KR101721114B1 - Method for Determining the Size of Grid for Clustering on Multi-Scale Web Map Services using Location-Based Point Data - Google Patents

Abstract

The present invention relates to a method capable of determining a proper size of a grid while minimizing a modifiable areal unit problem (MAUP) when clustering a point data including positional information on a multi-scale web map. That is, the present invention considers quantitative aspects and qualitative aspects in clustering, and as a result, it is possible to minimize the influence of the MAUP. In order to consider quantitative aspects, a proper number of grids to be expressed for each scale may be calculated by using Topfers Radical Law, which is one of map generalization operators. In order to consider qualitative aspects, a size of grids, which can maintain the intrinsic distribution characteristic of the data even during the clustering process is performed for each scale, is determined by using Morans I, which is one of the global spatial relevance indexes. Thus, it is possible for users of a map service to obtain the same visual information about the distribution characteristic of the original data even when the scale of the map changes and the influence of the MAUP can be minimized.

Description

[0001] The present invention relates to a method for determining a size of a grid for clustering point data including position information on a multi-scale web map,

The present invention relates to a method for minimizing a Modifiable Areal Unit Problem (MAUP) when clustered point data including positional information is clustered on a multi-scale web map by scale. More specifically, Is a method for determining the size of a grid using Topfer's Radical Law, which is a map generalization equation, and Moran's I , which is a spatial autocorrelation measure index, in consideration of qualitative aspects in order to consider quantitative aspects in clustering.

As the use of mobile smart devices with GPS is becoming commonplace, location-based social networks (LBSN) services such as Twitter, Facebook, Instagram are being actively used.

In order to effectively visualize such data on a multi-scale map service, there is a need to cluster and represent points. The point data generated through the LBSN service is especially concentrated in a specific area such as a downtown area where people are more crowded than conventional point data such as pollution sources and weather observation points, and a large amount of data is generated in real time. Therefore, in order to efficiently display the data on the map, a clustering technique capable of quick calculation must be applied, and a lattice-based clustering technique is appropriate in this respect. In this method, the target space is composed of a constant grid structure and all the clustering processes are executed in the corresponding grid. Since the method is independent of the number of objects and depends on the number of pre-calculated grids, the calculation amount is low and the processing speed is high .

Furthermore, in order to apply the grid-based clustering technique to the data generated by the LBSN service, the appropriate grid size must be determined according to the scale of the map. Since there is no standard for this, The researcher 's subjectivity must be intervened. At this time, a MAUP occurs in which the analysis result is changed according to the method of setting the spatial unit. The problem of building a new unit of space is closely related to geographical separation, which means that small scale areas are merged into large scale areas. However, it is possible to divide the same area into various ways according to the way of merging. That is, it is possible to generate the same area for various scales by the joint style, or to create an area having different compartments within the same scale. The problem that arises in the process of merging is referred to as MAUP, which is inevitable when dealing with an area-based spatial unit. Therefore, the influence of MAUP must be considered when using the grid-based clustering method.

Journal of the Korean Geographical Society. 6 (1). pp. Point Mapping Generalization of Digital Topographies Using Point Pattern Analysis. Ryu

SUMMARY OF THE INVENTION In view of the foregoing, it is an object of the present invention to provide a method and apparatus for determining a proper grid size while minimizing a MAID (Modified Arial Problem) The purpose of this is to present a method.

