CN111651502A - An urban functional area identification method based on multi-subspace model - Google Patents

Abstract

The invention discloses a method for identifying urban functional areas based on a multi-subspace model, comprising the following steps: acquiring taxi trajectory data and check-in data in a research area; constructing a partition-oriented time series feature matrix C based on visiting purposes; inputting time series features Matrix C to sparse subspace clustering algorithm, calculate the corresponding relationship between geographic units and urban functional areas; obtain the salient feature locations of each functional area, and then identify the main functions of each functional area. The method of the present invention The present invention utilizes the human activity information provided by the geographic big data, and overcomes the defects existing in the prior art based on the multi-subspace model, can more accurately identify urban functional areas, and analyze each functional area based on the geometric properties of the subspaces The uniqueness and abundance of urban functional areas provide precise and quantitative indicators for the management and development of urban functional areas.

Description

An urban functional area identification method based on multi-subspace model

technical field

The invention belongs to the technical field of geographic space information identification, relates to a method for identifying urban geographic information, and in particular relates to a method for identifying urban functional areas based on a multi-subspace model.

Background technique

Urban spatial structure is a core research content of urban geoinformatics, and it is also a concentrated reflection of the relationship between human and land, because urban space has an impact on human production and activities when it is affected by human activities. , small to travel, place recommendation. In the analysis of urban spatial structure, the distribution of urban functional areas is the result presented in geographic space under the influence of many factors.

There are many methods for analyzing urban functional areas, such as social surveys, but it is time-consuming and laborious to obtain data, and may be greatly affected by subjective factors during analysis. The biggest disadvantage is that it cannot directly reflect the key factor of urban development-human Activity. With the rapid development of mobile communication, Internet and satellite positioning technology, a series of electronic footprints are generated by mobile devices with positioning function. These electronic footprints are real records of urban residents' activities, which enable us to explore urban functional areas from the perspective of human activities. . There are existing methods using social media check-in data, mobile phone data, and taxi trajectory data to detect urban functional areas.

The existing technology is not yet perfect in the models used to analyze the data. The general steps are as follows. First, when processing geospatial big data, after mapping the time series feature information of human activities to the manually divided geographic units, each geographic unit can be expressed by a vector, and the information is stored in a high-dimensional in vector space. Then, they characterize these geographic units through some algorithms such as singular value decomposition, latent semantic analysis, latent Dirichlet and other analytical methods. Finally, clustering is carried out by the similarity of feature expression of geographic units, each clustering result represents a functional area, and the distribution of urban functional areas is obtained. However, these models have the following shortcomings.

First, in the process of feature expression, some algorithms first make strict assumptions about the features, such as the sample only has one set of features or obeys the same distribution. After the sample is characterized, it will be reduced from a high-dimensional space to a low-dimensional subspace, and these algorithms can be called single subspace algorithms. The strict assumption of the monadic space algorithm is easy to obtain feature patterns, and the distribution of functional areas can be obtained by clustering according to the relationship between samples and features, but if the weight of sample information is small, it will be marginalized after feature expression. , resulting in inaccurate clustering results. And there are feature differences between functional areas, and each functional area cannot be described concisely and accurately by using the same set of features. When the data is too large and the feature pattern is too complex, the assumption of the feature pattern in the monad space model will limit the feature mining. So they can't handle more complex data.

Second, these models ignore the geometric meaning of vector spaces. The geometric properties of subspaces are related to the characteristics of urban functional areas, and the prior art ignores the discussion and consideration of this.

SUMMARY OF THE INVENTION

In view of this, the purpose of the present invention is to provide a method for identifying urban functional areas based on a multi-subspace model. The present invention utilizes the human activity information provided by geographic big data, and the multi-subspace-based model overcomes the defects existing in the prior art. , which can more accurately identify urban functional areas.

