Spatial weight matrix construction method based on airline space-time network

Abstract

The invention discloses a space weight matrix construction method based on an airline space-time network, which comprises the following steps: collecting related data of the airline space-time network, establishing a corresponding airline space-time network analysis database, and carrying out data preprocessing to determine a research object and a research area range; defining an airline network formed by airport nodes and connection paths thereof in a research area range as an undirected weighted graph, and constructing an airline space-time network graph; the initial space weight of each airport node is calculated by combining the air transportation volume, the airport throughput and the airline distance at different times, and a space weight matrix based on the airline space-time network is obtained after standardization. According to the method, the air transportation flow and distance are combined, the influence of time change is added, namely, the weight matrix is calculated according to the related data of each time point, and the time-varying space weight matrix is constructed, so that the contribution of air transportation to the economic overflow effect can be reflected more accurately.

Description

Technical Field

[0001] The present invention relates to the technical field of transportation economic analysis, and in particular to a method for constructing a spatial weight matrix based on a route space-time network. Background Art

[0002] As a basic, leading and strategic industry of the national economy, the aviation transportation industry is an important condition for promoting the coordinated development of regional social economy. Aviation transportation can solve the problem of constraints on production factors between regions, realize the rapid and convenient circulation of lacking factors between regions, promote industrial agglomeration, and thus form a spatial spillover effect. However, there are many differences between different regions in terms of economy, population, transportation infrastructure, etc. When the transportation conditions in a certain region are improved, it will drive the development of other industries in the surrounding area, thereby promoting new supply and demand in the entire industrial chain. The new supply and demand will be stimulated by the industrial chain brought by aviation transportation, so that the surrounding industries will form a cluster effect and promote the economic growth of the surrounding areas, thus forming a positive spatial spillover effect. However, since the regions with better economic development levels have obtained most of the production resources, the limited resources in the regions with lower economic development levels have flowed outward and lost the advantage of sufficient resources, which has a certain negative impact on economic development, namely the negative spatial spillover effect. Therefore, how aviation transportation affects resource flow and factor aggregation needs to be reflected in the spatial weight matrix that reflects the individual spatial relationship. Scientifically describing the multidimensional spatial relationship of individual aviation, economy, etc., can effectively evaluate the spatial spillover effect between aviation transportation and regional economic development.

[0003] Since space itself has spatial dependence and correlation, the task of achieving coordinated development of transportation regions should be studied from multiple dimensions. The spatial weight matrix reflects the important parameters of the spatial dependence of individuals. It is usually an n×n non-negative matrix with elements W ij It reflects the spatial correlation strength between spatial units i and j, and is also the premise and basis for spatial econometric analysis. In the field of transportation economics, there are already several methods to construct a spatial weight matrix to measure spatial correlation. In the evaluation of transportation spatial spillover effects, the most commonly used calculation methods are 0-1 adjacency matrix, inverse distance matrix, economic characteristic matrix, etc.

[0004] (1) 0-1 adjacency matrix: In the adjacency matrix, if two objects are adjacent in space, the value is 1, otherwise it is 0. Although the calculation is simple, it can only indicate that the research objects are adjacent in geographical location, ignoring the relationship between non-adjacent but related objects, and the description of the overall spatial relationship is not comprehensive enough.

[0005] (2) Inverse distance matrix: Each element in the inverse distance matrix is ​​a power exponential form of the reciprocal of the distance between two objects. The power exponent is usually 1 or 2. The distance can be the geographical distance or the difference between variables. Although the inverse distance matrix takes the distance factor into account, it only considers a single factor during calculation and cannot capture the complex correlation in space well.

[0006] (3) Economic characteristics matrix: The economic characteristics matrix is ​​a matrix used to describe the economic relations and characteristics between different individuals. It mainly considers various economic characteristics and indicators of these individuals, and does not target specific research issues.

[0007] The calculation of the spatial weight matrix should be objective and close to its true state, but there are some shortcomings in the construction of the spatial weight matrix at this stage: whether the weight matrix is ​​easy to construct; the spatial weight matrix calculation method is subjectively selected, lacking the pertinence of the analysis problem; it is mainly a static spatial weight matrix, which cannot reflect the time series correlation of variables.

[0008] Therefore, in the evaluation of the spatial spillover effect of air transport, simply relying on adjacency or distance function cannot fully represent the relationship between different individual air transports. A more reasonable spatial weight matrix is ​​to consider other aspects of influence, such as traffic volume, travel mode, etc., based on the geographical dimension. Therefore, the limitations of the current construction of the spatial weight matrix are still technical problems that cause the low accuracy of the spatial spillover effect evaluation.