(A) the point data collection module of the user terminal collects data using an open application programming interface (API) provided by a location-based social network (LBSN) service; Collecting point data including location information of a desired area; (b) the current lean analysis module of the user terminal identifies and analyzes the original spatial distribution characteristics of the point data collected using the Nearest Neighbor Index (RN) of Nearest Neighbor Analysis (NNA) step; (c) calculating a number of a plurality of clusters according to a scale value (C) according to a scale value using Topfer's Radical Law, by the map generalization operation module of the user terminal; (d) The control module of the user terminal generates point data including positional information collected for a region desired to be collected in the step (a), grid data for various sizes for the corresponding range, Performing a Spatial Join operation on the data; (e) the control module of the user terminal calculates the total number of grids excluding the grids not combined with any point data in the step (d); (f) The control module of the user terminal determines whether the number of grids calculated in the step (e) is the same among a plurality of grid numbers for each scale and C value derived in the step (c) If there is a value, the operation is repeated until the number of grids in the step (e) that is equal to the number of all the plurality of grids for each scale and C value is obtained. If there is no value, the process returns to the step (d) Repeatedly performing the spatial combining operation and the step (e) on the grid data and the point data of different sizes; (g) analyzing a distribution characteristic of the grid size distribution characteristic of the user terminal by using the Moran's I , analyzing distribution characteristics of the result performed in the step (f) for each scale and C value; (h) the control module of the user terminal compares the distribution characteristic analysis result of the step (g) according to the original distribution characteristic of the point data derived in the step (b) and the coefficient value (C) (i) the control module of the user terminal finally deriving a coefficient value (C) that best preserves the original distribution characteristic of the point data analyzed in the step (h) It is characterized by providing a method of determining the size of a grid in order to cluster point data on a multi-scale web map.

In the present invention, (j) the control module of the user terminal repeats the steps (d) to (i) for all the scales required for clustering for each count value C, And calculating the length (the size of the lattice) of one side of the lattice according to the derived C value.

Further, in the present invention, in the step (b), the latest Lindsey number (R)

는 각각의 포인트 데이터로부터 가장 가까운 포인트 데이터까지의 거리의 평균이고,

는 i포인트 데이터로부터 가장 가까운 포인트 데이터까지의 거리이며, n은 전체 포인트의 개수이고,

는 CSR 하에서 기대되는 최근린 거리이며, A는 수집을 원하는 지역의 전체 면적이다.)을 이용하여 도출할 수 있다.(here,

Is the average of the distance from each point data to the closest point data,

Is the distance from the i point data to the closest point data, n is the number of all points,

Is the recent lean distance expected under CSR, and A is the total area of the area you want to collect).

Also, in the present invention, in the step (c), Topfer's Radical Law may be expressed by the following equation,

는 결과 지도의 포인트 수이고,

는 입력 지도의 포인트 수이며,

는 입력 지도의 축척계수이고,

는 결과 지도의 축척계수이며, 그리고 C 는 심볼계수이다.)을 이용하여 도출할 수 있다.(here,

Is the number of points in the result map,

Is the number of points in the input map,

Is the scale factor of the input map,

Is the scale factor of the result map, and C is the symbol coefficient).

Further, in the present invention, in the step (g), Moran's I is calculated by the following equation

는 공간가중행렬이며,

는 i번째 변수(i번째 격자의 Joint_Count 값)이고,

는 x의 평균이다.)을 이용하여 도출할 수 있다.(Where n is the number of all spatial units made up of i and j ,

Is a space weighting matrix,

Is the i- th variable (the Joint_Count value of the i-th grid)

Is the average of x ).

According to the present invention, when a point data including position information is cluster-based on a multi-scale map, a method of determining an appropriate size of a grid is proposed. In the clustering, quantitative and qualitative aspects , Which in turn can minimize the effect of space unit randomness problem (MAUP). That is, in order to consider the quantitative aspect, it is necessary to calculate the number of appropriate grids to be displayed for each scale by using Topfer's Radical Law, one of the map generalization operators, and to calculate the qualitative aspect, The user of the map service can obtain the distribution characteristic of the original data even when the scale of the map is changed by deriving the size of the grid capable of maintaining the distribution characteristic of the original data even while the clustering process is performed by using the Moran's I , It is possible to obtain not only the same visual information but also the effect of the problem of spatial randomness (MAUP).

