CN107705019A - A kind of smart city Huimin service level evaluation method - Google Patents
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Abstract
The present invention relates to a kind of smart city Huimin service level evaluation method, comprise the following steps：Gather the data and sub-indicator data of all Huimin service-evaluating indexes in all cities to be evaluated；The sub-indicator data in all cities to be evaluated are standardized using PCA, draw each principal component scores in each city to be evaluated, Huimin service level evaluation model is obtained, and then obtains the evaluation score of the Huimin service level in each city to be evaluated；Obtain ranking, analysis report and the improvement idea of the Huimin service level in each city to be evaluated.The evaluation method of the present invention determines the principal component scores and Huimin service level evaluation model in each city to be evaluated by PCA, the evaluation score of the Huimin service level in each city to be evaluated is obtained, while foundation is provided for each decision-making of the city future to be evaluated in terms of Huimin service.
Description
Technical Field
The invention belongs to the field of evaluation of smart cities, and particularly relates to a method for evaluating the citizen-benefitting service level of a smart city.
Background
Since the ministry of residence and construction in 2012 and the issue of temporary management of test points in national smart cities and the index system of test points in national smart cities (districts and towns) (trial), nearly 300 test points in smart cities in China have been published.
The smart city senses, analyzes and integrates various key information of a city operation core system by using technical means such as information, communication and the like, and intelligently responds to various demands of cities and residents including people's livelihood, environmental protection, public safety, city service, industrial and commercial activities according to the obtained information. The smart city is a system engineering which implements a novel national urbanization development strategy, promotes the happiness and satisfaction of people and promotes transformation and upgrading of a city development mode. The evaluation of the construction effect of the smart city is an important work in the construction of the smart city.
The method has the advantages that the smart city construction of different cities and regions is evaluated, so that the current development condition of smart cities in China can be better known, the blindness of city construction is avoided, a theoretical basis is provided for scientifically and reasonably formulating smart city development plans and policies in the future, however, how to evaluate the construction effect and level of smart cities in various regions at present is lack of a set of complete, scientific and systematic evaluation system, and the evaluation result of the smart cities cannot be accurately and quickly obtained.
Disclosure of Invention
According to the problems in the prior art, the invention provides a method for evaluating the citizen-benefitting service level of a smart city, which is a complete, scientific and systematic evaluation system, can accurately and quickly obtain the evaluation score of the citizen-benefitting service level of each city to be evaluated, and provides a basis for future decision-making of each city to be evaluated in the aspect of the citizen-benefitting service.
In order to achieve the purpose, the invention provides a method for evaluating the citizen-benefitting service level of a smart city, which comprises the following steps:
s1, collecting data of all citizen-benefitting service evaluation indexes of all cities to be evaluated, and obtaining subentry index data of each evaluation index according to the data of the evaluation indexes;
s2, by using a main cause analysis method, firstly carrying out standardization processing on the subentry index data of all cities to be evaluated, establishing a factor load matrix, determining the main components and the accumulated variance contribution rate of each factor, obtaining each main component score of each city to be evaluated, obtaining a citizen-benefitting service level evaluation model, and further obtaining the evaluation score of the citizen-benefitting service level of each city to be evaluated.
Preferably, the evaluation method further comprises a step S3 of obtaining the ranking of the citizen-benefitting service level of each city to be evaluated according to the evaluation score of the citizen-benefitting service level of each city to be evaluated; and obtaining an analysis report and an improvement suggestion of the citizen-benefitting service level of each city to be evaluated through the principal component score of each city to be evaluated.
Further preferably, in step S1, the collected data of the citizen-benefitting service evaluation index is derived from government public data, namely, a statistical yearbook and a work report of each city.
