which is able to enhance the effectiveness of data quality evaluation across various complex scenarios.

In an MCS system, the sensing platform cannot directly evaluate the quality of the submitted data due to the absence of the ground truth. However, in scenarios with historical sensing data, prediction methods can be employed to estimate the ground truth. Thus, we propose a CFSTTN to learn from historical data and predict the ground truth of the submitted sensing data.

As shown in Fig. 3, the CFSTTN comprises three components: an embedding module, a global spatio-temporal module, and a local spatio-temporal module. First, the embedding module adjusts the dimensions of the input data. Then, the global spatio-temporal module deploys a spatio-temporal Transformer framework based on a multi-head attention mechanism to extract multidimensional global spatial and temporal characteristics from the input data. Finally, the local spatio-temporal module uses densely connected convolutional neural networks to further extract local spatio-temporal information based on the global characteristics of the input data.

Our proposed CFSTTN improves the original model by integrating a correlation-focused part with a long-range residual connection with the input data. As presented in Fig. 3, our CFSTTN predicts a spatio-temporal relationship weight matrix, which is subsequently multiplied with the input data to derive the final output. The integration of the long-range residual connection enhances the spatio-temporal correlations between the output and input data, thus improving the prediction accuracy.

The CFSTTN uses historical data in the sensing task for prediction purposes. We represent the mean values of the data at time slot $t$ as a column vector $\bm{M}^{t}=\left[M_{1}^{t},M_{2}^{t},...,M_{N}^{t}\right]^{\mathsf{T}}$ where

is the mean value of the data sensed at time slot $t$ in region $n$. We construct a matrix $\left[\bm{M}^{t-p+1},...,\bm{M}^{t}\right]\in\mathbb{R}^{N\times p}$ as the input of the CFSTTN, which consists of the mean values of data derived from the preceding $p$ time slots up to $t$, where $0<p<T$ is a hyperparameter. The predicted ground truth, which includes the mean values of the data at time slot $t+1$ from every region, is denoted as $\widehat{\bm{G}}^{t+1}=\left[\widehat{G}_{1}^{t+1},\widehat{G}_{2}^{t+1},...,\widehat{G}_{N}^{t+1}\right]^{\mathsf{T}}$. Additionally, we use $f(\cdot)$ to represent a series of operations conducted within the three components of the CFSTTN. The spatio-temporal correlation weight matrix can be represented as $f(\bm{M}^{t-p+1},...,\bm{M}^{t})$. Finally, we obtain the prediction of the ground truth at time slot $t+1$ by performing matrix multiplication between the spatio-temporal correlation weight matrix and the input data:

In this paper, the mean absolute error (MAE) is utilized as the training metric. Specifically, we use the backpropagation method to minimize the MAE between the predicted ground truth $\widehat{\bm{G}}^{t+1}$ and the mean values of the actual submitted data $\bm{M}^{t+1}$, which can be expressed as follows:

where $\theta$ represents the parameters in the CFSTTN, which are learned and updated during the training process. However, the prediction results in an MCS task may be inaccurate because of the noise in the training data and the bursty values in the sensing data. Therefore, the output of the CFSTTN prediction module cannot be directly used to evaluate the quality of the data.

In the MCS system, implicit correlations are present among the sensing data with spatial and temporal correlations. We denote the implicit correlation among the sensing data points as $implication$, which reflects the extent to which one data point can predict or support another. For example, consider the scenario shown in Fig. 4 where MUs collect traffic flow data on a one-way road. In this case, the traffic flow on segment C is the sum of the traffic flows on segment A and segment B at any period $t$. Therefore, when the traffic data points submitted by MUs satisfy $v_{1,A}^{t}+v_{2,B}^{t}=v_{3,C}^{t}$, the implications among these data points are strong, as they mutually support each other’s accuracy. In contrast, the implications are weak when the data points follow $v_{1,A}^{t}+v_{2,B}^{t}\neq v_{3,C}^{t}$, which means that some of these MUs have submitted incorrect data that thus contradict the other data. Similarly, in most MCS scenarios, we can infer the existence of implications among the sensing data. However, owing to the complex spatial and temporal correlations among the data, quantitatively analyzing these implications is challenging in most cases. Therefore, we attempt to understand these implications from historical data. Specifically, we perform a series of computations in this module to quantify these implications from the output of the CFSTTN prediction module. Before providing the detailed calculations, we define the degree of implication as follows:

Specifically, $imp(d_{i,n}^{t},d_{j,n^{\prime}}^{t^{\prime}})\!=\!0$ indicates a lack of implication between data points $d_{i,n}^{t}$ and $d_{j,n^{\prime}}^{t^{\prime}}$, whereas $imp(d_{i,n}^{t},d_{j,n^{\prime}}^{t^{\prime}})>0$ indicates mutual support between the data, and $imp(d_{i,n}^{t},d_{j,n^{\prime}}^{t^{\prime}})<0$ means that the data contradict each other. Implications close to 1 indicate that the data points strongly support each other, whereas implications close to -1 suggest that the data points are likely to be entirely contradictory.

To calculate the degree of implication between sensing data points, we first reduce the dimensionality [42] of the sensing data $d_{i,n}^{t}=\left(i,t,n,v_{i,n}^{t}\right)$ to extract the features. Specifically, since sensing errors can reflect the characteristics of data [11, 12], we calculate the sensing errors as data features. Since the actual ground truth of the sensing data are unknown to us during a sensing task, we calculate the sensing errors of the data points based on the ground truth prediction results (i.e., the output of the CFSTTN). When the corresponding predicted ground truth $\widehat{G}_{n}^{t}\neq 0$, the error of data point $d_{i,n}^{t}$ is calculated as

In most MCS scenarios, the sensing errors in the data are caused primarily by two factors [12]. The first factor is related to external sensing circumstances, such as weather conditions, which are influenced by the time and location of the data collection. The second factor is related to the MUs, such as issues with the devices or improper operations when sensing data. Therefore, we decompose the sensing errors in the data into two components, which are defined below.

Hence, the total sensing error of a data point $d_{i,n}^{t}$ can be divided into the circumstance-related error and the user-related error as follows:

On this basis, we learn that the error vector $[\dot{\delta}_{n}^{t},\ddot{\delta}_{i}^{t}]$ corresponds to, and is uniquely related to, the data point $d_{i,n}^{t}$. Therefore, we use the error vector of a data point as its data feature, which can reflect most of the characteristics of that data point. Specifically, we can analyze the relationship between the features of the data points and the implications among them through the following conjecture, which allows us to infer the implications among data points based on their features.

This conjecture is applicable in most MCS scenarios. The reason is that data features reflect their patterns; thus, data with similar features usually follow a similar pattern and can infer each other. In our work, the features we extract from the sensing data include both circumstance-related errors and user-related errors. Therefore, if two data points have similar features, their circumstance-related errors and user-related errors are similar. According to Definitions 2 and 3, these two data points may be collected by users with similar characteristics (e.g., using similar devices or similar operations) in similar circumstances (e.g., under similar weather conditions). In such cases, the two data points can strongly support each other’s authenticity [31]. For example, when traffic flow data are sensed on different road segments with similar traffic characteristics (e.g., parallel roads with comparable traffic flows), if the data from two segments are very close, they can mutually support each other. Hence, the implication between two data points with similar features is strong. In contrast, data points with dissimilar features may contradict each other; therefore, the implications among these data are weak. Consequently, we can infer that in most MCS scenarios, Conjecture 1 is reasonable.

Based on Conjecture 1, we calculate the cosine similarity of the data features to determine the degree of implication between the data points as shown in Fig. 5(b). Even though the cosine similarity focuses only on direction, it is an appropriate choice for calculating the similarity of data features because our data features already contain magnitude information. The detailed process of calculating the data features and degrees of implication is as follows.

Calculate the circumstance-related error $\bm{\dot{\delta}_{n}^{t}}$. In our MCS system, the proportion of malicious MUs is low [27, 33, 21], and the MCS platform can identify and exclude these malicious MUs during sensing tasks. Therefore, we assume that the impact of malicious MUs on the calculations is limited.