The purpose of the present invention is to achieve this, a method for identifying urban functional areas based on a multi-subspace model, comprising the following steps:

Step 1: Obtain the taxi trajectory data and check-in data in the research area;

Step 2, constructing a partition-oriented time series feature matrix C based on the visiting purpose;

Step 3, input the time series feature matrix C to the sparse subspace clustering algorithm, and calculate the corresponding relationship between the geographic unit and the urban functional area;

Step 4, obtain the salient feature locations of each functional area, and then identify the main function of each functional area.

Specifically, the construction process of the time series feature matrix C described in step 2 includes the following steps:

Step 201, dividing the research area to obtain N geographic units;

Step 202, preprocessing the taxi trajectory data, removing abnormal points, extracting the end point and arrival time of each trip, and mapping the end point with the geographic unit to obtain the visit record of the geographic unit;

Step 203, matching the check-in data record with the visit record of the geographic unit, and classifying the purpose of each visit;

Step 204, constructing a time series feature matrix C with M rows and N columns, which represents the human activity dynamics carried by the geographic unit within a period of time, where M=T×D, T represents the number of divided time periods, and D represents the number of categories for visiting purposes. , each column in C represents the number of people visiting the corresponding geographic unit for different purposes in different time periods.

Specifically, the sparse subspace clustering algorithm described in step 3 includes the following steps:

Step 301, solve the coefficient matrix Z, the size is N×N, the matrix Z needs to satisfy the minimization under the constraint of l ₁ :

CZ=C, Z _ii =0

表示l₁范数，l₁范数最小化使得系数矩阵Z稀疏，从而迫使每个地理单元的时序特征仅需用同一子空间中其他地理单元的时序特征的线性组合来表示；in

Represents the _l1 norm, and the minimization of the _l1 norm makes the coefficient matrix Z sparse, thus forcing the time series feature of each geographic unit to be represented only by a linear combination of the time series features of other geographic units in the same subspace;

Step 302, then use the coefficient matrix to establish a data similarity matrix W=|Z|+|Z| ^T , the size of W is N×N, and the value in the matrix is the similarity in time series characteristics between the geographic units corresponding to the index Spend;

The similarity matrix W is a block diagonal matrix, that is, only the main diagonal has non-zero sub-matrices, and the rest of the sub-blocks are zero matrices. Each non-zero sub-matrix is a subspace, and the same subspace contains multiple Geographical units with very similar time series characteristics, geographical units in different subspaces have large differences in time series characteristics, so the subspace is the urban functional area to be detected;

Step 303: Calculate the number of subspaces by using the normalized Laplacian matrix L of the similarity matrix W, L=ID ^{-1/ 2} WD ^-1/2 , where I is the identity matrix, D=∑ _i W _ij , Arrange the eigenvalues of L in ascending order, and calculate the difference λ _{k+1 -} λ _k of each two adjacent eigenvalues. The k corresponding to the largest difference is the number of subspaces to be sought, that is, the number of urban functional areas to be detected. number;

In step 304, the K-means clustering method is used for the similarity matrix W, and the number of clusters is set to k obtained in step 303, and the corresponding relationship between geographic units and k categories, that is, the corresponding relationship with k urban functional areas, is completed. Urban functional area detection.

Specifically, obtaining the salient feature locations of each functional area described in step 4 includes: extracting _a subspace matrix S1 corresponding to each urban functional area from the similarity matrix W generated in step 302 by using the corresponding relationship in step 304 , ..., S _i , ..., S _k , and perform principal component analysis, the obtained eigenvectors [e ₁ , e ₂ , ..., e _p , ..., e _M ] _i are called S The characteristic location of _i , the _eigenvectors [e ₁ , e _{2 , .}

Specifically, the identification of the main function of each functional area includes: transforming each salient feature location of each functional area into a matrix with D rows and T columns, each row indicating that the feature location is in T time periods with The main activity pattern of the functional area is obtained by changing the activity level for the purpose of D, and the function area is marked with the most active function in the main activity pattern to complete the identification of the urban functional area.