Preferably, the evaluation indexes of the citizen-benefitting service comprise nine evaluation indexes of government affairs service, traffic service, social security service, medical service, education service, employment service, city service, help service and e-commerce service; the government affair service comprises three sub-indexes of electronic license utilization rate, one-stop handling rate and online uniform entrance rate, the traffic service comprises three sub-indexes of urban traffic operation index issuing condition, public gasoline and electric vehicle incoming information real-time forecasting rate and public traffic electronic payment utilization rate, the social security service comprises three sub-indexes of social security service online handling condition, social security self-service opening rate and social security remote business online handling condition, the medical service comprises three sub-indexes of electronic medical record popularity of more than two levels of medical institutions, reservation diagnosis and treatment rate of more than two levels of medical institutions and outpatient service health file retrieval rate of more than two levels of medical institutions, the education service comprises three sub-indexes of school multimedia classroom popularity rate, teacher network learning space coverage rate and school wireless network coverage rate, the employment service comprises employment information service coverage crowd condition, employment service online handling condition two sub-indexes, the urban service comprises three sub-indexes of school multimedia classroom popularity, mobile internet urban service utilization condition and one-application condition, the enterprise service comprises two sub-index of electronic information account occupation ratio, two sub-index of internet commodity access barrier ratio and two sub-item online commodity transaction indexes of electronic business transaction.
More preferably, the specific steps of step S2 are as follows:
s21, collecting data of 24 subentry indexes of p cities to be evaluated, namely the utilization rate of electronic certificates with citizen identity numbers or uniform social credit codes of legal persons and other organizations as unique identifiers, the one-stop handling rate, the online uniform entrance rate, the urban traffic operation index release condition, the real-time forecast rate of public gasoline and electric vehicle incoming information, the electronic payment utilization rate of public traffic riding, the online handling condition of social security service, the opening rate of social security self-service of street communities, the online handling condition of social security service, the popularization rate of electronic medical records of more than two medical institutions, the reservation and diagnosis rate of more than two medical institutions, the visiting health record rate of more than two medical institutions, the popularization rate of multimedia classrooms of schools, the learning space coverage rate of living networks, the coverage rate of wireless networks of schools, the coverage of employment information services, the online handling condition of employment services, two subentry indexes, the provision condition of mobile internet urban service, the use condition of mobile internet urban service, the condition of one-user electronic information files, the establishment rate of electronic files, the sharing access rate of obstacles to the internet, the Internet disabilities, the online transaction ratio of the sharing of the electronic files, the retail transaction ratio of 24 subentry transaction data of the sharing of the online transaction, and the sharing of the retail network, and setting i as the data of the ith subentry index arranged according to the sequence, i =1,2,3, \823024, and 24, obtaining an original variable matrix X with 24X p order:
i.e. 24 itemized indices of p cities, is denoted x i,j ，x i,j Data representing the ith subentry index of the jth city, wherein i =1,2,3, \8230, 24, j =1,2,3, \8230, p;
s22, carrying out standardization processing on the original variable matrix X, eliminating dimension and magnitude influence, and obtaining a standardized matrix Z, wherein the formula of the standardized matrix Z is as follows:
wherein, the first and the second end of the pipe are connected with each other,
represents the sample mean of the jth column data of the original variable matrix X,sample standard deviation of j-th column data of the original variable matrix X is represented;
the normalization matrix Z is then expressed as follows:
wherein zx ij Data representing the ith row and the jth column of the normalized matrix Z;
s23, calculating a correlation coefficient matrix R according to the normalized matrix Z:
Z T is a transpose matrix of the standardized matrix Z, and the standardized matrix Z is recorded with a variable index zx 1 ,zx 2 ,…,zx p Wherein zx 1 ＝(zx 11 ,zx 21 ,…,zx 24,1 ) T ，zx 2 ＝(zx 12 ,zx 22 ,…,zx 24,2 ) T ，…，zx p ＝(zx 1p ,zx 2p ,…,zx 24,p ) T Then r is ab (a, b =1,2, \8230;, p) is the correlation coefficient of the variable index of the normalized matrix Z, r ab The calculation formula of (c) is as follows:
wherein zx ka To normalize the data in the k-th row and a-th column of the matrix Z, zx kb Data of a k row and a b column of the standardized matrix Z;to normalize the sample mean of the data of column a of matrix Z,sample mean of the b-th column data of the normalized matrix Z;
