Traffic time sequence prediction method based on data smoothing and polynomial activation function

Abstract

The invention belongs to the technical field of traffic time series prediction, and particularly relates to a traffic time series prediction method based on data smoothing and a polynomial activation function, and the method comprises the steps: carrying out the preprocessing of an input traffic data matrix, and obtaining a preprocessed traffic data matrix; constructing a polynomial activation function, combining the polynomial activation function with the graph convolutional network to extract features of nodes in the preprocessed traffic data matrix, and outputting a node feature matrix; constructing a traffic data time series prediction model processing node feature matrix; and in the training of the traffic data time series prediction model, introducing a residual error with a scaling factor, inputting the residual error with the scaling factor as a new feature into the traffic data time series prediction model of the next time step, and performing prediction output by adopting the trained traffic data time series prediction model. The method has remarkable advantages when traffic data with high complexity and uncertainty is processed.

Description

Technical Field

[0001] The present invention belongs to the technical field of traffic time series prediction, and particularly relates to a traffic time series prediction method based on data smoothing and polynomial activation function. Background Art

[0002] Traffic time series prediction refers to analyzing traffic data such as traffic flow, vehicle speed, and road occupancy rate, and using time series methods to predict future traffic states. Traffic prediction is a key link in intelligent transportation systems and is widely applied in fields such as traffic management, road planning, traffic control, and travel planning. Accurate traffic prediction can help optimize traffic flow, reduce traffic congestion, improve travel efficiency, reduce energy consumption, and enhance the reliability of public transportation systems.

[0003] Deep learning methods have now become a popular choice for solving high-dimensional traffic flow prediction. For example, cascaded convolutional neural networks and recurrent neural networks (RNNs) are widely used to handle spatio-temporal dependencies in road networks. CNNs can effectively capture local correlations in spatial grids, but in actual traffic data, data missing or noise problems make the application of CNNs in non-grid structured road networks more difficult. For this reason, graph convolutional networks (GCNs) are proposed to handle non-Euclidean spatial structures suitable for road networks, which can better capture spatio-temporal correlations between traffic nodes. However, most existing GCN methods rely on static adjacency matrices and cannot reflect the dynamic changes of spatial dependence relationships in road networks.

[0004] There are also some methods, such as SFTGNN, which combines dynamic time warping (DTW) technology to capture the similarity between traffic nodes through the shape matching of data sequences. Nevertheless, the spatial dependence between nodes is not only related to the shape similarity of data sequences but also closely related to their semantic correlations. Just like in natural language processing, sentences with similar semantics may have different language structures. Therefore, new methods need to be developed in the future that can not only solve data noise problems but also more effectively incorporate semantic knowledge into the model to improve the accuracy and robustness of traffic flow prediction. Summary of the Invention

[0005] In order to overcome the problems in the prior art, the present invention proposes a traffic time series prediction method based on data smoothing and polynomial activation function.

[0006] The technical solution of the present invention to solve the above technical problems is as follows: The present invention provides a traffic time series prediction method based on data smoothing and polynomial activation function, including the following steps: Preprocess the input traffic data matrix to obtain a preprocessed traffic data matrix; Construct a polynomial activation function, combine the polynomial activation function with a graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix, and output a node feature matrix; Build a traffic data time series prediction model to process the node feature matrix and capture the spatial correlation between different nodes in the traffic road network; In the training of the traffic data time series prediction model, introduce a residual with a scaling factor, and use the residual with the scaling factor as new features to input into the traffic data time series prediction model at the next time step, so as to obtain a trained traffic data time series prediction model; Use the trained traffic data time series prediction model for prediction output.

[0007] Furthermore, the preprocessing of the input traffic data matrix includes smoothing processing by using a mean filter method.

[0008] Furthermore, the construction of the polynomial activation function is specifically as follows: the polynomial activation function is set to six-segment curves, and the intervals are as follows: ; Among them, in the intervals and are two quadratic polynomial functions, and in the intervals , , and are four cubic polynomial functions.

[0009] Furthermore, the polynomial activation function is specifically as follows: ; In the above formula, represents a piecewise function; represents the unknown of the current piecewise function.

[0010] Furthermore, the graph convolutional network is used to extract the spatial features in the traffic network, specifically including: modeling the traffic network as a graph, where nodes represent intersection detection points on the road, and edges represent the connection relationships between roads; the graph convolutional network updates the feature representation of each node by aggregating the information of neighboring nodes.