Further, the method for identifying urban functional areas further includes the following steps:

Step 5, calculate the similarity of each functional area;

Step 6: Calculate the uniqueness of each functional area, and sort each functional area according to the uniqueness.

Specifically, the calculation of the similarity of the functional areas is calculated according to the main angle between the corresponding subspaces, and the similarity aff(S _k , S _l ) of the corresponding subspaces _Sk and S _l of any two functional areas Calculated as follows,

是

的第i个最大奇异值，U^k和U^l分别是S_k和S_l的正交基，

是子空间之间的主要角，d_k∧d_l表示S_k和S_l的空间维数d_k与d_l中的较小值；in,

Yes

The ith largest singular value of , U ^k and U ^l are the orthonormal basis of S _k and S _l , respectively,

is the main angle between the subspaces, d _k ∧ d _l represents the smaller of the spatial dimensions d _k and d _l of S _k and S _l ;

Specifically, the uniqueness of the functional areas is inversely proportional to the similarity. If the similarity between the subspaces is high, the functions of the corresponding functional areas will be very similar, and the uniqueness of the functional areas is low. The formula for calculating the _uniqueness of region Si is as follows:

where k is the total number of functional areas, and S _{-i represents} the functional areas other than Si.

Further, the method for identifying urban functional areas further includes the following steps:

Step 7, calculate the abundance of each functional area, and sort each functional area according to the described abundance.

Specifically, the abundance of the functional areas is related to the reconstruction error of the salient feature locations of each functional area, which is calculated as follows:

是由S_i的显著特征地点重构的矩阵，|| ||_F表示矩阵的弗罗贝尼乌斯范数。where C(S _i ) is a matrix consisting of primitive vectors belonging to subspace S _i ,

is the matrix reconstructed from the _salient feature locations of Si, and || || _F denotes the Frobenius norm of the matrix.

The method of the present invention proposes a model based on multiple subspaces, and considers that urban functional areas have multiple sets of characteristics. When the spatiotemporal activity information of geographic units is expressed by vectors, the vector samples are located in the high-dimensional space formed by the joint subspace, and are located in the same subspace. The dynamic characteristics of human activities carried by the geographical units of the space are similar, and can be clustered into a functional area. The identification of urban functional areas can be realized by finding subspaces, and the uniqueness and abundance of each functional area are analyzed based on the geometric properties of the subspaces. It provides precise and quantitative indicators for the management and development of urban functional areas.

Description of drawings

Fig. 1 is the schematic flow chart of the method of the present invention;

Fig. 2 is a schematic flowchart of a method embodiment of the present invention.

Fig. 3 uses the similarity matrix that the sparse subspace clustering method obtains in the embodiment of the present invention;

4 is the result of detecting urban functional areas according to an embodiment of the present invention;

5 is the functional activity level of the salient feature locations of each functional area in the embodiment of the present invention;

Fig. 6 Similarity of functional areas calculated by an embodiment of the present invention;

Fig. 7 Uniqueness and abundance of functional regions calculated by an embodiment of the present invention.

Detailed ways

The present invention will be further described below in conjunction with the embodiments and the accompanying drawings, but the present invention is not limited in any way, and any transformation or replacement based on the teachings of the present invention belongs to the protection scope of the present invention.

As shown in Figure 1, a method for identifying urban functional areas based on a multi-subspace model includes the following steps:

Step 1: Obtain the taxi trajectory data and check-in data in the research area;

Step 2, constructing a partition-oriented time series feature matrix C based on the visiting purpose;

Step 3, input the time series feature matrix C to the sparse subspace clustering algorithm, and calculate the corresponding relationship between the geographic unit and the urban functional area;

Step 4, obtain the salient feature locations of each functional area, and then identify the main function of each functional area.