s24, solving all characteristic roots lambda through a characteristic equation | R-lambda I =0 of a correlation coefficient matrix R, wherein lambda is a characteristic root of the characteristic equation, and I is a unit matrix c (c =1,2, \8230;, p), and is λ from large to small 1 ≥λ 2 ≥…≥λ p ≥0；
S25, obtaining the cumulative variance contribution rate alpha of the f factor according to a cumulative variance contribution rate calculation formula f ：
According to the cumulative variance contribution rate alpha f Not less than 0.85, obtaining m number of main components, respectively recording as main component F 1 ,F 2 ,…,F m To obtain a main component F 1 ,F 2 ,…,F m Arranging the m characteristic roots from large to small corresponding to the m characteristic roots, namely lambda 1 ≥λ 2 ≥…≥λ m >0；
S26, aiming at the original variable matrix X, if the original variable index is recorded as X 1 ,x 2 ,…,x p Wherein x is 1 ＝(x 11 ,x 21 ,…,x 24,1 ) T ，x 2 ＝(x 12 ,x 22 ,…,x 24,2 ) T ，…，x p ＝(x 1p ,x 2p ,…,x 24,p ) T Setting the new variable after dimensionality reduction as z 1 ,z 2 ,…,z m (m.ltoreq.p), then
Wherein l gh The eigenvectors corresponding to the values of the m larger eigenroots of the correlation coefficient matrix R,
wherein λ is g For the m larger eigenroots of the correlation coefficient matrix R eigenequation,is a characteristic root of lambda g Corresponding feature vector, andfurther to find outRepresenting feature vectorsThe h component of (2);
by a 1 gh Obtaining a factor load matrix L:
s27, adding gh Multiplying with a normalized matrix Z to obtain a principal component F 1 ,F 2 ,…,F m Expression (c):
will l gh Substituted into new variable z after dimensionality reduction 1 ,z 2 ,…,z m (m is less than or equal to p) to obtain each main component F 1 ,F 2 ,…,F m Score of (c):
s28, using the eigenvalue lambda corresponding to the m main components g (g =1,2, \8230;, m) is weighted to obtain an evaluation model F:
preferably, according to the evaluation score of the citizen-benefitting service level of each city to be evaluated, the cities corresponding to the evaluation scores from large to small are the ranking of the citizen-benefitting service levels; and finding out corresponding subentry indexes of the city to be evaluated, which are beneficial to the citizen-benefiting service level and not beneficial to the citizen-benefiting service level, according to the principal component scores of the city to be evaluated, and providing a basis for future decisions of the city to be evaluated on the citizen-benefiting service.
The invention has the beneficial effects that:
1) Acquiring data of all the citizen-benefitting service evaluation indexes of all cities to be evaluated, and obtaining subentry index data of each evaluation index according to the data of the evaluation indexes; by utilizing a principal component analysis method, firstly, carrying out standardization processing on the subentry index data of all cities to be evaluated, establishing a factor load matrix, determining the principal components and the cumulative variance contribution rate of each factor, obtaining each principal component score of each city to be evaluated, obtaining a citizen-benefitting service level evaluation model, and further obtaining the evaluation score of the citizen-benefitting service level of each city to be evaluated; finally, according to the evaluation score of the citizen-benefitting service level of each city to be evaluated, obtaining the ranking of the citizen-benefitting service level of each city to be evaluated; and obtaining an analysis report and an improvement suggestion of the citizen-benefitting service level of each city to be evaluated through the principal component score of each city to be evaluated. The evaluation method determines the principal component of each city to be evaluated through a principal component analysis method, obtains each principal component score of each city to be evaluated, obtains a citizen-benefitting service level evaluation model, and further obtains the evaluation score of the citizen-benefitting service level of each city to be evaluated. According to the evaluation score of the citizen-benefitting service level of each city to be evaluated, the cities corresponding to the evaluation scores from large to small are the ranking of the citizen-benefitting service levels; and finding out corresponding subentry indexes of the city to be evaluated, which are beneficial to the people-benefit service level and are not beneficial to the people-benefit service level, according to the scores of the main components of the city to be evaluated, and providing a basis for future decisions of the city to be evaluated on the people-benefit service.
Drawings
FIG. 1 is a flow chart of the evaluation method of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1, a method for evaluating a citizen-benefit service level of a smart city includes the following steps:
s1, collecting data of all the citizen-benefitting service evaluation indexes of all cities to be evaluated, and obtaining subentry index data of each evaluation index according to the data of the evaluation indexes;
specifically, the collected data of the citizen-benefitting service evaluation indexes are derived from government public data, namely the statistics yearbook and the working report of each city.