1 illustrates an exemplary point data generated through a location-based social network service in the present invention.
Figure 2 illustrates clustering and clustering of point data in the present invention.
3 illustrates an example of scale-by-scale appearance in which markers are not clustered on a map in the present invention.
FIG. 4 shows a comparison between before and after clustering for effectively visualizing point data on a multi-scale web map in the present invention.
FIG. 5 is a diagram exemplarily showing a scale for each zoom level according to the present invention. FIG.
Figure 6 is an illustration of the scale effect and the compartment effect in the problem of space unit randomness (MAUP) in the present invention.
7 is a diagram illustrating a system for implementing a method of determining a size of a grid to cluster point data including positional information on a multi-scale web map according to an embodiment of the present invention.
8 is a flowchart illustrating a method of determining a size of a grid to cluster point data including positional information according to the present invention on a multi-scale web map.
9 illustrates an exemplary calculation of a plurality of points per zoom level according to the C value in the present invention.
10 illustrates an exemplary spatial coupling operation in the present invention.
11 illustrates an example of the number of clusters and the number of clusters to be represented by clusters according to the spatial combining operation in the present invention.
12 shows an exemplary spatial distribution in the present invention.
13 is a diagram showing a spatial weighting matrix for spatial distribution in the present invention.

Hereinafter, a method for determining a size of a grid for clustering point data including positional information according to the present invention on a multi-scale web map will be described in detail with reference to the accompanying drawings.

First, specific terms used in the present invention will be defined.

In FIG. 1, data generated through a Location-Based Social Network (LBSN) service such as Twitter, Instagram, and PayBook is referred to as Point Data. Furthermore, LBSN service users can include location information (x, y coordinates) along with their own articles by using the geotagging function. Therefore, the data generated through the service is a spatial object having attributes of points can see. At this time, the location information may be the current location of the user, the location where the uploaded photograph was taken, or the location designated by the user. In addition, point data is mainly used, and point data can be used in various fields. Typical examples are location of pollution sources, weather observation points, and population. Furthermore, as smart devices such as smart phones were developed in the early 2000s, point data generated through LBSN services such as Twitter, Instagram, and Facebook newly appeared, and such LBSN point data is compared with existing point data It is concentrated in the same places as the downtown area where people are attracted to many people, and a large amount of data is generated in real time.

2, the original meaning of clustering is to group physical or abstract objects into similar objects, which are similar to objects in the same cluster (cluster), and have different characteristics from those of other clusters I have. In the present invention, among various clustering techniques, a grid-based clustering technique is used, which expresses points included in the same grid by grouping them into one cluster. Moreover, as a difference between clustering and clustering, clustering means the process of clustering, and clustering means the result of clustering. Therefore, the present invention is based on a lattice-based clustering technique, and since the lattice itself is treated as a cluster, the cluster means a unit lattice.

Also, in Fig. 3, clustering in the map field is mainly used for visual purposes. For example, the following (DAUM) agora and netizens voluntarily produced 'Sufi Damage Map' based on SNS and Internet bulletin board based on the location information of Google Maps, Although useful as a shared platform, markers on the map were packed or unclustered without clustering, making it difficult to intuitively grasp accurate information under small scale.

Therefore, clustering is essential to effectively visualizing point data on a multi-scale web map. This can be seen from FIG. 4 with reference to a photograph of the world map before and after clustering.

Next, in FIG. 5, a scale (by scale) according to the zoom level of the map is displayed, but it is not necessary to perform the clustering operation for all the zoom levels. For example, if clustering is performed for Seoul, clustering is meaningless because zoom levels 0 to 4 are too small when viewed from the Seoul area, and zoom levels 17 to 19 are relative It may be said that it is more appropriate to express it in the form of data originally, that is, in the form of individual points, rather than being represented by clustering. Finally, zoom levels 5 through 16 are clustering targets. Therefore, the range of the zoom level to be clustering depends on the object and purpose of the experiment, and may be determined by the operator.

