Traffic Time Series Forecasting Method Based on Data Smoothing and Multinomial Activation Function

Abstract

This invention belongs to the field of traffic time series prediction technology, specifically relating to a traffic time series prediction method based on data smoothing and a multinomial activation function. The method includes: preprocessing an input traffic data matrix to obtain a preprocessed traffic data matrix; constructing a multinomial activation function, combining the multinomial activation function with a 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 to process the node feature matrix; introducing residuals with scaling factors during the training of the traffic data time series prediction model, using these residuals as new features input into the traffic data time series prediction model at the next time step, and using the trained traffic data time series prediction model for prediction output. This invention demonstrates significant advantages when processing traffic data with high complexity and uncertainty.

Description

Technical Field

[0001] This invention belongs to the field of traffic time series prediction technology, specifically relating to a traffic time series prediction method based on data smoothing and multinomial activation function. Background Technology

[0002] Traffic time series forecasting refers to the analysis of traffic data such as traffic flow, vehicle speed, and road occupancy to predict future traffic conditions using time series methods. Traffic forecasting is a crucial component of intelligent transportation systems and is widely used in traffic management, road planning, traffic control, and travel planning. Accurate traffic forecasting can help optimize traffic flow, reduce congestion, improve travel efficiency, reduce energy consumption, and enhance the reliability of public transportation systems.

[0003] Deep learning methods have become a popular choice for solving high-dimensional traffic flow prediction problems. For example, cascaded convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are widely used to handle spatiotemporal dependencies in road networks. CNNs can effectively capture local correlations in spatial grids, but in real-world traffic data, missing data or noise issues make their application in non-grid road networks more difficult. To address this, graph convolutional networks (GCNs) have been proposed to handle non-Euclidean spatial structures suitable for road networks, better capturing the spatiotemporal correlations between traffic nodes. However, most existing GCN methods rely on static adjacency matrices, failing to reflect the dynamic changes in spatial dependencies within the road network.

[0004] Other methods, such as SFTGNN, combine Dynamic Time Warp (DTW) technology to capture the similarity between traffic nodes through shape matching of data sequences. However, the spatial dependencies between nodes are not only related to the shape similarity of the data sequences but also closely related to their semantic relevance. Just as in natural language processing, semantically similar sentences may have different linguistic structures. Therefore, future research needs to develop new methods that can not only address data noise issues but also more effectively integrate semantic knowledge into the model, improving the accuracy and robustness of traffic flow prediction. Summary of the Invention

[0005] To overcome the problems in the prior art, this invention proposes a traffic time series prediction method based on data smoothing and multinomial activation functions.

[0006] The technical solution of the present invention to solve the above-mentioned technical problems is as follows:

[0007] This invention provides a traffic time series prediction method based on data smoothing and multinomial activation functions, comprising the following steps:

[0008] The input traffic data matrix is ​​preprocessed to obtain the preprocessed traffic data matrix;

[0009] 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 the node feature matrix;

[0010] A time series prediction model for traffic data is constructed to process the node feature matrix and capture the spatial correlation between different nodes in the traffic network.

[0011] In the training of the traffic data time series prediction model, residuals with scaling factors are introduced and used as new features to input the traffic data time series prediction model at the next time step, thereby obtaining the trained traffic data time series prediction model.

[0012] The predicted output is generated using a pre-trained traffic data time series prediction model.

[0013] Furthermore, the preprocessing of the input traffic data matrix includes smoothing using a mean filtering method.

[0014] Furthermore, the construction of the polynomial activation function specifically involves: using the polynomial activation function... Set as a six-segment curve, with the following intervals:

[0015] ;

[0016] In the interval and The above are two quadratic polynomial functions, in the interval... , , and It is a four-segment cubic polynomial function.

[0017] Furthermore, the polynomial activation function Specifically:

[0018] ;

[0019] In the above formula, Represents a piecewise function; This represents the unknowns of the current piecewise function.

[0020] Furthermore, the graph convolutional network is used to extract spatial features from the traffic network, specifically including: modeling the traffic network as a graph, where nodes represent intersection detection points in the road and edges represent the connection relationships between roads; the graph convolutional network updates the feature representation of each node by aggregating information from neighboring nodes.

