Time map construction method based on improved moving least square method and graph convolutional neural network

Abstract

The invention relates to a time map construction method based on an improved moving least square method and a graph convolutional neural network. The time map construction method comprises the following steps: constructing a traffic travel spatio-temporal data set and carrying out data preprocessing; performing coordinate transformation of the control points relative to the central point to obtain new coordinates of the control points; solving an affine transformation matrix by using a moving least square method improved by introducing a KD tree, thereby deducing new coordinates of map boundary points based on the new coordinates of the control points, and obtaining a time reachable center type time map; correcting the time map based on the actual reachability index to obtain an actual reachability comprehensive central time map; correcting the time map based on the economic value reachability index to obtain a value reachability comprehensive central time map; and based on each level of center type time map, constructing an edge weight map by adopting a graph convolutional neural network introduced with an attention mechanism, performing coordinate prediction on boundary nodes, and constructing a network type time map. Compared with the prior art, the method has the advantages that element dimensions of the central time map are diverse, the solving calculation amount of the network time map is small, and geometric shape and position distortion is small.

Description

Technical Field

[0001] The present invention relates to the technical field of time map construction, and in particular to a time map construction method based on an improved moving least squares method and a graph convolutional neural network. Background Art

[0002] With the rapid development of modern transportation and communication technologies, and with travelers' increasing demands for travel comfort and efficiency, people's perception of distance is increasingly shifting from spatial distance to temporal duration. The rapid development of multimodal transportation has necessitated the strategic need for "Mobility as a Service" (Maas). However, traditional maps, which are limited to depicting spatial distance, struggle to intuitively capture the spatiotemporal heterogeneity of travel distance perception.

[0003] In recent years, cartograms, a representation method that emphasizes one or more attributes of geographic objects through simplification and deformation, have become an increasingly popular research topic in cartographic research. In the creation and representation of temporal maps, the rational deformation of map boundaries, the selection of appropriate weighting functions, the solution of affine transformation matrices, and the mining and integration of multidimensional data have become key factors in enhancing the readability of temporal maps and improving the practicality and decision-making support capabilities of models. However, resolving scale inconsistencies in maps while minimizing topological errors has become a core challenge in overcoming bottlenecks in cartographic technology.

[0004] Currently, mainstream time maps include two types of representations: center-based and network-based. Center-based time maps select a node as the center point and express the temporal distance relationship between the center point and surrounding points. For example, CN118623866A discloses a method for drawing a time map that incorporates travel time. The method includes obtaining the user's travel center point; generating a list of the user's destinations, which includes multiple points of interest; calculating the orientation of the points of interest relative to the travel center point; calculating the travel time from the travel center point to the points of interest based on the travel method determined by the user; and drawing a time map based on the orientation of the points of interest relative to the travel center point and the travel time from the travel center point to the points of interest. This type of time map is prone to topological errors and has a single dimensionality of map elements. Optimizing drawing techniques remains a major research challenge. Network-based time maps, on the other hand, aim to represent the temporal distance between all pairs of nodes in the map. However, these maps are limited by excessive computational complexity, non-unique map solutions, and significant geometric distortion, resulting in poor readability. Currently, they remain at the theoretical level, lacking reliable technology and practical application scenarios. Summary of the Invention

[0005] The purpose of the present invention is to provide a time map construction method based on an improved moving least squares method and a graph convolutional neural network, which considers the influence of multiple factors to construct a more accurate and effective central time map, and realizes efficient network time map construction, avoiding the problem of geometric distortion of existing network time maps.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A temporal map construction method based on an improved moving least squares method and a graph convolutional neural network includes the following steps:

[0008] Step S1, constructing a spatiotemporal data set of traffic travel;

[0009] Step S2, performing data preprocessing on the traffic travel spatiotemporal dataset, including center point and control point selection, geographic coordinate system transformation, and missing value and outlier processing;

[0010] Step S3: transform the coordinates of the control points relative to the center point based on the spatiotemporal variation parameters to obtain new coordinates of the control points; solve the affine transformation matrix using the moving least squares method improved by introducing the KD tree, thereby deducing the new coordinates of the map boundary points based on the new coordinates of the control points to obtain a time-reachable center-type time map based on the time reachability index;

[0011] Step S4, correcting the time accessibility index based on the multi-element traffic index to obtain the actual accessibility index, and correcting the time-accessible center-type time map to obtain the actual reachable comprehensive center-type time map;

[0012] Step S5: Correcting the time accessibility index based on the economic correction factor to obtain an economic value accessibility index, and correcting the time accessibility center-type time map to obtain a value accessibility comprehensive center-type time map;

[0013] In step S6, based on the central time maps at all levels, a graph convolutional neural network with an attention mechanism is used to construct an edge weight graph, coordinates of boundary nodes are predicted, and network time maps corresponding to the central time maps at all levels are constructed respectively.

[0014] The traffic travel spatiotemporal dataset includes node geographic coordinates, travel start and end points, travel duration and distance data, and the distance data is the travel distance or the spherical distance between the start and end points.