According to (5), we calculate the average sensing error of all the data collected in region $n$ as follows:

where $\bm{D}_{n}^{\tau}$ represents the set of data sensed in region $n$ at time slot $\tau$. We use $c_{n}^{t}$ to represent the amount of sensing data collected in region $n$ up until time slot $t$. Specifically, $c_{n}^{t}$ is calculated as follows:

Based on (7), we can rewrite (6) as follows:

Note that when simplifying (6) to (8), we utilize the property that the user-related error of each normal MU $i$ satisfies

The reason is that the long-term user-related error expectation for each normal MU in an MCS system should be zero.

However, the relationship between $\dot{\delta}_{n}^{t}$ and $\delta_{i,n}^{t}$ shown in (8) holds only as $t\to\infty$, which is not feasible in practice because the duration of a sensing task is limited. Therefore, we rewrite (8) in the following slot-based update form to calculate the estimated circumstance-related error $\dot{\delta}_{n}^{(t)}$ in region $n$ at time slot $t$:

Note that $\lim_{t\to\infty}\dot{\delta}_{n}^{(t)}=\dot{\delta}_{n}^{t}$. Thus, a longer sensing task duration and more recent time slots can result in more accurate estimates. Therefore, we use $\dot{\delta}_{n}^{(t)}$ calculated from (10) instead of $\dot{\delta}_{n}^{t}$ in the following calculations.

Calculate the user-related error $\bm{\ddot{\delta}_{i}^{t}}$. Suppose we have a case where $\widehat{G}_{n}^{t}\neq 0$, then $\ddot{\delta}_{i}^{t}$ can be calculated according to (4) and (5) as follows:

However, the calculation in (11) neglects the situation in which $\widehat{G}_{n}^{t}=0$. Considering that the cosine similarity between vectors remains unchanged when the vectors are scaled, we scale the error vector $[\dot{\delta}_{n}^{(t)},\ddot{\delta}_{i}^{t}]$ of data point $d_{i,n}^{t}$ by $\widehat{G}_{n}^{t}$ to form a new data feature $F_{i,n}^{t}=[\widehat{G}_{n}^{t}\dot{\delta}_{n}^{(t)},v_{i,n}^{t}-(1+\dot{\delta}_{n}^{(t)})\widehat{G}_{n}^{t}]$. The scaled feature $F_{i,n}^{t}$ can be utilized to calculate the degree of implication, and the calculation process remains valid even when $\widehat{G}_{n}^{t}=0$.

Calculate the degree of implication between sensing data points $\bm{d_{i,n}^{t}}$ and $\bm{d_{j,n^{\prime}}^{t^{\prime}}}$. We calculate the cosine similarity between the data feature vectors to determine the degree of implication as follows:

where $F_{i,n}^{t}$ is the scaled feature vector of the sensing data point $d_{i,n}^{t}$ and $F_{j,n^{\prime}}^{t^{\prime}}=[\widehat{G}_{n^{\prime}}^{t^{\prime}}\dot{\delta}_{n^{\prime}}^{(t)},v_{j,n^{\prime}}^{t^{\prime}}-(1+\dot{\delta}_{n^{\prime}}^{(t)})\widehat{G}_{n^{\prime}}^{t^{\prime}}]$ corresponds to the data point $d_{j,n^{\prime}}^{t^{\prime}}$. Note that when we calculate $imp(d_{i,n}^{t},d_{j,n^{\prime}}^{t^{\prime}})$ according to (12), the circumstance-related error of region $n^{\prime}$ is $\dot{\delta}_{n^{\prime}}^{(t)}$ instead of $\dot{\delta}_{n^{\prime}}^{(t^{\prime})}$. Since the time slots satisfy $t^{\prime}\leq t$ according to Definition 1, indicating that time slot $t$ is more recent than the other time slots are, the estimated circumstance-related error of region $n^{\prime}$ should be updated to $\dot{\delta}_{n^{\prime}}^{(t)}$, which is more accurate.