[0009] The invention with publication number CN118657447A discloses a method for measuring the spillover effect of enterprises based on geographical distance and technological similarity. The method uses the proportion of patents of different categories of enterprises to construct the technology vector of the enterprise, and measures the technology proximity weight based on the cosine similarity of the technology vectors between enterprises; uses the longitude and latitude data of the headquarters of the enterprise to calculate the geographical distance between enterprises, and uses the inverse of the square of the distance to construct the geographical distance matrix; multiplies the standardized matrix elements accordingly to generate a spatial weight matrix based on geographical distance and technological similarity; considers the geographical distance and technological distance between enterprises at the same time, covers more comprehensive information between enterprises, and can more accurately measure the degree of technological connection between enterprises, which is particularly critical for technology-intensive enterprises or fields. However, the invention cannot be applied in the field of air transportation, and does not consider the impact of time on the spillover effect. Summary of the invention

[0010] The purpose of the present invention is to disclose a method for constructing a spatial weight matrix based on a route space-time network, which combines air transport flow and distance, and adds the influence of time changes, that is, the weight matrix is ​​calculated according to the relevant data at each time point, and a time-varying spatial weight matrix is ​​constructed, so as to more accurately reflect the contribution of air transport to the economic spillover effect.

[0011] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0012] A method for constructing a spatial weight matrix based on a route space-time network, the method comprising the following steps:

[0013] S1, collect relevant data of route space-time network, establish corresponding route space-time network analysis database, and perform data preprocessing to determine the research object and research area;

[0014] S2, define the route network composed of each airport node and its connection paths within the study area as an undirected weighted graph, and construct a route spatiotemporal network graph;

[0015] S3, based on the route space-time network analysis database, combines the air transport volume, airport throughput and route distance at different times to calculate the initial spatial weights between each airport node, and obtains the spatial weight matrix based on the route space-time network after standardization.

[0016] Furthermore, in step S1, the relevant data of the route space-time network includes time distribution data of navigable airports, airport types, route distances, air transport flows, and airport throughput.

[0017] Furthermore, in step S1, the process of determining the research object and the scope of the research area includes:

[0018] S11, determine the overall research area and research time range, and collect the route network operation data corresponding to each unit time within the research time range, including route distance, route passenger and cargo volume, and airport passenger and cargo throughput;

[0019] S12, analyze the operational structure characteristics of the route network at different time points. The types of operational structure characteristics include point-to-point, hub-and-spoke, and spider-web;

[0020] S13, analyzing the topology of the route network based on the operational structure of the route network, the route network topology including the geometric ordering of the routes and nodes of the route network;

[0021] S14, based on the route network topology, calculate the connectivity of the route network at different time points, and take the airport nodes and routes in the route network with the largest connectivity as the research objects.

[0022] In step S2, the route space-time network graph is denoted as G = (V, EF, d, t); wherein V is the vertex set of the network, which refers to the airport set in the region, and V = {A1, A2, ···, A n}; E is the edge set of the network, which refers to the connection path between regions, E = {e ij},eij For Airport A i With A j The edge between them is 1 if it is navigable, otherwise it is 0. i , A j ∈V; F = {F ijt ,F it}, is the transport volume set, F ijt A i , A j The air traffic flow between at time t, F it For Airport A i Air traffic volume at time t; d = {d ij}, is the distance set, d ij Indicates A i With A j The route distance between them; t is the time dimension, which represents the situation of the route network at different times.

[0023] Furthermore, the following formula is used to calculate the initial spatial weight of each airport node by combining the air transport passenger volume, air passenger throughput and route distance at different times:

[0024]

[0025] Where W ijt is the weight value of time t between location i and location j, F ijt A i , A j The air traffic flow between at time t, F it For Airport A i Airline throughput at time t, d ij A i , A j The route distance between them, k is the distance decay exponent.

[0026] Furthermore, the following formula is used to standardize the initial spatial weights so that the sum of the weights of each row of the spatial weight matrix is ​​1:

[0027]

[0028] Where W it is the sum of the initial weights of each row.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] The spatial weight matrix construction method based on the route space-time network of the present invention combines air transport flow and distance, and adds the influence of time changes, that is, the weight matrix is ​​calculated according to the relevant data at each time point to construct a time-varying spatial weight matrix, which can better describe the temporal dynamic process of spatial relationships, such as the spillover effects caused by flow changes in the short term and the long-term cumulative effects, so that the spatial weight matrix constructed by the present invention can more accurately reflect the contribution of air transport to the economic spillover effects, and have a more accurate description of spatial relationships in the spatial econometric analysis of air transport. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 A flow chart of a method for constructing a spatial weight matrix based on a route spatiotemporal network according to the present invention;

[0032] Figure 2 It is a spatiotemporal network diagram of some routes in the embodiment. DETAILED DESCRIPTION

[0033] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0034] See also Figure 1 The present invention discloses a method for constructing a spatial weight matrix based on a route space-time network, and the method comprises the following steps:

[0035] S1, collect relevant data of the route space-time network, including the time distribution data of the airports, airport types, route distances, and air transport flow, establish the corresponding route space-time network analysis database, and perform data preprocessing to determine the research object and scope, such as all nodes in the study area and the time range.