Specifically, the construction process of the time series feature matrix C described in step 2 includes the following steps:

Step 201, dividing the research area to obtain N geographic units;

Step 202, preprocessing the taxi trajectory data, removing abnormal points, extracting the end point and arrival time of each trip, and mapping the end point with the geographic unit to obtain the visit record of the geographic unit;

Step 203, matching the check-in data record with the visit record of the geographic unit, and classifying the purpose of each visit;

Step 204, constructing a time series feature matrix C with M rows and N columns, which represents the human activity dynamics carried by the geographic unit within a period of time, where M=T×D, T represents the number of divided time periods, and D represents the number of categories for visiting purposes. , each column in C represents the number of people visiting the corresponding geographic unit for different purposes in different time periods.

Specifically, the sparse subspace clustering algorithm described in step 3 includes the following steps:

Step 301, solve the coefficient matrix Z, the size is N×N, the matrix Z needs to satisfy the minimization under the constraint of l ₁ :

CZ=C, Z _ii =0

表示l₁范数，l₁范数最小化使得系数矩阵Z稀疏，从而迫使每个地理单元的时序特征仅需用同一子空间中其他地理单元的时序特征的线性组合来表示；in

Represents the _l1 norm, and the minimization of the _l1 norm makes the coefficient matrix Z sparse, thus forcing the time series feature of each geographic unit to be represented only by a linear combination of the time series features of other geographic units in the same subspace;

Step 302, then use the coefficient matrix to establish a data similarity matrix W=|Z|+|Z| ^T , the size of W is N×N, and the value in the matrix is the similarity in time series characteristics between the geographic units corresponding to the index Spend;

The similarity matrix W is a block diagonal matrix, that is, only the main diagonal has non-zero sub-matrices, and the rest of the sub-blocks are zero matrices. Each non-zero sub-matrix is a subspace, and the same subspace contains multiple Geographical units with very similar time series characteristics, geographical units in different subspaces have large differences in time series characteristics, so the subspace is the urban functional area to be detected;

Step 303: Calculate the number of subspaces by using the normalized Laplacian matrix L of the similarity matrix W, L=ID ^{-1/ 2} WD ^-1/2 , where I is the identity matrix, D=∑ _i W _ij , Arrange the eigenvalues of L in ascending order, and calculate the difference λ _{k+1 -} λ _k of each two adjacent eigenvalues. The k corresponding to the largest difference is the number of subspaces to be sought, that is, the number of urban functional areas to be detected. number;

In step 304, the K-means clustering method is used for the similarity matrix W, and the number of clusters is set to k obtained in step 303, and the corresponding relationship between geographic units and k categories, that is, the corresponding relationship with k urban functional areas, is completed. Urban functional area detection.

Specifically, obtaining the salient feature locations of each functional area described in step 4 includes: extracting _a subspace matrix S1 corresponding to each urban functional area from the similarity matrix W generated in step 302 by using the corresponding relationship in step 304 , ..., S _i , ..., _Sk , and perform principal component analysis, the obtained eigenvectors [e ₁ , e ₂ , ..., e _p , ..., e _M ] _i are called _5i 's _Feature locations, the _eigenvectors [ _{e 1} , e ₂ , .

Specifically, the identification of the main function of each functional area includes: transforming each salient feature location of each functional area into a matrix with D rows and T columns, each row indicating that the feature location is in T time periods with D for the purpose of changing the activity level, get the main activity pattern of the functional area, and regard the most active function in the main activity pattern as the main function of the area.

Further, the method for identifying urban functional areas further includes the following steps:

Step 5, calculate the similarity of each functional area;

Step 6: Calculate the uniqueness of each functional area, and sort each functional area according to the uniqueness.

Specifically, the calculation of the similarity of the functional areas is calculated according to the main angle between the subspaces, and the calculation formula of the similarity of any two functional areas S _k and S _l is as follows:

是

的第i个最大奇异值，U^k和U^l分别是S_k和S_l的正交基，

是子空间之间的主要角，d_k∧d_l表示S_k和S_l的空间维数d_k与d_l中的较小值。in,

Yes

The ith largest singular value of , U ^k and U ^l are the orthonormal basis of S _k and S _l , respectively,

is the main angle between the subspaces, and d _k ∧ d _l denotes the smaller of the spatial dimensions d _k and d _l of _Sk and S _l .