[0011] Furthermore, combining the polynomial activation function with the graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix and output a node feature matrix specifically includes: Calculate the explicit feature map and the implicit feature map through graph convolution: ; ; In the above formula, represents the explicit feature map; represents the implicit feature map; is the adjacency matrix; is the adjacency matrix with self-loops added, represents the identity matrix; represents the degree matrix; a and b both represent learnable parameters; represents the activation function; Use the polynomial activation function for non-linear transformation to obtain the node feature matrix: ; In the above formula, represents the node feature matrix; represents the result of calculating the explicit feature map through the activation function; represents the result of calculating the implicit feature map through the activation function.

[0012] Furthermore, the traffic data time series prediction model is a gated recurrent unit.

[0013] Furthermore, the residual with a scaling factor is: ; In the above formula, represents the residual; represents the original sequence; represents the scaling factor.

[0014] Compared with the prior art, the present invention has the following technical effects: (1) The present invention preprocesses the input data and adopts a smoothing operation. Through this processing, the noise and outliers in the traffic data can be effectively removed, reducing their interference with the prediction results. This improvement makes the data more stable and reduces the negative impact of data fluctuations on model training. (2) The present invention innovatively first proposes and applies a self-created polynomial activation function. This brand-new activation function can better capture the non-linear relationships in traffic data and accurately fit complex patterns in the graph structure, thereby improving the prediction accuracy. By introducing this innovative activation function, the present invention can more precisely depict the dynamic changes of traffic flow, especially when dealing with traffic data with high complexity and uncertainty, showing significant advantages. Compared with traditional methods, in the process of modeling graph-structured data, the present invention not only improves the model's ability to express complex patterns, but also enhances its adaptability to abnormal fluctuations and long-term trends, further improving the accuracy and reliability of the prediction results. This makes the method have stronger practicality and promotion value in practical applications.

[0015] (3) To better enhance the model's ability to capture long-term correlations, the present invention designs an innovative scaled residual unit, aiming to effectively solve the problem of insufficient modeling of long-term dependencies in traditional neural networks when dealing with time series data. Time series data such as traffic flow often exhibits long-term dependencies, which may be affected by various factors, such as seasonal variations, special events, traffic policies, etc. Traditional models often struggle to accurately capture these long-term trends in a complex and dynamically changing environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0017] Figure 1 is a schematic flow chart of the present invention; Figure 2 is an interpolation curve graph of the present invention; Figure 3 is the original function image of the activation function of the present invention; Figure 4 is the original function, first derivative, and second derivative images of the activation function of the present invention; Figure 5 is the comparison graph of the MAE index of the present invention; Figure 6 is the comparison graph of the MAPE index of the present invention; Figure 7 is the comparison graph of the RMSE index of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] To further elaborate on the technical means and effects adopted by the present invention to achieve the intended invention purpose, the following, in combination with the accompanying drawings and preferred embodiments, details the specific implementation manners, structures, features, and effects of the technical solutions proposed according to the present invention. The specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the technical field to which the present invention belongs.

[0019] In an embodiment of the present invention, referring to Figures 1-7 , a traffic time series prediction method based on data smoothing and polynomial activation function is provided, including the following steps: Preprocess the input traffic data matrix to obtain the preprocessed traffic data matrix; Construct a polynomial activation function, combine the polynomial activation function with a graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix, and output a node feature matrix; Build a traffic data time series prediction model to process the node feature matrix and capture the spatial correlations between different nodes in the traffic road network; In the training of the traffic data time series prediction model, introduce a residual with a scaling factor, and use the residual with the scaling factor as new features to input into the traffic data time series prediction model at the next time step, so as to obtain a trained traffic data time series prediction model; Use the trained traffic data time series prediction model for prediction output.

[0020] The following expands each of the above steps in detail: Step 100: Preprocess the input traffic data matrix to obtain a preprocessed traffic data matrix.

[0021] Preprocess the input traffic data matrix, that is, smooth the input traffic data matrix by using a mean filter method to remove the noise and outliers in the traffic data and reduce their interference on the prediction results. This improvement makes the data more stable and reduces the negative impact of data fluctuations on model training. Specifically, the smoothing of the input traffic data matrix by using the mean filter method includes sliding window smoothing processing and boundary smoothing processing.