[0021] Furthermore, the polynomial activation function and graph convolutional network are combined to extract the features of nodes in the preprocessed traffic data matrix, and the node feature matrix is ​​output, specifically including:

[0022] The graph convolution process calculates both the displayed feature map and the implicit feature map:

[0023] ;

[0024] ;

[0025] In the above formula, Represents an explicit feature map; Represents implicit feature maps; It is an adjacency matrix; It is an adjacency matrix with self-loops added. Represents the identity matrix; Degree matrix; b and b both represent learnable parameters; Indicates the activation function;

[0026] A nonlinear transformation using a polynomial activation function is used to obtain the node feature matrix:

[0027] ;

[0028] In the above formula, Represents the node feature matrix; This indicates that the feature map will be processed by the activation function. This indicates that the implicit feature map has been processed by the activation function.

[0029] Furthermore, the traffic data time series prediction model is a gated cyclic unit.

[0030] Furthermore, the residual with the scaling factor is:

[0031] ;

[0032] In the above formula, Represents the residual; Represents the original sequence; This represents the scaling factor.

[0033] Compared with the prior art, the present invention has the following technical effects:

[0034] (1) The present invention preprocesses the input data by employing a smoothing operation. This processing effectively removes noise and outliers from the traffic data, 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.

[0035] (2) This invention innovatively proposes and applies a self-developed polynomial activation function for the first time. This novel activation function can better capture the nonlinear relationships in traffic data and accurately fit complex patterns in graph structures, thereby improving the accuracy of prediction. By introducing this innovative activation function, this invention can more meticulously characterize the dynamic changes in traffic flow, especially when dealing with traffic data with high complexity and uncertainty, demonstrating significant advantages. Compared with traditional methods, this invention not only improves the model's ability to express complex patterns in the modeling process of graph structure data, but also enhances its adaptability to abnormal fluctuations and long-term trends, further improving the accuracy and reliability of prediction results. This makes the method more practical and valuable for promotion in real-world applications.

[0036] (3) In order to better enhance the model's ability to capture long-term correlations, this invention designs an innovative scaling residual unit, which aims to effectively solve the problem of insufficient modeling of long-term dependencies in traditional neural networks when processing time series data. Time series data such as traffic flow often exhibit long-term dependencies, which may be affected by a variety of factors, such as seasonal changes, special events, and traffic policies. Traditional models often struggle to accurately capture these long-term trends in complex and dynamic environments. Attached Figure Description

[0037] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a schematic diagram of the process of the present invention;

[0039] Figure 2 This is an interpolation curve diagram of the present invention;

[0040] Figure 3 This is the original function image of the activation function of this invention;

[0041] Figure 4 The graphs of the activation function's original function, first derivative, and second derivative are shown in this invention.

[0042] Figure 5 This is a comparison chart of the MAE indicators of this invention;

[0043] Figure 6 This is a comparison chart of the MAPE indicators of the present invention;

[0044] Figure 7This is a comparison chart of the RMSE indicators of this invention. Detailed Implementation

[0045] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the specific implementation methods, structures, features, and effects of the technical solutions proposed according to the present invention are described in detail below with reference to the accompanying drawings and preferred embodiments. Specific features, structures, or characteristics in one or more embodiments may be combined in any suitable form. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0046] In one embodiment of the present invention, reference is made to... Figures 1-7 This paper presents a traffic time series forecasting method based on data smoothing and multinomial activation functions, including the following steps:

[0047] The input traffic data matrix is ​​preprocessed to obtain the preprocessed traffic data matrix;

[0048] 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 the node feature matrix;

[0049] A time series prediction model for traffic data is constructed to process the node feature matrix and capture the spatial correlation between different nodes in the traffic network.

[0050] In the training of the traffic data time series prediction model, residuals with scaling factors are introduced and used as new features to input the traffic data time series prediction model at the next time step, thereby obtaining the trained traffic data time series prediction model.

[0051] The predicted output is generated using a pre-trained traffic data time series prediction model.

[0052] The following is a detailed explanation of each of the above steps:

[0053] Step 100: Preprocess the input traffic data matrix to obtain the preprocessed traffic data matrix.

[0054] The input traffic data matrix is ​​preprocessed by applying mean filtering to smooth it, removing noise and outliers and 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.

[0055] Specifically, the input traffic data matrix is ​​smoothed using a mean filtering method, including sliding window smoothing and boundary smoothing.