Specifically, the uniqueness of the functional areas is inversely proportional to the similarity. If the similarity between the subspaces is high, the functions of the corresponding functional areas will be very similar, and the uniqueness of the functional areas is low. The formula for calculating the _uniqueness of region Si is as follows:

where k is the total number of functional areas, and S _{-i represents} the functional areas other than Si.

Further, the method for identifying urban functional areas further includes the following steps:

Step 7, calculate the abundance of each functional area, and sort each functional area according to the described abundance.

Specifically, the abundance of the functional areas is related to the reconstruction error of the salient feature locations of each functional area, which is calculated as follows:

是由S_i的显著特征地点重构的矩阵。where C(S _i ) is a matrix consisting of primitive vectors belonging to subspace S _i ,

is the matrix reconstructed from the _salient feature locations of Si.

The reconstruction error describes the difference between the original subspace matrix restored by the salient feature sites. The larger the reconstruction error, the more feature sites are needed to describe the dynamic changes in the functional area in addition to the dominant feature sites. Abundance examines the patterns of enrichment activity of people in an area and the functional development that supports this pattern of activity.

As shown in the flow chart in FIG. 2 , the experiment of the present invention includes the following steps.

(1) Data processing

Step 1.1: Select the main urban area of Shanghai as the study area, and divide the grid size into 500 meters × 500 meters. After excluding the water body units, 3166 geographic units are obtained.

Step 1.2: Preprocess the GPS trajectory data from 6,600 taxis in Shanghai, remove outliers, extract the end point and arrival time of each trip, and map the end point to the geographic unit to obtain 7,852,724 visit records.

Step 1.3: Match the check-in data records with the visit records of the geographic unit, classify the purpose of each visit, there are six types of visit purposes: home, transportation, work, dining, entertainment and other (referring to going to the park). , museums, libraries, etc.).

Step 1.4: Divide a day into hours to obtain 24 time periods, count the number of visits to each geographic unit in 24 time periods for each purpose (total 6), and obtain a time series feature matrix C with 144 rows and 3166 columns.

(2) Identification of urban functional areas

Step 2.1: Input the time series feature matrix C to the sparse subspace clustering algorithm to obtain the similarity matrix W. Figure 3 shows the visual similarity matrix result, which reveals the similarity between geographic units. If the similarity value is non-zero, it will be colored Black, it can be seen that there are five block diagonals, this structure reveals that the number of urban functional areas is 5.

Step 2.2: Calculate the number of subspaces by using the normalized Laplacian matrix L of W, L=ID ^-1/2 WD ^-1/2 , where I is the identity matrix, and D=∑ _i Wi _ii . Arrange the eigenvalues of L in ascending order, calculate the difference λ _{k+1 -} λ _k of each two adjacent eigenvalues, the k corresponding to the largest difference is 5, that is, the number of subspaces (urban functional areas) is 5, and The interpretation results of step 2.1 are consistent.

Step 2.3: Therefore, use the K-means clustering method for W, set the number of clusters to 5, complete the detection of urban functional areas, and obtain urban functional areas 1, 2, 3, 4, and 5. The visualization results of the clustering results on the map are shown in Figure 4. It can be seen that the central area is mainly covered by the functional area 5.

Step 2.4: Since the main function of the functional area is determined by the significant activity characteristics of the functional area, in order to determine the actual function of the detected urban functional area, the principal component analysis is performed on the subspace matrix corresponding to each functional area, and the Feature locations, it is found that the top 5 eigenvalues in functional areas 1, 2, 3, and 4 account for more than 90%, while the top 5 eigenvalues in functional area 5 account for less than 90%. Therefore, our previous 5 The basis vectors corresponding to the eigenvalues are used as the salient feature locations of each functional area, and when analyzing functional area 5, the basis vectors corresponding to the previous 10 eigenvalues are used as its salient feature locations.