In addition, since LBSN data including position information such as tweeter, Instagram, and Facebook includes coordinate information on a place referred to by the corresponding data, it takes the form of a point when it is expressed in space. In order to analyze point data collected in a certain spatial range, for example, Seoul, based on a specific spatial unit, that is, an administrative district or a grid, the original data of the point attribute should be combined with the data of the polygon attribute do. At this time, the researcher must select a space unit to be used for analysis or create a new space unit by manipulating an existing space unit. Since there is no definite criterion for this, the researcher must judge it.

The problem of establishing a new spatial unit is closely related to the regionalization, which means that the actual small scale area is spatially aggregated into a large scale area. However, the same area can be divided in various ways according to the aggregation scheme. In other words, it is possible to create regions of various scales according to the joint style, or to create regions having different divisions on the same scale. The problem that arises in the process of this integration is called the Modifiable Areal Unit Problem (MAUP).

Thus, the MAUP affects the analysis results depending on how the spatial unit used for the analysis is set. Spatial units can be merged or modified to create different scales or segments. That is, MAUP has two viewpoints: a scale effect and a zoning effect.

Further, in FIG. 6, the scale effect means that the results are different according to the scale when the analysis is performed on the spatial units of different scales, and the division effect is different results .

7 is a system for implementing a method of determining a size of a grid in order to cluster point data including positional information on a multi-scale web map in the present invention. The user terminal 10 includes a PC, a tablet, a smart phone, and the like, such as a desk top or a notebook computer. The user terminal 10 is installed with a clustering application. The clustering application includes a control module 11, a point data collection module 12, a current lean analysis module 13, a map generalization calculation module 14 and a grid size distribution characteristic analysis module 15. The user terminal 10 is connected to a location based social network (LBSN) 20 service such as Twitter, Instagram, Facebook, etc. through a communication network. The clustering application is accomplished by a commercial program, ArcMap, or a program that directly codes the algorithm through a programming language.

Next, a method for determining the size of a grid to cluster point data including positional information according to the present invention on a multi-scale web map will be described with reference to the flowchart of FIG.

)과 완전한 랜덤 분포(Complete Spatial Randomness, CSR) 하에서 기대되는 최근린 거리(

)를 비교한다. 이때, 기대되는 최근린 거리(

)에 대한 관측된 평균 최근린 거리(

)의 비율을 R이라고 한다. 이러한 최근린지수(R)는 다음의 수학식 1과 같다.First, the point data collection module 12 of the user terminal 10 uses the open application programming interface (API) provided by the location-based social network (LBSN) The point data is collected (S1). Then, the recent lean analysis module 13 of the user terminal 10 grasps the inherent spatial distribution characteristics of the collected point data using the Nearest Neighbor Index (RN) of the nearest neighbor analysis (NNA) (S2). The analyzed result is used in the next step (S8). The recent lean analysis is an analysis method for grasping the spatial distribution characteristic of point data. The average value of the distance from each point data to the closest point data (

) And the expected lean distance under Complete Spatial Randomness (CSR)

). At this time, the expected lean distance (

The observed mean recent lean distance (

) Is referred to as R. This latest Lindis number (R) is given by the following equation (1).

는 각각의 포인트 데이터로부터 가장 가까운 포인트 데이터까지의 거리의 평균이고,

는 i포인트 데이터로부터 가장 가까운 포인트 데이터까지의 거리이며, n은 전체 포인트의 개수이고,

는 CSR 하에서 기대되는 최근린 거리이며, A는 수집을 원하는 지역의 전체 면적이다.here,

Is the average of the distance from each point data to the closest point data,

Is the distance from the i point data to the closest point data, n is the number of all points,

Is the nearest lean distance expected under CSR, and A is the total area of the area you want to collect.

R is a value indicating how much the actual spacing of points is different from the spacing in the random distribution pattern. If R is 1, it is a complete random distribution type. If R is greater than 1, , And if R is less than 1, the clustered distribution type is interpreted.