Finally, the implication between any two data points can be extracted and utilized for the calculations in the subsequent module. Even in scenarios with bursty sensing data values, the implicit spatial and temporal correlations between data points remain stable [24] (e.g., when the traffic flow on a segment of a road undergoes a sudden change, the traffic flows on adjacent segments also exhibit certain changes). Therefore, although the prediction results based on historical sensing data are inaccurate in some cases, they retain spatio-temporal information, making it possible to extract accurate implications among data points. Thus, our method has greater advantages than prediction-based methods, which directly use predictions.

TD methods can estimate the ground truth based on submitted data and the weights of their providers. Traditional TD methods require a large amount of data for the same target (e.g., multiple MUs that sense the traffic flow data of the same segment of a road at the same time) to accurately estimate the corresponding ground truth. However, in an MCS system, the distributions of MU locations and periods may be sparse, and the amount of sensing data available for each target may vary, resulting in inaccurate estimates when traditional TD methods are used. Therefore, we design a reputation-based TD module that considers data implications, which allows for more accurate identification of low-quality sensing data and malicious MUs in scenarios characterized by data sparsity. Before providing a detailed description of this module, we first present the definitions that are used in the module.

Specifically, the closer the value of data point $d_{i,n}^{t}$ is to the ground truth, the higher the trustworthiness of this data point is, thereby making $q(d_{i,n}^{t})$ closer to 1.

Integrating a reputation mechanism into MCS can effectively reduce the misclassification of MUs. Even if normal MUs occasionally submit low-quality data under special circumstances (e.g., sudden device damage or abrupt weather changes), they can maintain a high reputation by consistently providing high-quality data over time [33]. In contrast, malicious MUs, which consistently submit low-quality or fake data, will maintain a persistently low reputation. Fig. 6 presents an example of how the reputation of a normal MU changes over time in relation to the quality levels of the submitted data. This example indicates that the reputations of MUs decrease when they submit low-quality sensing data but can remain high if they consistently submit high-quality data.

Like traditional TD methods [25, 26, 27], our reputation-based TD module consists of three steps, as follows.

Calculate the quality levels of the sensing data. We first consider the simple scenario shown in Fig. 5(a). This case includes two independent mobile users, MU $i$ and MU $j$, who collect data in region $n$ at time slot $t$. The values of their sensing data satisfy $v_{i,n}^{t}=v_{j,n}^{t}$. In this case, $v_{i,n}^{t}$ and $v_{j,n}^{t}$ are incorrect data values only if both MU $i$ and MU $j$ provide low-quality data simultaneously. Owing to the independence of the MUs, the probability of them providing simultaneous low-quality data should be $(1-r_{i}^{t})(1-r_{j}^{t})$. Therefore, the expected quality levels of data points $d_{i,n}^{t}$ and $d_{j,n}^{t}$ are given by $1-(1-r_{i}^{t})(1-r_{j}^{t})$, which represents the probability that data points $d_{i,n}^{t}$ and $d_{j,n}^{t}$ are correct. By generalizing the results to common scenarios, the expected quality level of data point $d_{i,n}^{t}$ can be calculated as follows:

where $\bm{I}(v_{i,n}^{t})$ represents the set of all MUs that submit data with values equal to $v_{i,n}^{t}$ in region $n$ at time slot $t$.

However, $1-r_{i}^{t}$ may approach 0 when MU $i$ has a high reputation, leading to the disappearance of the cumulative product term in (13). To address this problem, we define the reputation score of MU $i$ at time slot $t$ as

where $R_{i}^{t}\in\left[0,+\infty\right)$ as $r_{i}^{t}\in[0,1]$, and $\lim_{r_{i}^{t}\to 1}R_{i}^{t}=+\infty$. Similarly, the expected quality score of the sensing data point $d_{i,n}^{t}$ is defined as

where $\widehat{Q}(d_{i,n}^{t})\in\left[0,+\infty\right)$ and $\lim_{\hat{q}(d_{i,n}^{t})\to 1}\widehat{Q}(d_{i,n}^{t})=+\infty$. Subsequently, we can rewrite (13) with the reputation score and the expected quality score as follows:

Moreover, the implications between sensing data points can influence the quality levels of these data. Taking the scenario shown in Fig. 5(a) as an example, the values of the data points submitted by MUs $i$ and $k$ satisfy $v_{i,n}^{t}\neq v_{k,n}^{t}$. When $imp(d_{i,n}^{t},d_{k,n}^{t})>0$, data points $d_{i,n}^{t}$ and $d_{k,n}^{t}$ exhibit mutual support, so the trustworthiness of data point $d_{k,n}^{t}$ can increase the trustworthiness of $d_{i,n}^{t}$. Therefore, the quality level of data point $d_{i,n}^{t}$ increases the quality level of $d_{k,n}^{t}$. In contrast, the quality level of data point $d_{i,n}^{t}$ decreases the quality level of $d_{k,n}^{t}$ if $imp(d_{i,n}^{t},d_{k,n}^{t})<0$. Hence, the overall data quality score needs to consider both the expected quality and the influence of the implication as follows:

where $0<\rho<1$ is a hyperparameter that determines the proportion of the overall quality score influenced by the implication. $\bm{D}^{\prime}$ is a data cache that stores the sensing data derived from the previous $l$ time slots and is updated at the end of each time slot. When the hyperparameter $l$ is set to a larger value, more historical sensing data are considered when calculating the implications that influence the quality of the data. Thus, the data quality evaluation becomes more accurate, but the calculation time also increases. Finally, the quality level of the sensing data point $d_{i,n}^{t}$ can be calculated as follows:

Calculate the reputations of the MUs. The reputations of all the MUs need to be updated at each time slot $t\in\left\{1,2,...,T\right\}$. First, we initialize the reputation for every MU at time slot $t$ as

Note that when $t=1$, $r_{i}^{t}$ is initialized as $r_{i}^{0}$, which is the initial reputation of MU $i$ set by the sensing platform. Since each MU submits data at most once per time slot, we need only update the reputations of the MUs who submit data at the current time slot $t$. Specifically, the reputations of these MUs are updated based on the quality of the data they submit at time slot $t$. The reputation update function is designed according to [32]:

where $\alpha$ and $\beta$ are hyperparameters that determine the increasing and decreasing rates of the reputation update function, which satisfies $0<\alpha<\beta<1$, and $\gamma$ is the quality threshold set by the platform, which satisfies $0<\gamma<1$. Since the data quality level represents the trustworthiness of the data, sensing data with quality levels that are greater than or equal to $\gamma$ are identified as high-quality data, whereas data with quality levels lower than $\gamma$ are considered low-quality data. According to (20), the reputations of MUs who have submitted high-quality data increase, whereas those of MUs who have submitted low-quality data decrease.

The reputation update function shown in (20) satisfies the demands mentioned in [32] and [33] for monitoring the reputations of users in long-term multi-user scenarios and thus can be applied in MCS systems.

Update the data quality levels and the reputations of the MUs alternately until convergence is reached. When the reputations of the MUs are updated according to (20), the expected quality levels of the data submitted by these MUs may change accordingly. Consequently, the data quality levels should be updated again according to (16) to (18). Moreover, since the data quality level $q(d_{i,n}^{t})$ changes, the reputation of MU $i$ needs to be recalculated by (20). Therefore, as shown in Fig. 7, the data quality level $q(d_{i,n}^{t})$ and the MU reputation $r_{i}^{t}$ are alternately updated until convergence is achieved, resulting in the final quality level of data point $d_{i,n}^{t}$ and the final reputation of MU $i$ at time slot $t$.