Step 2.5: Transform each salient feature location of each functional area into a matrix with 6 rows and 24 columns, then each row represents the feature location in 24 hours at home (H), traffic (Tr), work (W) , catering (D), entertainment (E) and other (O, referring to parks, museums, libraries, etc.) for the purpose of activity level changes, the salient features of all functional areas are shown in Figure 5. It can be seen from the figure that family activities (H) are the most active among the salient features of functional area 1, dining activities (D) are ranked second, and entertainment activities (E) are also more prominent. Therefore, functional area 1 can be used as a restaurant. Residential area developed with entertainment facilities; similarly, the traffic activity (Tr) of functional area 2 is prominent as a transportation hub; the main activity of functional area 3 is work (W), so it is a work area; The influence of 10 salient feature locations, it is found that dining activities (D) and entertainment activities (E) are active, and they are regarded as commercial areas; functional area 4 corresponds to other functional areas such as parks, museums, and gas stations.

(3) Analysis of urban functional areas

Step 3.1: Calculate the proximity of the subspaces according to the main angle between the subspaces, that is, the similarity of the functional area, see Figure 6, the similarity of the functional area itself is not calculated, and is set to 0. The residential area and the commercial area in Figure 6 have the highest similarity, because the residential area is more likely to have dining and entertainment facilities, and the location of the commercial area in Figure 3 itself is also mixed with a large number of residential areas.

Step 3.2: Calculate the uniqueness of the functional area according to the similarity of the functional area. The results are shown in Figure 7. The overall value of the uniqueness of the functional area is higher, indicating that the overall functional area of the study area is significantly different. Among them, the uniqueness of residential area and commercial area is low, which is also consistent with the result of step 3.1 in (3).

Step 3.3: Calculate the abundance of functional regions, the results are shown in Figure 7. Among them, the reconstruction error of other functional areas (areas that provide other services) is the largest, which means that the activity patterns in other functional areas are the most complicated, because there are many facilities and the dynamic activity patterns vary greatly. The reconstruction error of residential area and commercial area is the smallest, because they are concentrated on living, dining and entertainment, respectively, and the functional dynamic activity mode is relatively simple.

It can be seen from the content of the invention and the examples that, in order to solve the problems existing in the prior art, the present invention proposes a model based on multiple subspaces, and considers that urban functional areas have multiple sets of characteristics. The vector samples are located in the high-dimensional space formed by the joint subspace, and the dynamic characteristics of human activities carried by the geographic units located in the same subspace are similar, and can be clustered into a functional area, and the identification of urban functional areas can be realized by finding the subspace. , and analyzes the uniqueness and abundance of each functional area based on the geometric properties of the subspace, providing a refined and quantitative indicator for the management and development of urban functional areas.

Claims (4)

1. an urban functional area identification method based on a multi-subspace model, is characterized in that, comprises the following steps: Step 1: Obtain the taxi trajectory data and check-in data in the research area; Step 2, constructing a partition-oriented time series feature matrix C based on the visiting purpose; Step 3, input the time series feature matrix C to the sparse subspace clustering algorithm, and calculate the corresponding relationship between the geographic unit and the urban functional area; Step 4, obtain the salient feature locations of each functional area, and then identify the main function of each functional area; Wherein, the construction process of the time series feature matrix C described in step 2 includes the following steps: Step 201, dividing the research area to obtain N geographic units; Step 202, preprocessing the taxi trajectory data, removing abnormal points, extracting the end point and arrival time of each trip, and mapping the end point with the geographic unit to obtain the visit record of the geographic unit; Step 203, matching the check-in data record with the visit record of the geographic unit, and classifying the purpose of each visit; Step 204, constructing a time series feature matrix C with M rows and N columns, which represents the human activity dynamics carried by the geographic unit within a period of time, where M=T×D, T represents the number of divided time periods, and D represents the number of categories for visiting purposes. , each column in C represents the number of people visiting the corresponding geographic unit for different purposes in different time periods; The sparse subspace clustering algorithm described in step 3 includes the following steps: Step 301, solve the coefficient matrix Z, the size is N×N, the matrix Z needs to satisfy the minimization under the constraint of l ₁ :