[0015] The number of the central point is only one, and the control points are points that have a traffic relationship with the central point and are distributed around the central point. The number of the control points is determined according to the accuracy of the time map.

[0016] In step S3, the coordinate transformation of the control point relative to the center point based on the spatiotemporal variation parameters is specifically as follows:

[0017] The contraction and expansion of the control points relative to the center point are based on the premise of ensuring orientation consistency. That is, the control points and the center point before and after the image change must satisfy the three-point collinearity. The temporal and spatial variation parameters are introduced to ensure that the sum of the spatial distances from the center point to each point is always constant before and after the transformation. The new coordinates of the control point i are calculated as follows:

[0018]

[0019] Where x′ i is the new horizontal coordinate of the control point i after the coordinate transformation, x0 is the horizontal coordinate of the center point, x i is the horizontal coordinate of the control point i before coordinate transformation, t i With s i Represent time distance and space distance respectively;

[0020] According to the linear transformation principle, the new vertical coordinate y′ of control point i is determined based on the new horizontal coordinate of control point i. i .

[0021] In step S3, deducing the new coordinates of the map boundary points based on the new coordinates of the control points includes the following steps:

[0022] The Gaussian weight function is used to dynamically calculate the weight of each control point, wherein the weight is calculated as follows:

[0023]

[0024] Where, d ij is the distance between each control point i and each boundary point j;

[0025] Based on the determined weights, a robust moving least squares optimization algorithm is constructed to optimize the affine transformation matrix. Its objective function is defined as:

[0026]

[0027] In the formula, (x′ i ,y′ i ) is the new coordinate of control point i, (x i ,y i ) is the original coordinate of control point i, is the least squares affine transformation matrix; in the process of optimizing and solving the affine transformation matrix, the moving least squares is improved by using a neighborhood search algorithm based on a KD tree, specifically by introducing an adaptive weight gating mechanism:

[0028] λ(x,y)=Sigmoid(α·KDE(x,y)-γ)

[0029] Where KDE(x,y) is the kernel density estimation of the control points, α is the slope factor of the control density sensitivity, and β is the density threshold offset. The KD tree is used when estimating the distance between the control points and the boundary points within the kernel density estimation radius g. By establishing a multidimensional spatial index structure, the neighborhood search and density calculation of the control points are accelerated.

[0030] Based on the affine transformation matrix obtained by optimization, the original coordinates (x j ,y j ) to perform coordinate transformation and obtain the new coordinates of the map boundary point (x′ j ,y′ j ):

[0031]

[0032] In the time-accessible center type time map, the time accessibility index between a location pair is the travel time between the two locations in the location pair.

[0033] In step S4, the actual reachability index is calculated as follows:

[0034] Considering multiple traffic indicators including travel time, departure convenience, and economy, the range normalization method is used to standardize travel time T, daily departure frequency N, and fare F. The original values ​​of the multiple traffic indicators are compressed to the interval [0, 1] through linear transformation. The entropy weight method is used to dynamically determine the weights of the multiple traffic indicators based on their information entropy. The actual accessibility index is determined based on the compressed multiple traffic indicators and their weights:

[0035]

[0036] Where w T 、w F 、w N are the objective weights calculated by the entropy weight method; T ij 、F ij 、N ij They are the standardized travel time, fare and daily departure frequency; is the actual accessibility index between location pair ij, Larger values ​​indicate better accessibility.

[0037] In step S5, the economic value accessibility index is calculated as follows:

[0038] Introducing the economic correction factor SEF ij Measure the economic interaction potential between location pairs ij and use it as a coefficient to modify the travel time T ij , and obtain the economic value accessibility index

[0039]

[0040] Where, P i , G i are the permanent population and annual GDP of location i, max(P) is the maximum permanent population among all locations, and max(G) is the maximum annual GDP among all locations.

[0041] The step S6 is specifically as follows:

[0042] The control points and their connection relationships are modeled as a weighted graph, in which the node set represents the location, and the edge set represents the node pairs that can be directly connected or have operating routes. Each edge has an edge weight, and the initial edge weight is set to the distance between the nodes. The new node coordinates are predicted based on the graph convolutional neural network, so that the geometric distance between the nodes is as close as possible to the target edge weight. The target edge weight is the time accessibility index, actual accessibility index or economic value accessibility index corresponding to the central time map. The graph convolutional neural network regards coordinate prediction as a regression process. Given the graph structure and edge weight, the initial self-coordinates of each node and the coordinates of its neighbors are used as input, and the adjacency matrix or attention coefficient is assigned according to the new edge weight information. The representation of each node is updated through the graph convolution operation, and then the representation is mapped to the target coordinate, and the predicted new coordinates are output.