According to a newly released notice (issue of improvement high skill [2016] 2476) about developing novel wisdom city evaluation work by organization to promote the health and rapid development of novel wisdom cities in 2016 (11, 22 days) of national improvement committee, evaluation indexes and subentry indexes of the wisdom city citizen-benefitting service level are determined, and are shown in table 1.
As shown in table 1, the citizen-benefitting service evaluation indexes include nine evaluation indexes, namely government affairs service, traffic service, social security service, medical service, education service, employment service, city service, help service and e-commerce service; the government affair service comprises three sub-indexes of electronic license utilization rate, one-stop handling rate and online uniform entrance rate, the traffic service comprises three sub-indexes of urban traffic operation index issuing condition, public gasoline and electric vehicle incoming information real-time forecasting rate and public traffic electronic payment utilization rate, the social security service comprises three sub-indexes of social security service online handling condition, social security self-service opening rate and social security remote business online handling condition, the medical service comprises three sub-indexes of electronic medical record popularity of more than two levels of medical institutions, reservation diagnosis and treatment rate of more than two levels of medical institutions and outpatient service health file retrieval rate of more than two levels of medical institutions, the education service comprises three sub-indexes of school multimedia classroom popularity rate, teacher network learning space coverage rate and school wireless network coverage rate, the employment service comprises employment information service coverage crowd condition, employment service online handling condition two sub-indexes, the urban service comprises three sub-indexes of school multimedia classroom popularity, mobile internet urban service utilization condition and one-application condition, the enterprise service comprises two sub-index of electronic information account occupation ratio, two sub-index of internet commodity access barrier ratio and two sub-item online commodity transaction indexes of electronic business transaction.
Table 1:
s2, carrying out standardization processing on the subentry index data of all cities to be evaluated by using a main cause analysis method, establishing a factor load matrix, determining main components and the cumulative variance contribution rate of each factor, obtaining each main component score of each city to be evaluated, obtaining a citizen-benefitting service level evaluation model, and further obtaining an evaluation score of the citizen-benefitting service level of each city to be evaluated; the method comprises the following specific steps:
s21, collecting data of 24 subentry indexes of p cities to be evaluated, namely the utilization rate of electronic certificates with citizen identity numbers or uniform social credit codes of legal persons and other organizations as unique identifiers, the one-stop handling rate, the online uniform entrance rate, the urban traffic operation index release condition, the real-time forecast rate of public gasoline and electric vehicle incoming information, the electronic payment utilization rate of public traffic riding, the online handling condition of social security service, the opening rate of social security self-service of street communities, the online handling condition of social security service, the popularization rate of electronic medical records of more than two medical institutions, the reservation and diagnosis rate of more than two medical institutions, the visiting health record rate of more than two medical institutions, the popularization rate of multimedia classrooms of schools, the learning space coverage rate of living networks, the coverage rate of wireless networks of schools, the coverage of employment information services, the online handling condition of employment services, two subentry indexes, the provision condition of mobile internet urban service, the use condition of mobile internet urban service, the condition of one-user electronic information files, the establishment rate of electronic files, the sharing access rate of obstacles to the internet, the Internet disabilities, the online transaction ratio of the sharing of the electronic files, the retail transaction ratio of 24 subentry transaction data of the sharing of the online transaction, and the sharing of the retail network, and let i be the data of the ith subentry index arranged in the aforementioned order, i =1,2,3, \ 823024, and a 24 × p-order original variable matrix X is obtained:
that is, the data of 24 subentries of p cities is represented as x i,j ，x i,j Data representing the ith subentry index of the jth city, wherein i =1,2,3, \8230, 24, j =1,2,3, \8230, p;