[0056] Sliding window smoothing: Experiments determined that the sliding window size should be 3, i.e. The window; its initial position is set at the second row and second column of the top left corner of the input traffic data matrix; A sliding window covers every position in the input traffic data matrix. The average value of the elements within the window is calculated, ensuring that the sum of the weights α, β, and γ within the window is 1, and that their values ​​decrease sequentially. This design aims to ensure that the elements of the preprocessed traffic data matrix B are always in the middle of the surrounding elements of the input traffic data matrix, avoiding excessively large or small extreme values. The calculated average value is assigned to the elements at the corresponding positions in the matrix to obtain a smoothed new matrix. The sliding window is moved sequentially until it covers the entire input traffic data matrix.

[0057] Boundary smoothing: Since the sliding window starts from the second row and second column, the boundary portion is not processed, i.e., the top, bottom, left, and right boundaries are not processed. The sum of all elements on each of these four boundaries is calculated. A division operation is performed on the sum of elements on each boundary to obtain the average value. This average value is assigned to the corresponding elements on the boundaries of the input traffic data matrix. Furthermore, a simple averaging operation is performed on the elements at the four corners of the input traffic data matrix, which typically involves averaging the elements of adjacent boundaries. Boundary smoothing is mainly suitable for situations where boundary information needs to be preserved to avoid abrupt changes or artifacts at the boundaries. Through this processing, the smoothed node embedding matrix B is obtained, i.e., the preprocessed traffic data matrix.

[0058] Sliding window smoothing and boundary smoothing reduce data volatility while preserving the overall matrix structure, making matrix elements smoother. Boundary smoothing ensures that there are no abrupt changes or artifacts at the boundaries, thereby improving the overall quality of the data.

[0059] The adjacency matrix is ​​calculated by smoothing the input traffic data matrix using a mean filter method. The formula for calculating the adjacency matrix is ​​as follows:

[0060] (1);

[0061] In the above formula,

[0062] ;

[0063] First, the calculation starts from the second row of matrix A, with the initial position set at the second row and second column of the upper left corner of the input traffic data matrix. A 3×3 sliding window is then applied to each position of the input traffic data matrix, and the average value of the elements within the window is calculated. This ensures that the sum of the weights α, β, and γ within the window is 1, and that their values ​​decrease sequentially. In this way, the element at the corresponding position in matrix B is calculated. This formula calculates the corresponding elements of the marginal matrix by averaging the data. Finally... Set the elements at the four corners of the matrix to the same value.

[0064] in, Represents the first in matrix B i Line number j Column elements; Represents the nth element in matrix A i The element in row j; This represents the element in the 0th row and 0th column of matrix B, which starts from the 0th row. This represents the element in the 0th row and (d-1)th column of matrix B; N is the number of nodes, where each node represents a detection point in the road. d α is the dimension; α, β, and γ are three parameters. Matrix It is a node embedding matrix, initially set to 0, and continuously updated as the program runs. .

[0065] use Functions to obtain the adjacency matrix As input for the next module:

[0066] (2);

[0067] (3);

[0068] (4);

[0069] In the formula, s represents the temperature variable; g represents random noise; u Represents a random number in a uniform distribution; hard Indicates a hardening operation; This represents the embedding matrix.

[0070] Step 200: Construct a polynomial activation function based on cubic Hermite interpolation.

[0071] A polynomial activation function is constructed based on cubic Hermite interpolation. Polynomial activation function It infinitely approximates LeakyRelu (Leaky Corrected Linear Unit) within a certain range because LeakyRelu has a significant advantage over activation functions such as Sigmoid, Tanh (hyperbolic tangent function), and Relu (Rectified Linear Unit) in improving model accuracy.

[0072] To enable the polynomial activation function To better approximate LeakyRelu, Set as a six-segment curve, with the following intervals: ,

[0073] In the interval and The above are two quadratic polynomial functions, in the interval... , , and It is a four-segment cubic polynomial function; a six-segment function is denoted as... .

[0074] Polynomial activation function In the interval , , and The construction on top. To make the construction... The process is simple and intuitive, using the cubic Hermite function to describe the interval. and A four-segment cubic polynomial function on the given surface. The definition is as follows:

[0075] (5);

[0076] in,

[0077] (6);

[0078] In the above formula, Represents the unknowns of the current piecewise function; Indicates the first Unknowns of segmental functions; Indicates the first i Unknowns of segmental functions; This represents the difference between any two adjacent piecewise functions.

[0079] Designing cubic polynomial functions using cubic Hermite function representation greatly simplifies the design process. Figure 2 It can be seen that when Once fixed, the shape of the cubic Hermite function is entirely determined by... , and The shape of the function is determined by three quantities. By adjusting the magnitude and direction of these three quantities, it is easy to design the shape of the function.