[0043] The loss function of the graph convolutional neural network is:

[0044] L=α·L coord +β·T smooth +γ·L angle

[0045] Where α, β, and γ are hyperparameters, and L coord is the coordinate consistency loss, L smooth is the graph smoothing regularization term, L angle for azimuth hold loss;

[0046]

[0047] Where W′ ij is the target edge weight, X′ i , X′ j are the predicted coordinates of nodes i and j respectively, E is the node set, A ij is the adjacency matrix element, n is the total number of nodes, θ ij is the azimuth in the original space, θ′ ij is the azimuth in the prediction space.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] (1) This paper introduces a data-driven dynamic weight allocation mechanism into the central temporal mapping algorithm, constructs an adaptive weight gating function based on kernel density estimation, and implements an intelligent switching strategy of "high-density areas trust the global model and low-density areas rely on local corrections", thereby avoiding potential topological errors in map drawing.

[0050] (2) In the existing technology, measuring accessibility through a single time indicator is rather one-sided. In order to expand the expression elements of the time map and depict travel convenience in multiple dimensions, the present invention further incorporates traffic indicators such as ticket prices and frequency and economic indicators such as population and GDP to correct time accessibility, thereby being closer to actual travel conditions and enriching the map content.

[0051] (3) This invention introduces KD tree (K-dimensional tree) to optimize the spatial query and density estimation process, significantly accelerating the neighborhood search and density calculation of control points. The traditional brute force search method has a serious performance bottleneck when processing the neighborhood query of control points, and the time complexity is O(n 2 ) order of magnitude, and the single calculation is time-consuming, which seriously restricts the computational efficiency of the model. The present invention innovatively introduces the KD tree into the algorithm to construct a hierarchical spatial index structure: by recursively dividing the spatial dimension, the unordered point cloud is converted into a balanced binary tree, so that the complexity of the nearest neighbor search is reduced to O(n*logn). Specifically, in the key link of kernel density estimation (KDE), the traditional point-by-point scanning method needs to traverse all control points for each query point, while the KD tree quickly locates the spatial neighborhood through a pruning strategy, which significantly reduces the time consumption of single-point KDE calculations. This breakthrough enables the algorithm to respond to dynamic queries in real time during the online reasoning stage, providing technical support for the construction of real-time and intelligent websites for subsequent map information systems.

[0052] (4) The present invention uses a graph convolutional network (GCN) to drive spatial mapping without central control points, and realizes anchor-free coordinate transformation through spatial topology self-learning, filling the research gap in the field of heterogeneous spatial benchmark conversion. In the special scenario of surveying and mapping network-type temporal maps that lack central control points, traditional coordinate transformation methods face fundamental limitations due to over-reliance on preset benchmark points. The present invention breaks through the control point-driven centralized temporal map drawing idea, and uses a decentralized spatial mapping framework with a graph convolutional network (GCN) as the core to realize center-free coordinate transformation through spatial topology self-learning, filling the research gap in the field of spatial temporal map drawing. Traditional methods often fall into a dilemma in the scenario without central control points: the global model based on regression fitting leads to extrapolation error accumulation due to the lack of benchmark reference, while the local interpolation rule causes topological distortion due to the break of spatial correlation. The present invention creatively introduces a graph convolutional network to reconstruct discrete control points into graph structure data - nodes represent coordinates, edge weights encode spatial proximity and temporal proximity, and proposes to use the sum of the azimuth errors between points before and after the change as a function to characterize the loss of geometric fidelity. Through multi-layer graph convolution operations, the model autonomously captures multi-scale spatial dependencies. Even if the control points are fragmented, it can still reconstruct global spatial constraints through message passing between neighboring nodes. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of the method of the present invention;

[0054] Figure 2 This is a diagram showing the contraction and expansion effects of the control points relative to the center point in an embodiment of the present invention;

[0055] Figure 3 This is a rendering of a railway travel center time map centered on location A in an embodiment of the present invention;

[0056] Figure 4 This is an effect diagram of an actually accessible comprehensive central time map incorporating corrections to multiple traffic indicators in an embodiment of the present invention;

[0057] Figure 5 The value of introducing the economic correction factor in the embodiment of the present invention can reach a comprehensive central time map effect diagram;

[0058] Figure 6 This is a rendering of a railway travel network time map in an embodiment of the present invention;

[0059] Figure 7 This is a rendering of a subway travel time map of area A centered at coordinate S in an embodiment of the present invention;

[0060] Figure 8 This is a rendering of a highway travel time map of location A centered at coordinate S in an embodiment of the present invention;

[0061] Figure 9 This is a comparison diagram of railway travel time maps before and after the opening of the urban airport line in area A in an embodiment of the present invention;

[0062] Figure 10 This is a time map rendering based on railway travel with location B as the center in an embodiment of the present invention;

[0063] Figure 11 This is a time map rendering based on air travel and centered on location B in an embodiment of the present invention;

[0064] Figure 12 This is a time map effect diagram based on road travel with location B as the center in an embodiment of the present invention;

[0065] Figure 13 This is a functional diagram of the infrastructure utility evaluation system based on time map of the present invention. DETAILED DESCRIPTION

[0066] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0067] Example 1

[0068] This embodiment provides a time map construction method based on improved moving least squares method and graph convolutional neural network, such as Figure 1 As shown, the following steps are included:

[0069] Step S1: Construct a spatiotemporal data set of traffic travel.