[0036] In step S1, the process of performing data preprocessing to determine the research object and the scope of the research area includes:

[0037] (1) Determine the overall research area and research time range, such as China's domestic air transport from 2015 to 2019. Collect route network operation data within the research time range, including route distance, route passenger and cargo volumes, and airport passenger and cargo throughput. Convert passenger volume into weight by the number of passengers*0.09, and sum it with cargo and mail volume (in tons) as route transportation volume; the throughput calculation method is similar.

[0038] (2) Analyze the operational structure characteristics of the route network at different time points t (each year), such as point-to-point, hub-and-spoke, or spider-web.

[0039] (3) Analyze the network topology based on the operational structure of the route network, that is, analyze the geometric ordering of the network's routes and nodes as the basis for constructing the route space-time network diagram.

[0040] (4) Based on the topological structure of the route network, the connectivity of the route network at different time points t (each year) is calculated, and the airport nodes and routes in the route network with the largest connectivity are taken as research objects to ensure the completeness of the research scope.

[0041] S2, the route space-time network graph is denoted as G = (V, EF, d, t); where V is the vertex set of the network, which refers to the airport set in the region, V = {A1, A2, ···, A n}; E is the edge set of the network, which refers to the connection path between regions, E = {e ij},e ij For Airport A i With A j The edge between them is 1 if it is navigable, otherwise it is 0. i , A j ∈V; F = {F ijt ,F it}, is the transport volume set, F ijt A i , A j The air traffic flow between at time t, F it For Airport A i Air traffic volume at time t; d = {d ij}, is the distance set, d ij Indicates A i With A j The route distance between them; t is the time dimension, which represents the situation of the route network at different times.

[0042] S3, based on the route space-time network analysis database, combined with the air transport passenger volume, air passenger throughput and route distance at different times, calculate the initial spatial weight of each airport node, and obtain the spatial weight matrix based on the route space-time network after standardization. Specifically, it includes the following steps:

[0043] S31, calculate the initial weights between each node according to the formula, the specific formula is: Where W ijt is the weight value of time t between location i and location j, F ijt A i , A j The number of air transport passengers at time t, F it For Airport A i Air passenger throughput at time t, d ij A i , A j The route distance between them, k is the distance decay index, usually 1 or 2. The left part of the formula represents A i , A jAir transport traffic between the two places accounts for Airport A j The ratio of total flow, the larger its value, the stronger the spatial connection between the two places; the right part is the distance attenuation function, the longer the distance, the smaller the weight value, and the attenuation index k can be adjusted according to the influence of distance in the weight.

[0044] The present invention combines air transport flow and distance, and the weight matrix can more accurately reflect the contribution of air transport to economic spillover effects. Inter-regional connections with larger flows are usually accompanied by more flows of people, goods and information, and the spillover effect is more obvious. Air transport flow can be regarded as a proxy variable for the intensity of interaction between regions. The larger the flow, the stronger the spatial correlation between the two places may be. Therefore, air transport flow becomes an important construction basis in the spatial weight matrix.

[0045] In addition, in spatial analysis, the distance decay effect is a basic assumption, that is, as the distance increases, the mutual influence between regions will gradually weaken. For air transportation, although airplanes shorten the time distance, physical distance still has an important impact on the spillover effect. Shorter route distances often mean more frequent flights, lower transportation costs, and higher economic connections between regions, so the distance factor is introduced into the weight matrix as part of the weight decay.

[0046] S32, spatial weight standardization, let W it is the sum of the initial weights of each row. By standardization, the sum of the weights of each row of the matrix is ​​made 1 to ensure the rationality of the relative weights of the matrix.

[0047] Examples

[0048] The spatial weight matrix construction method of the present invention is further illustrated by an example below.