CZ=C, Z _ii =0 in

Represents the _l1 norm, and the minimization of the _l1 norm makes the coefficient matrix Z sparse, thus forcing the time series feature of each geographic unit to be represented only by a linear combination of the time series features of other geographic units in the same subspace; Step 302, then use the coefficient matrix to establish a data similarity matrix W=|Z|+|Z| ^T , the size of W is N×N, and the value in the matrix is the similarity in time series characteristics between the geographic units corresponding to the index Spend; Step 303: Calculate the number of subspaces by using the normalized Laplacian matrix L of the similarity matrix W, L=ID ^-1/2 WD ^-1/2 , where I is the identity matrix, D=∑ _i W _ij , Arrange the eigenvalues of L in ascending order, and calculate the difference λ _{k+1 -} λ _k of each two adjacent eigenvalues. The k corresponding to the largest difference is the number of subspaces to be sought, that is, the number of urban functional areas to be detected. number; In step 304, the K-means clustering method is used for the similarity matrix W, and the number of clusters is set to k obtained in step 303, and the corresponding relationship between geographic units and k categories, that is, the corresponding relationship with k urban functional areas, is completed. Urban functional area detection. 2 . The method for identifying urban functional areas according to claim 1 , wherein the obtaining of the salient feature locations of each functional area described in step 4 comprises: using the corresponding relationship in step 304 to generate the similarity from step 302 . 3 . _Extract the _{subspace matrices S 1} , . ., e _p , ..., e _M ] _i is called the feature location of Si _, and the first _r accumulated eigenvalues account for more than 90% of the eigenvectors [e ₁ , e ₂ , ..., er ] _i is the _salient feature location of Si; The identification of the main function of each functional area includes: transforming each salient feature location of each functional area into a matrix with D rows and T columns, each row representing that the feature location takes D as the purpose in T time periods. The main activity pattern of the functional area is obtained, and the function area is marked with the most active function in the main activity pattern to complete the identification of the urban functional area. 3. The method for identifying urban functional areas according to claim 1 or 2, wherein the method for identifying urban functional areas further comprises the following steps: Step 5, calculate the similarity of each functional area; Step 6: Calculate the uniqueness of each functional area, and sort each functional area according to the uniqueness; The calculation of the similarity of the functional area is calculated according to the main angle between the corresponding subspaces, and the calculation formula of the similarity aff(S _k , S _l ) of the corresponding subspaces S _k and S _l of any two functional areas is as follows ,

in,

Yes

The ith largest singular value of , U ^k and U ^l are the orthonormal basis of S _k and S _l , respectively,

is the main angle between subspaces, d _k ∧ d _l represents the smaller of the spatial dimensions d _k and d _l of S _k and S _l ; The uniqueness of the functional areas is inversely proportional to the similarity. If the similarity between the subspaces is high, the functions of the corresponding functional areas will be extremely similar, and the uniqueness of the functional areas is low, and each functional area S _i The uniqueness calculation formula of is as follows:

where k is the total number of functional areas, and S _{-i represents} the functional areas other than Si. 4. The method for identifying urban functional areas according to claim 3, wherein the method for identifying urban functional areas further comprises the following steps: Step 7: Calculate the abundance of each functional area, and sort each functional area according to the abundance; The abundance of the described functional areas is related to the reconstruction error of the salient feature sites of each functional area, which is calculated as follows:

where C(S _i ) is a matrix consisting of primitive vectors belonging to subspace S _i ,

is the matrix reconstructed from the _salient feature locations of Si, and || || _F denotes the Frobenius norm of the matrix.

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