[0070] In this embodiment, the required spatiotemporal data set of traffic travel is constructed by crawling, web search or other means, including node geographic coordinates, travel start and end points, travel duration (i.e., travel time) and travel distance (or spherical distance between start and end points).

[0071] Step S2: preprocessing the traffic travel spatiotemporal dataset, including selecting center points and control points, transforming geographic coordinate systems, and processing missing values ​​and outliers.

[0072] The acquired spatiotemporal data set of transportation was preprocessed, including: ① center point selection (selecting the S coordinate of location A as the center point); ② control point selection (selecting 522 railway stations that can be directly reached by rail by S coordinate point as control points); ③ geographic coordinate system transformation (performing corresponding coordinate transformation in the WGS-84 coordinate system).

[0073] In this embodiment, there is only one center point. Control points are points that have a traffic relationship with the center point and are distributed around the center point. The number of control points is determined according to the accuracy of the time map. Increasing the number of control points can make the map presentation more rigorous and accurate.

[0074] In step S3, the coordinates of the control points relative to the center point are transformed based on the spatiotemporal change parameters to obtain new coordinates of the control points; the affine transformation matrix is ​​solved using the moving least squares method improved by introducing the KD tree, so as to deduce the new coordinates of the map boundary points based on the new coordinates of the control points, and obtain a time-reachable center-type time map based on the time accessibility index.

[0075] S31, performing coordinate transformation of the control points.

[0076] The contraction and expansion of the control points relative to the center point are based on the premise of ensuring orientation consistency. That is, the control points and the center point before and after the image transformation must satisfy the three points collinearity. To avoid geometric distortion of the map and to maintain map scale consistency to the greatest extent possible, a spatiotemporal variation parameter is introduced to ensure that the sum of the spatial distances from the center point to each point remains constant before and after the transformation. The new coordinates of control point i are calculated as follows:

[0077]

[0078] Where x′ i is the new horizontal coordinate of the control point i after the coordinate transformation, x0 is the horizontal coordinate of the center point, x i is the horizontal coordinate of the control point i before coordinate transformation, t i With s i Represent time distance and space distance respectively;

[0079] According to the linear transformation principle, the new vertical coordinate y′ of control point i is determined based on the new horizontal coordinate of control point i. i .

[0080] Based on this, taking point A as the center point, the contraction and expansion of the control points relative to the center point are as follows: Figure 2 As shown in the figure, the red arrows indicate outward expansion and the blue arrows indicate inward contraction.

[0081] S32, deducing new coordinates of the map boundary points based on the new coordinates of the control points, specifically includes the following steps:

[0082] S321, dynamically calculate the weight of each control point using a Gaussian weight function, where the weight is calculated as follows:

[0083]

[0084] Where, d ij is the distance between each control point i and each boundary point j.

[0085] S322, based on the determined weights, construct a robust moving least squares optimization algorithm to optimize and solve the affine transformation matrix. Its objective function is defined as:

[0086]

[0087] In the formula, (x′ i ,y′ i ) is the new coordinate of control point i, (x i ,y i ) is the original coordinate of control point i, is the least squares affine transformation matrix.

[0088] In the process of optimizing the solution of the affine transformation matrix, a neighborhood search algorithm based on KD tree is used to improve the moving least squares. The computational complexity is reduced by multi-dimensional data retrieval. In order to suppress noise interference and balance global and local contributions, an adaptive weight gating mechanism is introduced:

[0089] λ(x,y)=Sigmoid(α·KDE(x,y)-β)

[0090] Where KDE(x,y) is the kernel density estimate of the control points, and α and β are obtained through cross-validation learning.

[0091]

[0092] K is the Epanechnikov kernel function, h is the optimal bandwidth calculated using the Silverman criterion, and n is the number of control points. α is the slope factor that controls density sensitivity; larger values ​​result in steeper weight shifts when density changes. β is the density threshold offset, which determines the balance between the global and local models.

[0093] When performing kernel density estimation, the traditional point-by-point scanning method requires traversing all control points for each query point. Therefore, this paper introduces the K-dimensional tree algorithm. The KD tree significantly accelerates the neighborhood search and density calculation of the control point by establishing a multi-dimensional spatial index structure, which greatly reduces the time consumption of single-point KDE calculation. Specifically, when kernel density estimation is performed on the distance between the control point and the boundary point within the statistical radius h, the KD tree is used to reduce the query complexity from O(n 2 ) is reduced to O(nlogn).

[0094] S323, based on the affine transformation matrix obtained by optimization, the original coordinates (x j ,y j ) to perform coordinate transformation and obtain the new coordinates of the map boundary point (x′ j ,y′ j ):

[0095]

[0096] In this embodiment, if the coordinates of 67,899 boundary points are directly deduced based on 522 control points, 522×67,899 coordinate calculations are required. However, the moving least squares method is improved by using a neighborhood search algorithm based on K-Dimensional Tree. By using multi-dimensional data retrieval, the computational complexity is reduced, thereby shortening the data processing time and improving the overall efficiency. This avoids the exponential increase in the number of control points and boundary nodes, which causes the algorithm to crash. Based on this, a railway travel center time map centered on location A is drawn as follows: Figure 3 shown.