[0022] Sliding window smoothing processing: Determine through experiments that the size of the sliding window is 3, that is, the window; the initial position is set at the second row and second column in the upper left corner of the input traffic data matrix; Cover the sliding window of

[0023] Boundary smoothing: Since the sliding window starts from the second row and second column, the boundary parts are not processed, that is, the four boundaries of top, bottom, left, and right are not processed. Calculate the sum of all elements on each of these four boundaries; perform a division operation on the sum of elements of each boundary to obtain the average value of that boundary; assign the calculated average value to the corresponding elements on the boundary of the input traffic data matrix; in addition, perform a simple average operation on the elements at the four corners of the input traffic data matrix, which usually involves taking the average of adjacent boundary elements. Boundary smoothing is mainly applicable to situations where boundary information needs to be retained to avoid mutations or artifacts at the boundaries. Through such processing, the node embedding matrix B after data smoothing is obtained, that is, the preprocessed traffic data matrix.

[0024] While retaining the overall structure of the matrix, sliding window smoothing and boundary smoothing reduce the volatility of the data, making the matrix elements smoother. Boundary smoothing ensures that there are no mutations or artifacts at the boundaries, thus improving the overall quality of the data.

[0025] The input traffic data matrix is smoothed using the mean filtering method to calculate the adjacency matrix. The calculation formula of the adjacency matrix is as follows: (1); In the above formula, ; First, start calculating from the second row of matrix A, and set the initial position at the second row and second column in the upper left corner of the input traffic data matrix; cover the 3×3 sliding window to each position of the input traffic data matrix, calculate the average value of the elements in the window, ensure that the sum of the weights α, β, γ in the window is 1, and the values decrease sequentially, and thus calculate the elements at the corresponding positions in matrix B. This formula calculates the corresponding elements of the edge matrix through data averaging. Finally , set the elements at the four corners of the matrix to the same value.

[0026] Among them, represents the element in the i th row and j th column of matrix B; represents the element in the i th row and jth column of matrix A; represents the element in the 0th row and 0th column of matrix B, and matrix B starts from the 0th row; represents the element in the 0th row and (d - 1)th column of matrix B; N is the number of nodes, that is, the nodes represent the detection points on the road; d is the dimension; α, β, γ are three parameters. Matrix is the node embedding matrix, with an initial value of 0, which will be continuously updated according to the operation of the program, 。

[0027] Use a function to obtain the adjacency matrix as the input for the next module: (2); (3); (4); In the formula, s represents the temperature variable; g represents the random noise; u represents a random number in the uniform distribution; hard represents the hardening operation; represents the embedding matrix.

[0028] Step 200: Construct a polynomial activation function based on cubic Hermite interpolation.

[0029] Construct a polynomial activation function based on cubic Hermite interpolation , and the polynomial activation function infinitely approximates LeakyRelu (Leaky Rectified Linear Unit) within a certain range, because Leaky_Relu has obvious advantages over activation functions such as Sigmoid, Tanh (hyperbolic tangent function), and Relu (Rectified Linear Unit) in improving the model accuracy.

[0030] To make the polynomial activation function better approximate LeakyRelu, set to six-segment curves, and the intervals are as follows: , where within the intervals and are two-segment quadratic polynomial functions, and within the intervals , , and are four-segment cubic polynomial functions. The six-segment function is denoted as .

[0031] The construction of the polynomial activation function within the intervals , , and . To make the construction process simple and intuitive, use the cubic Hermite function to describe the four-segment cubic polynomial functions within the intervals and , which are defined as follows: (5); Among them, (6); In the above formula, represents the unknown of the current piecewise function; represents the unknown of the piecewise function of the represents the i unknown of the piecewise function of the represents the difference between any two adjacent piecewise functions.

[0032] Designing a cubic polynomial function using the cubic Hermite function representation form will greatly simplify the design process. As Figure 2 can be seen, when is fixed, the shape of the cubic Hermite function is completely determined by , and These three quantities. Adjusting the magnitudes and directions of these three quantities can easily design the shape of the function.

[0033] Based on the principle of approximating Leaky_Relu, at the points and the corresponding values should be equal to Leaky_Relu, that is , , , and . Based on the optimization of through interactive design, take . .

[0034] In formula (5), , and can be determined by the continuity equation of the cubic spline function. The construction of

[0035] Secondly, through , at satisfies continuity, and construct the quadratic polynomial from formula (8).