[0080] Based on the principle of approximating Leaky_Relu At point and The corresponding value should be equal to Leaky_Relu, that is... , , , and , Based on interaction design Optimization, take .

[0081] In equation (5) , and It can be determined by the continuity equation of the cubic spline function. The construction is complete.

[0082] Secondly, through , exist Satisfying Continuous, construct a quadratic polynomial using formula (8) .

[0083] (7);

[0084] In formula (7) , and for At the endpoint The second derivative, the first derivative, and the original function value at point [value]. It is an adjustable parameter. Simplifying and rearranging formula (8) yields... If the form is given, then this quadratic function is the required quadratic polynomial function. Simplifying (7) gives:

[0085] (8);

[0086] Will endpoints at Substituting the second derivative, first derivative, and original function value into the equation, we can obtain the first polynomial function.

[0087] (9);

[0088] Similarly, , exist Satisfying Continuous, will endpoints at Substituting the second derivative, first derivative, and original function value into equation (8) and simplifying, we can obtain the sixth polynomial function:

[0089] (10);

[0090] The activation function constructed in summary is as follows:

[0091] (11).

[0092] The activation function in ordinary graph convolution is used with This activation function has stronger expressive power and better performance, and can better handle complex graph-structured data. Compared to the Leaky_ReLU activation function, Activation functions have a wider activation range and smoother gradients, enabling them to better fit complex graph structures and improve model performance and generalization ability.

[0093] Step 300: Combine the polynomial activation function and the graph convolutional network to extract the features of nodes in the preprocessed traffic data matrix and obtain the node feature matrix.

[0094] Graph convolutional networks are used to extract spatial features from transportation networks. Specifically, they model the transportation network as a graph, where nodes represent intersection detection points on roads, edges represent connections between roads, and the graph convolutional network updates the feature representation of each node by aggregating information from neighboring nodes.

[0095] (12);

[0096] (13);

[0097] In the above formula, Represents an explicit feature map; Represents implicit feature maps; It is an adjacency matrix; It is an adjacency matrix with self-loops added. Represents the identity matrix; Degree matrix; b and b both represent learnable parameters; This represents the activation function.

[0098] A multinomial activation function is applied after the graph convolutional layer to enhance the model's ability to capture complex traffic patterns. The multinomial activation function is used for nonlinear transformation to obtain the node feature matrix.

[0099] (14);

[0100] In the above formula, Represents the node feature matrix; This indicates that the feature map will be processed by the activation function. This indicates that the implicit feature map has been processed by the activation function.

[0101] Step 400: Construct a time series prediction model for traffic data to process the node feature matrix and capture the spatial correlation between different nodes in the traffic network;

[0102] The traffic data time series prediction model employs a gated recurrent unit (GRU). The GRU is a variant of the LSTM network with a time-aware topology layer. Compared to LSTM, the GRU has a simpler structure, fewer training parameters, and is more effective at overcoming the vanishing and exploding gradient problems. The feedforward recursion of the GRU with the time-aware topology layer is as follows:

[0103] (15);

[0104] In the above formula, Indicates a hidden state; This represents the update gate in GRU; This refers to the reset gate in the GRU; Represents the candidate hidden state in GRU; Indicates the final hidden state; This indicates the hidden state at the previous moment; This indicates the current input data; This represents the input data from the previous time step.

[0105] Step 500: In the training of the traffic data time series prediction model, a residual with a scaling factor is introduced. The residual with the scaling factor is used as a new feature and input into the traffic data time series prediction model at the next time step to obtain the trained traffic data time series prediction model.

[0106] Scaling residuals is used to balance the effects of outliers and noise in the data. In traffic time series forecasting, capturing long-term correlations is particularly important due to the existence of long-term data spanning different scales. Therefore, residual block units are further designed to enhance the model's ability to capture long-term correlations. The core idea of ​​typical residual connections is to input the residuals (i.e., the difference between observed values ​​and model predictions) as new features into the prediction model at the next time step. However, in traffic time series forecasting, the existence of long-term data spanning different scales may lead to gradient vanishing or gradient exploding problems.

[0107] A constant scaling factor is introduced to enhance the model's gradient propagation and stability. The optimal scaling value is determined experimentally. By scaling the residuals, the influence of outliers and noise can be balanced, thereby improving the model's robustness. This constant scaling mechanism provides a way to adjust the degree of residual influence, allowing the model to better adapt to different data characteristics and noise levels. Furthermore, by introducing the constant scaling factor, the residual network can better handle long-term series correlations. The scaling factor can adjust the degree of residual influence, allowing the model to better adapt to series data at different time scales. This design enables the model to more effectively utilize historical information when making predictions, thereby better capturing long-term correlations and improving prediction accuracy and stability.