[0097] S33, construct a time map of time-reachable center.

[0098] For steps S3-S5, the present invention aims to construct a multi-dimensional accessibility indicator system based on map expression elements, including time accessibility, actual accessibility, and value accessibility, comprehensively explaining "accessibility" and "reach" from multiple perspectives. The expression elements presented in the map are, in order, the time accessibility indicator (i.e., travel time), the actual accessibility indicator (i.e., travel time corrected by traffic factors), and the value accessibility indicator (i.e., travel time corrected by economic factors).

[0099] Among them, in the time-accessible center time map, only the travel time is measured to intuitively express the time distance. The time accessibility index between places ij That is, the travel time T between the two places ij (Hour):

[0100]

[0101] However, measuring accessibility using a single time metric is rather one-sided. To expand the expressive elements of time maps and depict travel convenience in multiple dimensions, the present invention further incorporates transportation indicators such as fares and frequency, as well as economic indicators such as population and GDP, to modify time accessibility, thereby more closely reflecting actual travel conditions and enriching the map's content. This specifically includes steps S4 and S5.

[0102] Step S4: Based on the multivariate traffic index, the time accessibility index is corrected to obtain the actual accessibility index, and the time-accessible center-type time map is corrected to obtain the actual accessible comprehensive center-type time map.

[0103] Considering that people’s daily travel concerns are not only focused on the length of travel time, but also on travel convenience (frequency) and economy (fare) are important considerations, this embodiment sets the shortest train travel time T between two places. ijAdd two parameters based on the fare F ij is the geometric mean of the lowest fare and the average economy class fare (yuan), and the daily departure frequency N ij Represents the total number of trains running in both directions every day (trips / day). In order to avoid the subjectivity of artificial formula weighting, this study uses the entropy weight method to dynamically determine the weight of each indicator based on its information entropy, thereby constructing an actual accessibility index.

[0104] First, considering multiple traffic indicators including travel time, departure convenience, and economy, the range normalization method is used to standardize travel time T, daily departure frequency N, and fare F. The original values ​​of the multiple traffic indicators are compressed to the interval [0,1] through linear transformation.

[0105] Then, the entropy weight method is used to dynamically determine the weight of each multivariate traffic indicator based on its information entropy;

[0106] Finally, the actual accessibility index is determined based on the compressed multi-modal traffic indicators and their weights:

[0107]

[0108] Where w T 、w F 、w N are the objective weights calculated by the entropy weight method; T ij 、F ij 、N ij They are the standardized travel time, fare and daily departure frequency; is the actual accessibility index between location pair ij, Larger values ​​indicate better accessibility.

[0109] Based on this, a comprehensive central time map with actual accessibility and multiple traffic index correction is drawn, such as Figure 4 shown.

[0110] Step S5: correct the time accessibility index based on the economic correction factor to obtain the economic value accessibility index, and correct the time-accessible central time map to obtain the value-accessible comprehensive central time map.

[0111] Transportation is not only a spatial connection, but also a carrier of economic energy and population vitality. Based on this, this embodiment further enriches map elements from the demand level and introduces the economic correction factor SEF ij Measure the economic interaction potential between location pairs ij and use it as a coefficient to modify the travel time T ij , and obtain the economic value accessibility index

[0112]

[0113] Where, P i , G i are the permanent population (10,000 people) and annual GDP (100 million yuan) of location i, max(P) is the maximum permanent population among all locations, and max(G) is the maximum annual GDP among all locations.

[0114] Based on this, the value of introducing economic correction factors can be drawn into a comprehensive central time map such as Figure 5 shown.

[0115] In step S6, based on the central time maps at all levels, a graph convolutional neural network with an attention mechanism is used to construct an edge weight graph, coordinates of boundary nodes are predicted, and network time maps corresponding to the central time maps at all levels are constructed respectively.

[0116] Step S6 is specifically as follows:

[0117] The control points and their connections are modeled as a weighted graph G = (V, E), where the node set V = {v1, v2, ..., vn} represents the location and the edge set Represents a pair of nodes that can be directly connected or have an operating line, and each edge has an edge weight W ij It is used to characterize the distance or travel time between nodes vi and vj. The initial edge weight is set to the distance between the nodes. When drawing the time map, it is replaced by the travel time to form a new edge weight distribution W′ ij Based on the graph convolutional neural network, new node coordinates are predicted so that the geometric distance between nodes fits the target edge weight as closely as possible. In this embodiment, the target edge weight is the time accessibility index, actual accessibility index or economic value accessibility index corresponding to the central time map. The graph convolutional neural network (GCN) treats coordinate prediction as a regression process. Given the graph structure and edge weights, it takes the initial coordinates of each node and its neighbor coordinates as input, assigns the adjacency matrix or attention coefficient according to the new edge weight information, updates the representation of each node through the graph convolution operation, and then maps the representation to the target coordinates, and outputs the predicted new coordinates. Unlike traditional global optimization based on Euclidean space, this method can quickly predict the new edge weight after training is completed without the need for repeated overall iterative solution of the layout of the entire graph.