)를 계산한다. Topfer's Radical Law는 다음의 수학식 2와 같다.Next, the map generalization operation module 14 of the user terminal 10 calculates the number of clusters according to the count value C by scale using Topfer's Radical Law (S3). That is, the map generalization operation module 14 increases the symbol coefficient ( C ) value of Topfer's radical law, which is a map generalization operation expression, from 0.1 to 1.9 in increments of 0.1 in 19 steps. In each case, the number of appropriate points (

). Topfer's Radical Law is expressed by Equation 2 below.

는 결과 지도의 포인트 수이고,

는 입력 지도의 포인트 수이며,

는 입력 지도의 축척계수이고,

는 결과 지도의 축척계수이며, 그리고 C 는 심볼계수이다. 바람직하게는 입력 지도의 포인트 수는 (S1) 단계에서의 수집된 포인트 데이터 수이고, 입력 지도의 축척은 사용자가 선택한 줌 레벨의 범위 중 가장 대축척이며, 그리고 입력 지도는 클러스터링을 하지 않기 때문에 결과 지도의 축척계수는 최대 19개가 될 수 있다. 즉 지도의 축척계수는 구글 맵(Google Maps)에서 줌 레벨별로 제공하는 축척값을 이용할 수 있으며, 이는 도 5에 도시되었다. 이를 이용하여 클러스터링이 필요한 축척에 대한 범위를 설정한다. 더욱이 C값의 범위와 지도의 축척은 사용자의 선택에 따라 조절이 가능하다. 다시 말해,

와

값은 도 5의 스케일을 이용한다.here,

Is the number of points in the result map,

Is the number of points in the input map,

Is the scale factor of the input map,

Is the scale factor of the result map, and C is the symbol coefficient. Preferably, the number of points in the input map is the number of collected point data in step (S1), the scale of the input map is the largest of the range of the zoom level selected by the user, and since the input map does not clustering, Can be a maximum of 19 scale factors. That is, the scale factor of the map can use a scale value provided for each zoom level in Google Maps, which is shown in FIG. Using this, we set the scope for the scale that needs clustering. Furthermore, the range of C values and the scale of the map can be adjusted according to the user's choice. In other words,

Wow

The values use the scale of FIG.

Figure 9 is an exemplary illustration of the calculation of a plurality of points per zoom level according to the value of C; For example, when the number of points seen at zoom level 19 is 1,000, the number of appropriate points to be seen at zoom level 15 can be calculated using Equation (2) as follows (when C = 1).

)를 축척별(줌 레벨별)로 도출되어야 할 적절한 클러스터(격자)의 개수(n)로 간주한다.That is, when the number of points seen at zoom level 19 is 1,000, the appropriate number of points to show at zoom level 15 is 250. At this time, the number of derived points (

) As the number ( n ) of appropriate clusters (grids) to be derived by scale (per zoom level).

In the present invention, it is important to maintain the original distribution characteristics even when the point data is clustered according to the zoom level. Therefore, the number of appropriate points calculated for each zoom level is regarded as the number ( n ) of clusters (grids). In other words, what is sought in the present invention is to determine the size of a cluster (grid), i.e., the length l of one side, from which the number n of appropriate clusters derived from the step S3 is derived will be.

Therefore, if we know the number, we can say that we can not know its size, but this is not a matter of simple substitution. This is because not all clusters (grids) are displayed on the map. In some cases, there may be a grid that does not need to be represented as a cluster. This will be described in step S4 and step S5, respectively.

The control module 11 of the user terminal 10 generates point data including positional information collected for a region desired to be collected in the step S1 and lattice data for various sizes for the corresponding range, Spatial Join operation is performed on the lattice data (S4). At this time, various sizes do not mean that they are generated according to the scale, but mean that they generate grids of various sizes as random as possible out of scale. This grid data is different from the grid for the point in step (S3).

In FIG. 10, it can be seen that 'Join_Count' is generated when the attribute table of the point + lattice that overlaps the point data and the lattice data is generated. This is inevitably generated when the spatial join operation is used. And the number of point data.