Finally, we present Algorithm 1, which outlines the process of enhancing the quality of the sensing data with the proposed PRBTD method at time slot $t$. First, as shown in Fig. 2, the PRBTD method predicts the ground truth $\widehat{\bm{G}}^{t}$ via the CFSTTN prediction module. The data feature and implication calculation module subsequently uses the prediction results to calculate the sensing errors of the submitted data as features and uses these features to determine the degrees of implication between the data. The PRBTD method ultimately evaluates the quality levels of the data and the reputations of the MUs with the reputation-based TD module while considering the implications between the data. Moreover, sensing data with quality levels lower than $\gamma$ are eliminated, whereas the remaining data are stored in a high-quality data cache $\bm{\widehat{D}}^{t}$, thus achieving data cleansing and quality enhancement. Similarly, PRBTD can identify malicious MUs in MCS systems. After the task begins, the sensing platform can periodically check the reputations of the MUs and identify those whose reputations consistently remain below the predefined threshold as malicious MUs.

We first evaluate the convergence performance of the CFSTTN prediction module in our PRBTD framework. The training and validation loss curves produced by the CFSTTN on the TaxiBJ dataset are shown in Fig. 8. The CFSTTN converges after approximately 220 epochs, with an average training time of 82.56 seconds per epoch, leading to an average convergence duration of 5.04 hours. These results were obtained after repeating the training 6 times and indicate that the convergence time of the CFSTTN is acceptable.

We analyze the prediction performance of the CFSTTN via the root mean square error (RMSE) and the coefficient of determination (R2). The RMSE measures the difference between the prediction results and the ground truth. Therefore, a lower RMSE reflects better performance. R2 represents the explanatory ability of the prediction method. An R2 closer to 1 indicates a higher prediction accuracy. In our experiment, which used the TaxiBJ dataset, the CFSTTN achieves an RMSE of 16.88 and an R2 of 0.9583. Moreover, we compare our CFSTTN with the following 6 baselines:

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  ARIMA. The auto-regressive integrated moving average (ARIMA) is a popular time series prediction model that combines auto-regression, differencing, and moving average to predict future values.

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  SARIMA. The seasonal auto-regressive integrated moving average (SARIMA) extends ARIMA by including seasonal components, allowing it to model and predict data with seasonal patterns.

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  VAR. The vector auto-regressive (VAR) model is a multivariate time series model that captures linear interdependencies among multiple time series.

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  ST-ANN. The spatio-temporal artificial neural network (ST-ANN) extracts spatial and temporal features and uses an artificial neural network to model complex dependencies for prediction.

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  DeepST. This deep neural network-based model employs convolutional neural networks (CNNs) to model spatial dependencies and recurrent neural networks (RNNs) to capture temporal dependencies.

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  ST-ResNet. The spatio-temporal residual networks (ST-ResNet) utilize residual learning to capture spatial and temporal dependencies in data.

The model comparisons are presented in Table III, demonstrating that our CFSTTN outperforms the baselines.

Finally, we analyze the ability of the CFSTTN by visualizing its prediction results obtained on the TaxiBJ dataset and comparing them with the predictions of ST-ResNet, which is the best-performing method among the baselines. We take region (24,9) as an example. Fig. 9(a) shows that the prediction results of the CFSTTN for this region closely align with the ground truth and are better than those of ST-ResNet. Moreover, Figs. 9(b) and (c) show that the errors of the CFSTTN in the prediction results are smaller than those of ST-ResNet, thus highlighting that the CFSTTN has a good prediction ability.

We analyze the performance of the PRBTD method based on the following metrics.

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  F1-score. F1-scores of the methods when classifying normal and malicious MUs. The F1-score is a metric that combines precision and recall and can be used to evaluate the ability of a method to correctly classify normal and malicious MUs in the MCS system.

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  Reputation distance. Interclass reputation distance between normal MUs and malicious MUs. A larger reputation distance indicates better performance in terms of classifying normal MUs and malicious MUs in MCS systems.

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  Noise reduction ratio. Proportion of noise removed relative to the total noise after applying the enhancement method. Specifically, we calculate the noise reduction ratio as 1 minus the ratio of the average noise in the enhanced data to the average noise in the original data. A higher noise reduction ratio indicates better performance in identifying low-quality data and enhancing data quality.

Each set of experiments in our simulations is repeated 6 times, and the results reflect the mean results obtained across the repetitions.