[0118] When constructing the loss function of a graph convolutional neural network, the most important constraint is to maintain the consistency between the distance between nodes in the network and the target edge weight. To this end, the mean squared error (MSE) metric can be selected, and the difference between the Euclidean distance between nodes in the predicted coordinates and the corresponding edge weight is used as the loss term for penalty, that is:

[0119]

[0120] Where, L coord is the coordinate consistency loss, W′ ij is the target edge weight, X′ i , X′ j are the predicted coordinates of nodes i and j respectively, and E is the node set.

[0121] To avoid overfitting or unusually large coordinate shifts, a graph smoothing regularization term is added to encourage directly connected nodes to remain relatively close in space. This balances distance consistency with local smoothness, allowing the model to maintain a reasonable coordinate distribution during generalization:

[0122]

[0123] Where, L smooth is the graph smoothing regularization term, A ij is the adjacency matrix element.

[0124] Introducing azimuth angle keeping loss L angle Maintain the similarity of the orientation angles between nodes before and after coordinate transformation

[0125]

[0126] Where N is the total number of nodes, θ ij is the azimuth in the original space, θ′ ij is the azimuth in the prediction space. Then the loss function of the graph convolutional neural network is:

[0127] L=α·L coord +β·L smooth +γ·L angle

[0128] Where α, β, and γ are hyperparameters.

[0129] During the training and reasoning process of the graph convolutional neural network, it is necessary to prepare "original coordinate-edge weight" combinations in different scenarios as training samples. The present invention derives the node location and the distance between railway stations from the real geographic coordinates as the initial edge weight, and then generates the travel time between nodes based on the railway operation data, and then obtains a set of target coordinates for training reference through methods such as multi-dimensional scaling. After forming a training set with several groups of similar "old edge weight-coordinate / new edge weight-coordinate" pairs, the graph neural network can be iteratively updated with the help of stochastic gradient descent or other optimization strategies. Due to the large scale of the network, the graph sampling method GraphSAGE and the attention mechanism GAT are used in the calculation to enhance the computational efficiency and expression ability of the model. In the reasoning stage, when there is a new travel time or other metric as the edge weight input, the model can give a new node coordinate prediction without resolving the entire model, thereby achieving rapid adaptation to dynamic changes.

[0130] Based on this, the network-type time map constructed by the present invention based on the graph convolutional neural network is as follows Figure 6 shown.

[0131] Example 2

[0132] This embodiment provides an infrastructure utility evaluation system based on a time map. Figure 13 As shown in the figure, its main functions include: real-time evaluation of the operation status of the transportation network, evaluation of the role of major transportation infrastructure, analysis of the accessibility pattern of multi-scale and multi-modal transportation modes, actual accessibility index evaluation and transportation resource optimization assistance, and value accessibility index evaluation and exposure of hidden supply and demand contradictions. The specific explanations are as follows:

[0133] 1. Real-time evaluation function of traffic line network operation status.

[0134] Complex transportation networks often exhibit a variety of configurations, including checkerboard, radial, and circular radials. This makes it difficult to intuitively and accurately assess their overall and local operational status. Temporal maps can be used to shape and reconstruct urban forms. The expansion and contraction of temporal maps in both east-west and north-south directions can then be used to assess the nonlinearity coefficient and congestion levels of travel in different directions and regions within the city, thereby comprehensively evaluating the real-time operational status of the transportation network. Figure 7 、 Figure 8The figures show the subway and highway travel time maps of area A centered on coordinate S. As can be seen from the figure, the subway travel time map of area A shows significant east-west compression and north-south expansion. This is because the radial subway network is densely populated on the east-west trunk lines, while the average detour coefficient of the north-south subway is 1.4. The large non-linear coefficient causes north-south travel to rely on transfers and detours, which is time-consuming and inefficient. The well-connected, circular radial highway network in area A uses a multi-path compensation mechanism to make the highway travel time map shrink evenly as a whole, with the omnidirectional time compressed by about 30%. The high-density grid roads balance the impact of congestion through path redundancy, maintaining the time mapping in the form of an administrative map.

[0135] 2. Function of evaluating the role of major transportation infrastructure.

[0136] If major new infrastructure is constructed within an existing transportation network, such as opening a core rail line or building a new expressway or freeway within a highway network, it is necessary to carefully compare the network's utility before and after the construction of the major infrastructure to determine and evaluate its impact. By integrating different traffic characteristics such as direct access, transfers, and confluences within the time map, we can assess the benefits of major transportation infrastructure construction in different areas of the city, thereby accurately evaluating its impact. Figure 9 Presented in the figure is a comparison map of railway travel time before and after the opening of the urban airport line in Area A, which intuitively reflects the role of urban rail as a major transportation infrastructure: the east-west urban airport line has further shortened the east-west travel time in Shanghai, with significant results, and some areas with convenient transfers in the north-south direction have benefited from the opening of the urban airport line, and their accessibility has also been enhanced.