s22, carrying out standardization processing on the original variable matrix X, eliminating dimension and magnitude influence, and obtaining a standardized matrix Z, wherein the formula of the standardized matrix Z is as follows:
wherein, the first and the second end of the pipe are connected with each other,
represents the sample mean of the jth column data of the original variable matrix X,column j data representing original variable matrix XSample standard deviation of (a);
the normalization matrix Z is then expressed as follows:
wherein zx ij Data representing the ith row and jth column of the normalized matrix Z;
s23, calculating a correlation coefficient matrix R according to the normalized matrix Z:
Z T is a transposed matrix of the standardized matrix Z, and the standardized matrix Z is recorded with a variable index zx 1 ,zx 2 ,…,zx p Wherein zx 1 ＝(zx 11 ,zx 21 ,…,zx 24,1 ) T ，zx 2 ＝(zx 12 ,zx 22 ,…,zx 24,2 ) T ，…，zx p ＝(zx 1p ,zx 2p ,…,zx 24,p ) T Then r is ab (a, b =1,2, \ 8230;, p) is the correlation coefficient of the variable index of the normalization matrix Z, r ab The calculation formula of (c) is as follows:
wherein zx ka For normalizing the data of the k-th row and a-th column of the matrix Z, zx kb Data of a k row and a b column of the standardized matrix Z;to normalize the sample mean of the data of column a of matrix Z,sample mean of the b-th column data of the normalized matrix Z;
s24, solving all characteristic roots lambda through a characteristic equation | R-lambda I =0 of a correlation coefficient matrix R, wherein lambda is a characteristic root of the characteristic equation, and I is a unit matrix c (c =1,2, \ 8230;, p) and is in descending order of λ 1 ≥λ 2 ≥…≥λ p ≥0；
S25, obtaining the cumulative variance contribution rate alpha of the f factor according to a cumulative variance contribution rate calculation formula f ：
According to the cumulative variance contribution rate alpha f Not less than 0.85, and respectively marking as principal component F 1 ,F 2 ,…,F m To obtain a principal component F 1 ,F 2 ,…,F m Arranging the m characteristic roots from large to small corresponding to the m characteristic roots, namely lambda 1 ≥λ 2 ≥…≥λ m >0；
S26, aiming at the original variable matrix X, if the original variable index is recorded as X 1 ,x 2 ,…,x p Wherein x is 1 ＝(x 11 ,x 21 ,…,x 24,1 ) T ，x 2 ＝(x 12 ,x 22 ,…,x 24,2 ) T ，…，x p ＝(x 1p ,x 2p ,…,x 24,p ) T Setting the new variable after dimensionality reduction as z 1 ,z 2 ,…,z m (m.ltoreq.p), then
Wherein l gh The eigenvectors corresponding to the values of the m larger eigenvalue roots of the correlation coefficient matrix R,
wherein λ is g For the m larger eigenroots of the correlation coefficient matrix R eigenequation,is a characteristic root λ g Corresponding feature vector, andthen obtain the result Representing feature vectorsThe h component of (a);
by a 1 gh Obtaining a factor load matrix L:
s27, adding gh Multiplying with a normalized matrix Z to obtain a principal component F 1 ,F 2 ,…,F m Expression (c):
will l gh Substituted into new variable z after dimensionality reduction 1 ,z 2 ,…,z m (m is less than or equal to p) to obtain each main component F 1 ,F 2 ,…,F m Score of (c):
s28, using the eigenvalue lambda corresponding to m main components g (g =1,2, \ 8230;, m) accounts for all the main componentsAnd taking the proportion of the sum of the characteristic values as weight to obtain an evaluation model F:
s3, obtaining ranking of the citizen-benefitting service levels of the p cities to be evaluated according to the evaluation scores of the citizen-benefitting service levels of the p cities to be evaluated; and obtaining the analysis report and the improvement suggestion of the number p of the cities to be evaluated for the number of the people-benefitting service levels through the m principal component scores of the number p of the cities to be evaluated.
In summary, the evaluation method of the invention determines the principal component of each city to be evaluated through a principal component analysis method, obtains each principal component score of each city to be evaluated, and then obtains the evaluation model of the citizen-benefitting service level, thereby obtaining the evaluation score of the citizen-benefitting service level of each city to be evaluated. According to the evaluation score of the citizen-benefitting service level of each city to be evaluated, the cities corresponding to the evaluation scores from large to small are the ranking of the citizen-benefitting service levels; and finding out corresponding subentry indexes of the city to be evaluated, which are beneficial to the citizen-benefiting service level and not beneficial to the citizen-benefiting service level, according to the principal component scores of the city to be evaluated, and providing a basis for future decisions of the city to be evaluated on the citizen-benefiting service. The evaluation method can accurately and quickly obtain the evaluation result and the improvement suggestion of the citizen-benefitting service level of the smart city.