[0036] (7); In formula (7), , and are at the endpoints The second derivative value, the first derivative value, and the original function value at are adjustable parameters. Simplify and organize Equation (8) into In the form of, then this quadratic function is the required quadratic polynomial function. Simplify (7) to get: (8); Substitute The endpoint is at The second derivative value, the first derivative value, and the original function value into it to obtain the first segment of the polynomial function, that is, (9); Similarly, , At Satisfy Continuous, substitute The endpoint is at The second derivative value, the first derivative value, and the original function value into Equation (8) and simplify to obtain the sixth segment of the polynomial function, that is: (10); In summary, the constructed activation function is as follows: (11).

[0037] Use the activation function in the ordinary graph convolution as , this activation function has stronger expressive power and better performance, and can better process complex graph structure data. Compared with the Leaky_ReLU activation function, The activation function has a wider activation range and a smoother gradient, can better fit complex graph structures, and improve the performance and generalization ability of the model.

[0038] Step 300: Combine the polynomial activation function with the graph convolutional network to extract the features of the nodes in the preprocessed traffic data matrix to obtain the node feature matrix.

[0039] The graph convolutional network is used to extract the spatial features in the traffic network, specifically including: modeling the traffic network as a graph, where the nodes of the graph represent the intersection detection points on the road, the edges of the graph represent the connection relationships between the roads, and the graph convolutional network updates the feature representation of each node by aggregating the information of neighboring nodes: (12); (13); In the above formula, Represents the explicit feature map; Represents the implicit feature map; Is the adjacency matrix; is the adjacency matrix with self-loops added, represents the identity matrix; represents the degree matrix; both \(a\) and \(b\) represent learnable parameters; represents the activation function.

[0040] Apply the polynomial activation function after the graph convolutional layer to enhance the model's ability to capture complex traffic patterns. Use the polynomial activation function for non-linear transformation to obtain the node feature matrix: (14); In the above formula, represents the node feature matrix; represents the calculation of the explicit feature map through the activation function; represents the calculation of the implicit feature map through the activation function.

[0041] Step 400: Construct a traffic data time series prediction model to process the node feature matrix and capture the spatial correlation between different nodes in the traffic road network; The traffic data time series prediction model uses a gated recurrent unit. The gated recurrent unit GRU is a variant of the LSTM network and has a time-aware topological layer. Compared with LSTM, the GRU structure is simpler, has fewer training parameters, and is easier to overcome the problems of gradient vanishing and explosion. The feedforward propagation recursion of the GRU with a time-aware topological layer is: (15); In the above formula, represents the hidden state; represents the update gate in GRU; represents the reset gate in GRU; represents the candidate hidden state in GRU; represents the final hidden state; represents the hidden state at the previous moment; represents the current input data; represents the input data at the previous moment.

[0042] Step 500: In the training of the traffic data time series prediction model, introduce the residual with a scaling factor and use the residual with a scaling factor as the new feature to input into the traffic data time series prediction model at the next time step, so as to obtain the trained traffic data time series prediction model.

[0043] The influence of data outliers and noise is balanced by scaling the residuals. In traffic time series prediction tasks, due to the existence of sequence data with long time ranges and different scales, capturing long-term correlations becomes particularly important. Therefore, a residual block unit is further designed to enhance the model's ability to capture long-term correlations. The core idea of the usual residual connection is to use the residual (i.e., the difference between the observed value and the model prediction value) as new features and input them into the prediction model at the next time step. However, in traffic time series prediction, due to the existence of sequence data with long time ranges and different scales, problems such as gradient disappearance or gradient explosion may be encountered.

[0044] A constant scaling factor is introduced to enhance the gradient propagation and stability of the model. The constant scaling factor is determined through experiments to find the optimal scaling value. By scaling the residuals, the influence of outliers and noise can be balanced, thereby improving the robustness of the model. This constant scaling mechanism provides a way to adjust the degree of influence of the residuals, enabling the model to better adapt to different data characteristics and noise levels. Additionally, by introducing the constant scaling factor, the residual network can better handle the problem of long-time series correlations. The scaling factor can adjust the degree of influence of the residuals, allowing the model to better adapt to sequence data of different time scales. This design enables the model to more effectively utilize historical information during prediction, thereby better capturing long-term correlations and improving the accuracy and stability of the prediction.

[0045] (16); In formula (16), represents the residual; represents the original sequence; represents the scaling factor, preferably .

[0046] The scaled residuals are added as new features to the input feature set; in the prediction at the next time step, the residual features at the current time step are input into the traffic data time series prediction model together with other features; the traffic data time series prediction model is retrained using the new data set containing the residual features.