In addition, the control module 11 of the user terminal 10 calculates the total number of grids excluding the grids not combined with any point data at step S4 (S5). That is, in step (S5), the total number of grids excluding the grid not combined with any point data is calculated in step S4, meaning that the value of Join_Count in the point + grid attribute table is The number of grid points of 0 is calculated. The reason is that a grid not combined with any point does not need to be represented by a cluster and is not included in the number of appropriate clusters derived in the step S3.

The control module 11 of the user terminal 10 calculates the number of grids excluding the grid with Join_Count equal to 0 and the number of grids according to the scale and C value derived in the step (S3) If there is the same value, it is judged whether or not there is the same value. If there is the same value, it is judged whether or not the same value exists (S5 If there is no identical value, the process returns to step S4 to repeat the spatial combining operation on the grid data and the point data of different sizes and the step (S5) repeatedly until the number of grids in the step (S6). Thus, the size of the grid data for all the grid numbers for each scale and C value is determined.

On the other hand, in FIG. 11, the steps (S3) to (S6) are explained more easily. That is, in step (S3), the number (n) of clusters (grids) for each zoom level (scale) according to the C value is calculated. For example, if the C value is 19 and the zoom level is 10 in total, a total of 190 n is calculated. If the number of grids is nine when the pointer data and the lattice data are computed by spatial combination at step S4 and step S5, the number of grids whose Joint_Count is 0 as a result of spatial combination is 2, The number of grids is seven. Therefore, if the number n of clusters coincides with the number of grids to be represented by clusters in step S6, step S7 is performed. Otherwise, steps S4 and S5 are repeated.

If the number of grids in step S5 is equal to the total number of grids for each scale and C value in step S3, the grid size distribution characteristic analysis module 15 of the user terminal 10 calculates Moran's I is used to analyze the distribution characteristics of the results performed in step S6 for each scale and C value (S7). That is, the user terminal 10 analyzes the distribution characteristics of each of the scales and the C values for the result of the step (S6) using Moran's I in the lattice size distribution characteristic module 15. [ Therefore, Moran's I can be calculated as shown in Equation 3 below.

는 공간가중행렬이며,

는 i번째 변수(i번째 격자의 Joint_Count 값)이고,

는 x의 평균이다.Where n is the number of all spatial units made up of i and j ,

Is a space weighting matrix,

Is the i- th variable (the Joint_Count value of the i-th grid)

Is the average of x .

는 도 13의 공간가중행렬로, 도 12의 공간분포의 예시에서, 이웃하면 1 아니면 0의 값을 가지며, 자기 자신은 이웃으로 취급하지 않기 때문에 대각선의 값은 0이 된다. Moran's I 는 공간적 자기상관성을 측정하기 위한 통계량으로, 거의 -1과 1 사이의 값을 가지며, -1에 가까울수록 분산된 분포, 0에 가까울수록 랜덤한 분포, 1에 가까울수록 클러스터된 분포를 보인다고 해석한다.At this time,

Is a space weighting matrix of FIG. 13, in the example of the spatial distribution in FIG. 12, has a value of 1 or 0 in the neighborhood, and the value of the diagonal line is 0 because it does not treat itself as a neighbor. Moran's I is a statistic for measuring spatial autocorrelation. It has a value between -1 and 1, and the closer to -1, the more scattered, the closer to 0, the closer to 1, the more clustered Interpret.