Claims (6)
1. A method for evaluating the citizen-benefitting service level of a smart city is characterized by comprising the following steps:
s1, collecting data of all the citizen-benefitting service evaluation indexes of all cities to be evaluated, and obtaining subentry index data of each evaluation index according to the data of the evaluation indexes;
and S2, by utilizing a main cause analysis method, firstly carrying out standardization processing on the subentry index data of all cities to be evaluated, establishing a factor load matrix, determining the main components and the cumulative variance contribution rate of each factor, obtaining each main component score of each city to be evaluated, obtaining a citizen-benefitting service level evaluation model, and further obtaining the evaluation score of the citizen-benefitting service level of each city to be evaluated.
2. The method of claim 1, wherein the method comprises: the evaluation method also comprises a step S3 of obtaining the ranking of the citizen-benefitting service level of each city to be evaluated according to the evaluation score of the citizen-benefitting service level of each city to be evaluated; and obtaining an analysis report and an improvement suggestion of the citizen-benefitting service level of each city to be evaluated through the principal component score of each city to be evaluated.
3. The method of claim 2, wherein the method comprises: in step S1, the collected data of the citizen-benefitting service evaluation indexes come from government public data, namely the statistical yearbook and the working report of each city to be evaluated.
4. The method of claim 3, wherein the method comprises: the evaluation indexes of the citizen-benefitting service comprise nine evaluation indexes of government affairs service, traffic service, social security service, medical service, education service, employment service, city service, help service and e-commerce service; the government affair service comprises three subentries of electronic license utilization rate, one-stop handling rate and online uniform entrance rate which take citizen identity numbers or uniform social credit codes of legal persons and other organizations as unique identifiers, the traffic service comprises three subentries of urban traffic operation index release, real-time forecast rate of information of coming vehicles of a public gasoline and a public transport electronic payment utilization rate, the social security service comprises three subentries of social security service online handling rate, street community social security self-service opening rate and social security remote business networking handling rate, the medical service comprises three subentries of electronic medical record popularity of more than two levels of medical institutions, reservation diagnosis rate of more than two levels of medical institutions and clinic health file retrieval rate of more than two levels of medical institutions, the education service comprises three subentries of school multimedia popularity, teacher network learning space coverage rate and school wireless network coverage rate, the employment service comprises two subentries of employment information service coverage, two subentries of employment service online handling condition, the urban service comprises mobile internet service provision condition, mobile internet public service use condition, one-cartoon application service use condition and two subentries of information access, the electronic license utilization rate, the retail information access rate and the social security service comprises two subentries of electronic license utilization rate and the electronic transaction information access rate, and the electronic commodity access rate, and the social security access rate of the social security cross-transaction condition comprises two subentries of electronic access rate.
5. The method as claimed in claim 4, wherein the step S2 comprises the following steps:
s21, collecting data of 24 subentry indexes of p cities to be evaluated, namely the utilization rate of electronic certificates with citizen identity numbers or uniform social credit codes of legal persons and other organizations as unique identifiers, the one-stop handling rate, the online uniform entrance rate, the urban traffic operation index release condition, the real-time forecast rate of public gasoline and electric vehicle incoming information, the electronic payment utilization rate of public traffic riding, the online handling condition of social security service, the opening rate of social security self-service of street communities, the online handling condition of social security service, the popularization rate of electronic medical records of more than two medical institutions, the reservation and diagnosis rate of more than two medical institutions, the visiting health record rate of more than two medical institutions, the popularization rate of multimedia classrooms of schools, the learning space coverage rate of living networks, the coverage rate