[0047] MAE (Mean Absolute Error) is selected as the loss function to calculate the mean absolute error between the predicted value of the output and the true value. The formula corresponding to MAE is as follows: (17); In the above formula, represents the predicted value, represents the true value, represents the number of data. When the MAE value does not decrease for 15 consecutive rounds during iteration, the iteration ends.

[0048] Step 600: Perform predictive output using the trained traffic data time series prediction model.

[0049] The present invention generates a node feature map using a data smoothing matrix, and also fully considers neighbor information, the position of nodes in the network, and connection relationships, which makes the feature map more global; the polynomial activation function solves the problem of feature map fusion. Due to the particularity of graph data, traditional activation functions may not be able to fully exploit the features of graph data, and the polynomial activation function perfectly solves this problem. Scaling residuals helps balance data outliers and noise, thereby achieving accurate prediction of traffic time series.

[0050] Refer to Figures 5-7 To prove the effectiveness of the present invention, a comparison is made with relatively advanced prediction models. Among them, Model 1 is STFGNN (Spatial-Temporal Fusion Graph Neural Networks) for solving data prediction problems with time and space dependencies, Model 2 is STGODE (Spatial-Temporal Graph ODE Networks) which applies continuous graph neural networks to traffic prediction in multivariate time series prediction, Model 3 is Z-GCNETs (Time Zigzags at Graph Convolutional Networks) which introduces the concept of zigzag into the prediction model of time-aware graph convolutional networks, Model 4 is AGCRNs (Adaptive Graph Convolutional Recurrent Networks) which uses a model with node-learnable embeddings in graph convolution, and Model 5 is the prediction model proposed by the present invention, which mainly uses data smoothing and polynomial activation functions to solve problems in traffic prediction. It can be seen that the present invention performs well in three prediction metrics, including MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error), and RMSE (Root Mean Square Error). The smaller the metric, the higher the prediction accuracy.

[0051] The above embodiments are only used to illustrate the technical solutions of the present application, rather than limiting them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A traffic time series prediction method based on data smoothing and polynomial activation function, characterized in that, It includes the following steps: Preprocess the input traffic data matrix to obtain the preprocessed traffic data matrix; Construct a polynomial activation function, combine the polynomial activation function with a graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix, and output a node feature matrix; Build a traffic data time series prediction model to process the node feature matrix and capture the spatial correlation between different nodes in the traffic road network; In the training of the traffic data time series prediction model, introduce a residual with a scaling factor, and use the residual with the scaling factor as new features to input into the traffic data time series prediction model at the next time step, so as to obtain a trained traffic data time series prediction model; Use the trained traffic data time series prediction model for prediction output.

2. The traffic time series prediction method based on data smoothing and polynomial activation function according to claim 1, wherein The preprocessing of the input traffic data matrix includes smoothing processing by using a mean filter method.

3. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 1, characterized in that, The constructed polynomial activation function is specifically: The polynomial activation function is set to six-segment curves, and the intervals are as follows: ； wherein in the interval and are two quadratic polynomial functions, and in the intervals , , and are four cubic polynomial functions.

4. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 3, characterized in that, The polynomial activation function Specifically: ； In the above formula, represents a piecewise function; represents the unknown of the current piecewise function.

5. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 4, characterized in that The graph convolutional network is used to extract spatial features in the traffic network, specifically including: modeling the traffic network as a graph, where nodes represent intersection detection points on roads and edges represent connection relationships between roads; the graph convolutional network updates the feature representation of each node by aggregating the information of neighbor nodes.

6. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 5, characterized in that, Combining the polynomial activation function with the graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix and output a node feature matrix specifically includes: Calculating the display feature map and the implicit feature map through the graph convolutional network: ； ； In the above equation, represents the explicit feature map; represents the implicit feature map; is the adjacency matrix; is the adjacency matrix with self-loops added, represents the identity matrix; represents the degree matrix, and b both represent learnable parameters; represents the activation function; Performing a non-linear transformation using the polynomial activation function to obtain the node feature matrix: ； In the above formula, represents the node feature matrix; represents the calculation of the display feature map through the activation function; represents the calculation of the implicit feature map through the activation function.

7. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 1, characterized in that, The traffic data time series prediction model is a gated recurrent unit.

8. A traffic time series prediction method based on data smoothing and polynomial activation function according to claim 1, characterized in that, The residual with the scaling factor is: ； In the above formula, represents the residual; represents the original sequence; represents the scaling factor.

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