[0049] First, we select nodes and the time range of data according to the research object. In this example, we select Beijing, Shanghai, Guangzhou, Shenzhen and Chengdu hub airports, and the data from 2015 to 2019 as the basis for calculating the weight matrix. Table 1 is the route network data table. Secondly, we collect the route distances d between these five nodes. ij , the air transport passenger volume between each point from 2015 to 2019 (this example only considers passenger volume, not freight volume). Construct a space-time network of routes, Figure 2The following table shows part of the data. Again, the initial weights between nodes are calculated according to the formula. In this example, we want to observe the influence of the distance factor, so the distance decay index is selected as 1. Table 2 shows the initial weight calculation results. Finally, the matrix is ​​standardized, and the sum of the weight values ​​of each row is set to 1. The standardized weights are obtained according to the calculation formula. Table 3 shows the standardized weight values, which can more scientifically reflect the network correlation of air transportation between the two places.

[0050] The dynamic spatial weight matrix calculated by the above method is more accurate in describing the spatial relationship of each node in the air transport network. Table 4 is the aviation adjacency weight matrix, that is, according to the topological structure of the route network, routes are adjacent, with a value of 1, and no routes are 0. Compared with the results in Table 3, the dynamic spatial weight matrix not only considers the basic situation of the air transport network, calculates the weight value for the air passenger volume and route distance between each node of air transport, but also considers the possible impact of time changes. For example, in Table 3, the spatial weight of Chengdu Airport and other airport nodes is 0.25, but in Table 4, the weight with Shanghai is the largest, and the weight with Shenzhen is the smallest, and the annual changes can also be observed.

[0051] The time-varying dynamic spatial weight matrix constructed by this method can provide a solid foundation for subsequent spatial econometric model analysis.

[0052] Table 1 Route network data table

[0053]

[0054]

[0055] Table 2 Initial weights between nodes

[0056]

[0057] Table 3 Standardized time-varying spatial weight matrix

[0058]

[0059]

[0060] Table 4 Traditional adjacency matrix

[0061]

[0062]

[0063] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0064] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0065] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0066] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0067] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0068] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A method for constructing a spatial weight matrix based on a route spatiotemporal network, characterized in that: The spatial weight matrix construction method comprises the following steps: S1, collect relevant data of route space-time network, establish corresponding route space-time network analysis database, and perform data preprocessing to determine the research object and research area; S2, define the route network composed of each airport node and its connection paths within the study area as an undirected weighted graph, and construct a route spatiotemporal network graph; S3, based on the route space-time network analysis database, combines the air transport volume, airport throughput and route distance at different times to calculate the initial spatial weights between each airport node, and obtains the spatial weight matrix based on the route space-time network after standardization.

2. The method for constructing a spatial weight matrix based on a route spatiotemporal network according to claim 1, characterized in that: In step S1, the relevant data of the route space-time network includes time distribution data of navigable airports, airport types, route distances, air transport flows, and airport throughput.

3. The method for constructing a spatial weight matrix based on a route spatiotemporal network according to claim 1, characterized in that: In step S1, the process of determining the research object and the scope of the research area includes: S11, determine the overall research area and research time range, and collect the route network operation data corresponding to each unit time within the research time range, including route distance, route passenger and cargo volume, and airport passenger and cargo throughput; S12, analyze the operational structure characteristics of the route network at different time points. The types of operational structure characteristics include point-to-point, hub-and-spoke, and spider-web; S13, analyzing the topology of the route network based on the operational structure of the route network, the route network topology including the geometric ordering of the routes and nodes of the route network; S14, based on the route network topology, calculate the connectivity of the route network at different time points, and take the airport nodes and routes in the route network with the largest connectivity as the research objects.

4. In step S2, the route space-time network graph is denoted as G = (V, EF, d, t); where V is the vertex set of the network, which refers to the airport set in the region, and V = {A1, A2, ···, A n }; E is the edge set of the network, which refers to the connection path between regions, E = {e ij },e ij For Airport A i With A j The edge between them is 1 if it is navigable, otherwise it is 0. i , A j ∈V; F = {F ijt ,F it }, is the transport volume set, F ijt A i , A j The air traffic flow between at time t, F it For Airport A i Air traffic volume at time t; d = {d ij }, is the distance set, d ij Indicates A i With A j The route distance between them; t is the time dimension, which represents the situation of the route network at different times.

5. The method for constructing a spatial weight matrix based on a route spatiotemporal network according to claim 1, characterized in that: Combining the air transport passenger volume, air passenger throughput, airport throughput and route distance at different times, the following formula is used to calculate the initial spatial weight between each airport node: Where W ijt is the weight value of time t between location i and location j, F ijt A i , A j The air traffic flow between at time t, F it For Airport A i Airline throughput at time t, d ij A i , A j The route distance between them, k is the distance decay exponent.

6. The method for constructing a spatial weight matrix based on a route spatiotemporal network according to claim 1, characterized in that: The following formula is used to standardize the initial spatial weights so that the sum of the weights of each row of the spatial weight matrix is ​​1: Where W it is the sum of the initial weights of each row.

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