of wireless networks of schools, the coverage of employment information services, the online handling condition of employment services, two subentry indexes, the provision condition of mobile internet urban service, the use condition of mobile internet urban service, the condition of one-user electronic information files, the establishment rate of electronic files, the sharing access rate of obstacles to the internet, the Internet disabilities, the online transaction ratio of the sharing of the electronic files, the retail transaction ratio of 24 subentry transaction data of the sharing of the online transaction, and the sharing of the retail network, and setting i as the data of the ith subentry index arranged according to the sequence, i =1,2,3, \823024, and 24, obtaining an original variable matrix X with 24X p order:
i.e. 24 itemized indices of p cities, is denoted x i,j ，x i,j Data representing the ith subentry index of the jth city, wherein i =1,2,3, \8230, 24, j =1,2,3, \8230, p;
s22, carrying out standardization processing on the original variable matrix X, eliminating dimension and magnitude influence, and obtaining a standardized matrix Z, wherein the formula of the standardized matrix Z is as follows:
wherein the content of the first and second substances,
represents the sample mean of the jth column data of the original variable matrix X,a sample standard deviation of j column data of an original variable matrix X is represented;
the normalization matrix Z is then expressed as follows:
wherein zx ij Data representing the ith row and the jth column of the normalized matrix Z;
s23, calculating a correlation coefficient matrix R according to the standardized matrix Z:
Z T is a transpose matrix of the standardized matrix Z, and the standardized matrix Z is recorded with a variable index zx 1 ,zx 2 ,…,zx p Wherein zx 1 ＝(zx 11 ,zx 21 ,…,zx 24,1 ) T ，zx 2 ＝(zx 12 ,zx 22 ,…,zx 24,2 ) T ，…，zx p ＝(zx 1p ,zx 2p ,…,zx 24,p ) T Then r is ab (a, b =1,2, \ 8230;, p) is the correlation coefficient of the variable index of the normalization matrix Z, r ab The calculation formula of (a) is as follows:
wherein zx ka To normalize the data in the k-th row and a-th column of the matrix Z, zx kb Data of a k row and a b column of the standardized matrix Z;to normalize the sample mean of the data in column a of matrix Z,sample mean of the b-th column data of the normalized matrix Z;
s24, solving all characteristic roots lambda through a characteristic equation | R-lambda I | =0 of the correlation coefficient matrix R, wherein lambda is a characteristic root of the characteristic equation, and I is a unit matrix c (c =1,2, \8230;, p), and is λ from large to small 1 ≥λ 2 ≥…≥λ p ≥0；
S25, obtaining the cumulative variance contribution rate alpha of the f factor according to the cumulative variance contribution rate calculation formula f ：
According to the cumulative variance contribution rate alpha f Not less than 0.85, to obtainThe number of principal components is m, and the number is respectively marked as a principal component F 1 ,F 2 ,…,F m To obtain a principal component F 1 ,F 2 ,…,F m Arranging the m characteristic roots from large to small corresponding to the m characteristic roots, namely lambda 1 ≥λ 2 ≥…≥λ m >0；
S26, aiming at the original variable matrix X, if the original variable index is marked as X 1 ,x 2 ,…,x p Wherein x is 1 ＝(x 11 ,x 21 ,…,x 24,1 ) T ，x 2 ＝(x 12 ,x 22 ,…,x 24,2 ) T ，…，x p ＝(x 1p ,x 2p ,…,x 24,p ) T Let the new variable after dimensionality reduction be z 1 ,z 2 ,…,z m (m.ltoreq.p), then
Wherein l gh The eigenvectors corresponding to the values of the m larger eigenroots of the correlation coefficient matrix R,
wherein λ is g For the m larger eigenroots of the correlation coefficient matrix R eigenequation,is a characteristic root λ g Corresponding feature vector, andfurther to find out Representing feature vectorsThe h component of (a);
by a 1 gh Obtaining a factor load matrix L:
s27, mixing gh Multiplying with a normalized matrix Z to obtain a principal component F 1 ,F 2 ,…,F m The expression of (c):
will l gh Substituted into new variable z after dimensionality reduction 1 ,z 2 ,…,z m (m is less than or equal to p) to obtain each main component F 1 ,F 2 ,…,F m Score of (a):
s28, using the eigenvalue lambda corresponding to m main components g (g =1,2, \8230;, m) is weighted to obtain an evaluation model F:
6. the method of claim 5, wherein the method comprises: according to the evaluation score of the citizen-benefitting service level of each city to be evaluated, the cities corresponding to the evaluation scores from large to small are the ranking of the citizen-benefitting service levels; and finding out corresponding subentry indexes of the city to be evaluated, which are beneficial to the citizen-benefiting service level and not beneficial to the citizen-benefiting service level, according to the principal component scores of the city to be evaluated, and providing a basis for future decisions of the city to be evaluated on the citizen-benefiting service.
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