Next, the control module 11 of the user terminal 10 analyzes the distribution characteristics of the step S7 according to the original distribution characteristics of the point data derived in the step S2, (S8). Then, the control module 11 of the user terminal 10 finally derives a coefficient value C that best maintains the original distribution characteristic of the point data analyzed in the step S8 (S9). Therefore, the original distribution characteristic of the point data analyzed using the R value of the NNA at step S2 is compared with the analysis result through Moran's I at step S7. For example, if the R value is smaller than 1, since the distribution of the point data is originally meant to be clustered, the value of Moran's I calculated in the step (S7) It will be done. Therefore, the final result is the length ( l ) of one side of the appropriate cluster (grid) for each scale according to the determined C value. That is, the control module 11 of the user terminal 10 repeats the steps of (S4) to (S9) for all the scales required for clustering for each coefficient value C, (The lattice data of step (S4) obtained in the step (S6)) according to the value of C, that is, the length of one side of the lattice, in other words, the size of the lattice. This minimizes the effect of the MAUP.

While the invention has been shown and described with respect to the specific embodiments thereof, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined by the appended claims. Anyone with it will know easily.

10: user terminal 11: control module 12: point data collection module 13: current lean analysis module 14: map generalization calculation module 15: lattice size distribution characteristic analysis module 20: location based social network (LBSN)

Claims (5)

(a) The point data collection module of the user terminal uses the open application programming interface (API) provided by the location-based social network (LBSN) Collecting data;
(b) the current lean analysis module of the user terminal identifies and analyzes the original spatial distribution characteristics of the point data collected using the Nearest Neighbor Index (RN) of Nearest Neighbor Analysis (NNA) step;
(c) calculating a number of a plurality of clusters according to a scale value (C) according to a scale value using Topfer's Radical Law, by the map generalization operation module of the user terminal;
(d) The control module of the user terminal generates point data including positional information collected for a region desired to be collected in the step (a), grid data for various sizes for the corresponding range, Performing a Spatial Join operation on the data;
(e) the control module of the user terminal calculates the total number of grids excluding the grids not combined with any point data in the step (d);
(f) The control module of the user terminal determines whether the number of grids calculated in the step (e) is the same among a plurality of grid numbers for each scale and C value derived in the step (c) If there is a value, the operation is repeated until the number of grids in the step (e) that is equal to the number of all the plurality of grids for each scale and C value is obtained. If there is no value, the process returns to the step (d) Repeatedly performing the spatial combining operation and the step (e) on the grid data and the point data of different sizes;
(g) analyzing a distribution characteristic of the grid size distribution characteristic of the user terminal by using the Moran's I , analyzing distribution characteristics of the result performed in the step (f) for each scale and C value;
(h) the control module of the user terminal compares the distribution characteristic analysis result of the step (g) according to the original distribution characteristic of the point data derived in the step (b) and the coefficient value (C)
(i) the control module of the user terminal finally deriving a coefficient value (C) that best preserves the original distribution characteristic of the point data analyzed in the step (h) A method for determining the size of a grid to cluster point data on a multi-scale web map.
2. The method of claim 1, wherein the control module of the user terminal repeats the process of (d) to (i) And calculating a length of one side of the lattice (size of the lattice) corresponding to the derived C values, wherein the step of calculating the size of the lattice in order to cluster the point data including the position information on the multi- / RTI >
2. The method according to claim 1, wherein, in step (b), the latest Lindsey number (R)

(here,

Is the average of the distance from each point data to the closest point data,

Is the distance from the i point data to the closest point data, n is the number of all points,

Is the latest lean distance expected under the CSR, and A is the total area of the area desired to be collected). In order to cluster the point data including the position information on the multi-scale web map, How to determine.
The method of claim 1, wherein, in step (c), Topfer's Radical Law is expressed by the following equation:

(here,

Is the number of points in the result map,

Is the number of points in the input map,

Is the scale factor of the input map,

Is the scale factor of the result map, and C is the symbol factor). A method of determining the size of a grid to cluster point data including position information on a multi-scale web map.
2. The method of claim 1, wherein in step (g), Moran's I is calculated by the following equation:

(Where n is the number of all spatial units made up of i and j ,

Is a space weighting matrix,

Is the i- th variable (the Joint_Count value of the i-th grid)

Is the average of x .) A method for determining the size of a grid to cluster point data containing position information on a multi-scale web map.

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