[0137] 3. Function of analyzing accessibility patterns of multi-scale and multi-modal transportation modes.

[0138] By constructing a temporal map system based on different modes of transportation from a macro perspective, we can analyze accessibility patterns at the national or city scale. The changes in the shape of the temporal map allow us to measure and analyze differences in location and network hierarchy, as well as topographical constraints. Furthermore, by comparing the shape differences in temporal maps created by different modes of transportation, such as aviation, rail, and road, for the same region, we can study the layout and functional characteristics of different modes of transportation. Figure 10 、 11Figures 1 and 2 show the time maps based on railway, aviation, and road travel with B as the center. As can be seen from the figures, for railway travel, the road network in plain provinces is dense and uniform, and the time map is close to concentric circle diffusion. In mountainous / plateau provinces, railways are distributed along river valleys or fault zones, and the time map is dendritic fractal and appears as a comb-like network between parallel ridges and valleys. In general, the railway time map is radial along the main axis according to the trunk channel; for aviation travel, the time distribution is the most uniform, the map shape is the smallest, and it is a homogeneous coverage type; for road travel, the shape of the time map is directly related to the density of the road network within the grid, and it is a grid penetration type.

[0139] 4. Auxiliary functions for actual accessibility index evaluation and traffic resource optimization.

[0140] When departing from the same location, the same travel time does not necessarily mean the same accessibility to the destination. Therefore, a multi-dimensional assessment of a single time indicator, taking into account factors such as frequency and fare, is necessary to better reflect actual demand. A comprehensive central time map of actual accessibility can intuitively reflect the actual accessibility index, thereby helping to optimize departure frequency and fare strategies for high-demand routes, improving overall network efficiency and assisting in integrated transportation planning for urban agglomerations. Figure 4 Presented in the figure is an actual achievable comprehensive central time map that incorporates corrections to multiple transportation indicators. The figure shows that the degree of expansion in the northwest region has decreased, and the map has shifted toward the southwest, while the degree of contraction in the southeast has weakened. This is because most railway lines in the northwest region are supported by policies, the proportion of high-speed railways is low, and ordinary train fares are even lower. Ultimately, the contribution of low fares to the time disadvantage is weakened.

[0141] 5. Value attainable index assessment and hidden supply and demand contradiction disclosure function.

[0142] Poor accessibility in certain areas does not necessarily indicate a need for strengthening infrastructure and improving accessibility. Therefore, it is necessary to introduce economic correction factors to construct a demand system, fine-tuning the direction of infrastructure investment from the perspective of supply and demand balance, thereby shifting the focus from "how to go faster" to "for whom to go faster." A comprehensive, central, and time-based map of value accessibility can intuitively reflect the value accessibility index, thereby reconstructing the logic of spatial interaction, revealing hidden supply and demand contradictions, and helping to resolve the long-standing resource mismatch problem facing transportation planning. Figure 5 The figure shows a comprehensive central time map of the value of economic correction factors. The figure shows a significant western convergence mechanism. This is because the population density in the west is low, only 1 / 60 of that in the northeast, and the actual utilization rate of the corresponding railway is only 58%, triggering the marginal benefit decay function in the SEF model. The significant expansion of the northeast region in the figure can lead to the corresponding conclusion: the direct railway connection between the northeast region and the southeast coast should be strengthened.

[0143] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A temporal map construction method based on improved moving least squares method and graph convolutional neural network, characterized in that: The following steps are involved: Step S1, constructing a spatiotemporal data set of traffic travel; Step S2, performing data preprocessing on the traffic travel spatiotemporal dataset, including center point and control point selection, geographic coordinate system transformation, and missing value and outlier processing; Step S3, performing coordinate transformation of the control point relative to the center point based on the spatiotemporal variation parameters to obtain new coordinates of the control point; The affine transformation matrix is ​​solved by using the moving least squares method improved by introducing the KD tree. Based on the new coordinates of the control points, the new coordinates of the map boundary points are deduced, and a time-reachable center-type time map based on the time-reachability index is obtained. Step S4, correcting the time accessibility index based on the multi-element traffic index to obtain the actual accessibility index, and correcting the time-accessible center-type time map to obtain the actual reachable comprehensive center-type time map; Step S5: Correcting the time accessibility index based on the economic correction factor to obtain an economic value accessibility index, and correcting the time accessibility center-type time map to obtain a value accessibility comprehensive center-type time map; In step S6, based on the central time maps at all levels, a graph convolutional neural network with an attention mechanism is used to construct an edge weight graph, coordinates of boundary nodes are predicted, and network time maps corresponding to the central time maps at all levels are constructed respectively.

2. The method for constructing a time map based on an improved moving least squares method and a graph convolutional neural network according to claim 1, characterized in that: The traffic travel spatiotemporal dataset includes node geographic coordinates, travel start and end points, travel duration and distance data, and the distance data is the travel distance or the spherical distance between the start and end points.

3. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: The number of the central point is only one, and the control points are points that have a traffic relationship with the central point and are distributed around the central point. The number of the control points is determined according to the accuracy of the time map.

4. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: In step S3, the coordinate transformation of the control point relative to the center point based on the spatiotemporal variation parameters is specifically as follows: The contraction and expansion of the control points relative to the center point are based on the premise of ensuring orientation consistency. That is, the control points and the center point before and after the image change must satisfy the three-point collinearity. The temporal and spatial variation parameters are introduced to ensure that the sum of the spatial distances from the center point to each point is always constant before and after the transformation. The new coordinates of the control point i are calculated as follows: Where x′ i is the new horizontal coordinate of the control point i after the coordinate transformation, x0 is the horizontal coordinate of the center point, x i is the horizontal coordinate of the control point i before coordinate transformation, t i With s i Represent time distance and space distance respectively; According to the linear transformation principle, the new vertical coordinate y′ of control point i is determined based on the new horizontal coordinate of control point i. i .

5. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: In step S3, deducing the new coordinates of the map boundary points based on the new coordinates of the control points includes the following steps: The Gaussian weight function is used to dynamically calculate the weight of each control point, wherein the weight is calculated as follows: Where, d ij is the distance between each control point i and each boundary point j; Based on the determined weights, a robust moving least squares optimization algorithm is constructed to optimize the affine transformation matrix. Its objective function is defined as: In the formula, (x′ i ,y′ i ) is the new coordinate of control point i, (x i ,y i ) is the original coordinate of control point i, is the least squares affine transformation matrix; in the process of optimizing and solving the affine transformation matrix, the moving least squares is improved by using a neighborhood search algorithm based on a KD tree, specifically by introducing an adaptive weight gating mechanism: λ(x,y)=Sigmoid(α·KDE(x,y)-β) Where KDE(x,y) is the kernel density estimation of the control points, α is the slope factor of the control density sensitivity, and β is the density threshold offset. The KD tree is used when estimating the distance between the control points and the boundary points within the kernel density estimation radius h. By establishing a multidimensional spatial index structure, the neighborhood search and density calculation of the control points are accelerated. Based on the affine transformation matrix obtained by optimization, the original coordinates (x j ,y j ) to perform coordinate transformation and obtain the new coordinates of the map boundary point (x′ j ,y′ j ):

6. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: In the time-accessible center type time map, the time accessibility index between a location pair is the travel time between the two locations in the location pair.

7. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: In step S4, the actual reachability index is calculated as follows: Considering multiple traffic indicators including travel time, departure convenience, and economy, the range normalization method is used to standardize travel time T, daily departure frequency N, and fare F. The original values ​​of the multiple traffic indicators are compressed to the interval [0, 1] through linear transformation. The entropy weight method is used to dynamically determine the weights of the multiple traffic indicators based on their information entropy. The actual accessibility index is determined based on the compressed multiple traffic indicators and their weights: Where w T 、w F 、w N are the objective weights calculated by the entropy weight method; T ij 、F ij 、N ij They are the standardized travel time, fare and daily departure frequency; is the actual accessibility index between location pair ij, Larger values ​​indicate better accessibility.

8. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: In step S5, the economic value accessibility index is calculated as follows: Introducing the economic correction factor SEF ij Measure the economic interaction potential between location pairs ij and use it as a coefficient to modify the travel time T ij , and obtain the economic value accessibility index Where, P i , G i are the permanent population and annual GDP of location i, max(P) is the maximum permanent population among all locations, and max(G) is the maximum annual GDP among all locations.

9. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: The step S6 is specifically as follows: The control points and their connection relationships are modeled as a weighted graph, in which the node set represents the location, and the edge set represents the node pairs that can be directly connected or have operating routes. Each edge has an edge weight, and the initial edge weight is set to the distance between the nodes. The new node coordinates are predicted based on the graph convolutional neural network, so that the geometric distance between the nodes is as close as possible to the target edge weight. The target edge weight is the time accessibility index, actual accessibility index or economic value accessibility index corresponding to the central time map. The graph convolutional neural network regards coordinate prediction as a regression process. Given the graph structure and edge weight, the initial self-coordinates of each node and the coordinates of its neighbors are used as input, and the adjacency matrix or attention coefficient is assigned according to the new edge weight information. The representation of each node is updated through the graph convolution operation, and then the representation is mapped to the target coordinate, and the predicted new coordinates are output.

10. The method for constructing a time map based on improved moving least squares method and graph convolutional neural network according to claim 1, characterized in that: The loss function of the graph convolutional neural network is: L=α·L coord +β·T smooth +γ·L angle Where α, β, and γ are hyperparameters, and L coord is the coordinate consistency loss, L smooth is the graph smoothing regularization term, L angle for azimuth hold loss; Where W′ ij is the target edge weight, X′ i , X′ j are the predicted coordinates of nodes i and j respectively, E is the node set, A ij is the adjacency matrix element, n is the total number of nodes, θ ij is the azimuth in the original space, θ′ ij is the azimuth in the prediction space.

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