[0108] (16);

[0109] In formula (16), Represents the residual; Represents the original sequence; Indicates the scaling factor, preferably .

[0110] The scaled residuals are added as new features to the input feature set; in the prediction of the next time step, the residual features of the current time step are input into the traffic data time series prediction model along with other features; the traffic data time series prediction model is retrained using the new dataset containing the residual features.

[0111] The loss function chosen is MAE (Mean Absolute Error), which calculates the mean absolute error between the predicted and actual values. The formula for MAE is as follows:

[0112] (17);

[0113] In the above formula, Indicates the predicted value. Represents the actual value. This indicates the number of data points. The iteration ends when the MAE value stops decreasing for 15 consecutive rounds.

[0114] Step 600: Use the trained traffic data time series prediction model to make prediction output.

[0115] This invention utilizes a data smoothing matrix to generate node feature maps, while also fully considering neighbor information, node location within the network, and connectivity relationships, making the feature maps more global. The multinomial activation function solves the problem of feature map fusion; due to the unique characteristics of graph data, traditional activation functions may not be able to fully extract the features of graph data, but the multinomial activation function perfectly solves this problem. Scaling residuals helps balance outliers and noise in the data, thereby achieving accurate prediction of traffic time series.

[0116] Reference Figures 5-7 To demonstrate the effectiveness of this invention, it was compared with more advanced prediction models. Model 1 is STFGNN (Spatial-Temporal Fusion Graph Neural Networks), which is used to solve the problem of data prediction with temporal and spatial 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 utilizes the learnable embedding model of nodes in graph convolution. Model 5 is the prediction model proposed in this invention, which mainly uses data smoothing and multinomial activation functions to solve the problem in traffic prediction. It can be seen that the present invention performs well in all three prediction metrics, namely MAE (Mean Absolute Error), MAPE (Mean Absolute Percentage Error), and RMSE (Root Mean Square Error). The smaller the metric, the higher the prediction accuracy.

[0117] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A traffic time series prediction method based on data smoothing and multinomial activation function, characterized in that, Includes the following steps: The input traffic data matrix is ​​preprocessed 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 the node feature matrix; A time series prediction model for traffic data is constructed to process the node feature matrix and capture the spatial correlation between different nodes in the traffic network. In the training of the traffic data time series prediction model, residuals with scaling factors are introduced and used as new features to input the traffic data time series prediction model at the next time step, so as to obtain the trained traffic data time series prediction model. The predicted output is generated using a pre-trained traffic data time series prediction model. The construction of the polynomial activation function specifically involves: using the polynomial activation function... Set as a six-segment curve, with the following intervals: ； In the interval and The above are two quadratic polynomial functions, in the interval... , , and It is a four-segment cubic polynomial function; The polynomial activation function Specifically: ； In the above formula, Represents a piecewise function; Indicates the unknowns of the current piecewise function; The graph convolutional network is used to extract spatial features from the traffic network, specifically including: modeling the traffic network as a graph, where nodes represent intersection detection points in 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. The polynomial activation function and graph convolutional network are combined to extract the features of nodes in the preprocessed traffic data matrix, and the node feature matrix is ​​output, specifically including: The graph convolutional network computes both the explicit and implicit feature maps: ； ； In the above formula, Represents an explicit feature map; Represents implicit feature maps; It is an adjacency matrix; It is an adjacency matrix with self-loops added. Represents the identity matrix; Degree matrix, b and b both represent learnable parameters; Indicates the activation function; A nonlinear transformation using a polynomial activation function is used to obtain the node feature matrix: ； In the above formula, Represents the node feature matrix; This indicates that the feature map will be processed by the activation function. This indicates that the implicit feature map has been processed by the activation function.

2. The traffic time series prediction method based on data smoothing and multinomial activation function according to claim 1, characterized in that, The preprocessing of the input traffic data matrix includes smoothing using a mean filter method.

3. The traffic time series prediction method based on data smoothing and multinomial activation function according to claim 1, characterized in that, The traffic data time series prediction model is a gated cyclic unit.

4. The traffic time series prediction method based on data smoothing and multinomial 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; This represents the scaling factor.

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