CN107545380A - Livable City evaluation model based on principal component analysis - Google Patents
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Abstract
The invention discloses a kind of Livable City evaluation model based on principal component analysis, by the various data for directly handling different dimensions, and the characteristic value and characteristic vector for passing through dependency relation matrix, the combined weight number of each index is determined, so as to obtain the Livable City of linear combination evaluation scoring model.The model is carried out as follows：Problem is modeled and proposes reasonable assumption and symbol description；Important feasible evaluation index is determined by index analysis on its rationality；Data normalization processing；Calculate correlation matrix R；Calculate characteristic value and characteristic vector；P principal component is selected, establishes comprehensive evaluation model；Influence power analysis is carried out to evaluation index using factorial analysis.The present invention effectively utilizes comprehensive evaluation analysis ability of the PCA when handling many factors, is applied to Livable City problem analysis, and evaluation index influence power is judged based on factorial analysis.
Description
Technical field
The invention belongs to the model evaluated Livable City, specifically a kind of city based on principal component analysis
City's Livability assessment model.
Background technology
21st century urban construction has become the focus of world research with development, but the complexity in city itself causes
A series of optimization problem of the whole world facing to urban construction and development.Currently, the urban development theory of developed country has turned
To model that is comfortable and pleasant, and having moulded city good for habitation, and the China during Fast Urbanization and industrialization development is still
In the stage of fumbling that is theoretical and building., to lifting life of urban resident quality, improve city function and improve city operations and imitate
Rate is significant.
The livable property in city is one of much-talked-about topic of urban science research field, has material impact to urban development,
It is the emphasis of government and people's concern.Build harmonious city good for habitation has turned into the important goal of China's urban development at this stage,
It is the important component of currently proposed Chinese dream.Livable City is improved, to uplifting the people's living standard, improves city
Function has important social effect.
Will not only there be perfect infrastructure and good development prospect in one livable city, should also focus on people's
Heart is experienced.Can city carries the life of people, improve the life of people, and broad masses for the weighing apparatus of city good for habitation
Amount standard.Numerous scholars are studied Livable City and livable assessment of levels.Li Ye brocades et al. summarize city good for habitation
Progress and main academic viewpoint, emphasis looked back the research contents such as Conception of Livable City, intension, concentration discusses livable
Influence factor, appraisement system and the evaluation method in city, and point out the also existing weak point of city good for habitation's research and future
Research direction.Zhang Wenzhong has inquired into the intension of city good for habitation, analyzes city good for habitation and human settlement, living environment, ecological city
The similarities and differences of the related notions such as city, and in terms of safe and healthy, convenient, trip facility and comfortable for living etc. five of living, structure
The assessment indicator system of Jian Liao city good for habitatioies.Dong Xiao peaks et al. elaborate the livable progress of international city, analyze China city
The rise of livable Journal of Sex Research, discuss the direction of challenge and the theoretical work of China's Livable City.Jiang Jialin is more by establishing
Layer linear model (HLM) has carried out proof analysis to city good for habitation's influence to the construction factor.Jasmine et al. chooses economic development water less entirely
Five flat, eco-environmental quality, social civilization level, life comfort level and infrastructure construction aspects, build livable property and refer to
Mark appraisement system.Using provincial capital and city is directly under the jurisdiction of as research object, using AHP method of decision analysis, to China main cities
Livable property evaluated.Point out the livable property city skewness weighing apparatus in China, its geographical position, economic development and level of education etc.
Livable property important of the aspect to city.
The content of the invention
In place of the present invention is in order to overcome the shortcomings of the prior art, the quantitative data of principal component analysis is made full use of to integrate
Analysis ability, propose a kind of Livable City evaluation model based on principal component analysis, it is therefore intended that effectively utilize urban evaluation
The various data of index, evaluation model is established based on the dependency relation between data, while determine each index to common factor
Contribution, the invention calculating process simplicity result is clear and definite, is easy to degree livable to city to carry out the judgement of accurate science, and to how fast
Speed lifting Livable City is horizontal to make effectively analysis.
In order to realize foregoing invention purpose, the present invention adopts the following technical scheme that：
Livable City evaluation model based on principal component analysis, by directly handling the various data of different dimensions, and
By the characteristic value and characteristic vector of dependency relation matrix, the combined weight number of each index is determined, so as to obtain linear group
The Livable City evaluation scoring model of conjunction form.
Further, the model is carried out in accordance with the following steps：
Step 1：Problem is modeled and proposes reasonable assumption and symbol description；
Step 2：Important feasible evaluation index is determined by index analysis on its rationality；
Step 3：Data normalization processing；
Step 4：Calculate correlation matrix R；
Step 5：Calculate characteristic value and characteristic vector；
Step 6：P principal component is selected, establishes comprehensive evaluation model；
Step 7：Influence power analysis is carried out to evaluation index using factorial analysis.
Further, in step 1,
The modeling symbol includes：I is the i-th city；J is jth index；Z is characteristic vector；aijIt is target variable；It is
Standardized index；μjIt is j-th of index sample average；sjIt is i-th of index sample standard deviation；rijIt is i-th of index and finger
Target coefficient correlation；λ is matrix R characteristic value；U is standardized feature vector；yjIt is principal component；bjIt is the information tribute of principal component
Offer rate；apIt is the accumulation contribution rate of principal component；Z is comprehensive score；bizIt is z-th of characteristic vector of i-th of index；T be it is main into
Divide number；C is principal component contributor rate.
Further, in step 2,
Choose and use x1,x2,x3…xn(n=7) respectively represent GDP per capita, controlled income of each urban resident, room rate,
Green percentage, road mileage, the tertiary industry rank this seven indexs to contribution rate, the National urban crime rate of economic growth as shadow
Ring the index of the livable degree in city；M cities to be evaluated are represented respectively with i=1,2,3 ..., m, and i-th of j-th of city index becomes
Measure xjValue be denoted as aij, structural matrix A=(a)m×n。
Further, in step 3,
I-th of j-th of city target variable xjValue aijChange into standardized indexI.e.
Wherein：
That is μj、sjThe sample average and sample standard deviation of j-th of index；Accordingly, claim
For standardized index variable.
Further, in step 4,
Correlation matrix such as formula (3)
R=(rij)n×n (3)
Wherein
In formula (3)：rii=1, rij=rji, rijIt is the coefficient correlation of i-th of index and j-th of index.
Further, in step 5,
Calculate correlation matrix R eigenvalue λ1≥λ2≥......≥λn>=0, and corresponding standardized feature vector
u1,u2,.....,un, wherein uj=(u1j,u2j,......,unj)T, n new target variables are formed by characteristic vector：
In formula (4)：y1It is the principal component of first index；y2It is the principal component ... of second index, ynIt is n-th of index
Principal component.
Further, in step 6,
P principal component is selected, wherein, p≤n, calculate and establish comprehensive evaluation value model；
Step 6.1, eigenvalue λ is calculatedj(j=1,2 ... information contribution rate 7) and accumulation contribution rate, claim
For principal component yjInformation contribution rate；
For principal component y1,y2,…ypAccumulation contribution rate, work as αpClose to 1 (αp=0.85,0.90,0.95) when, then select
Preceding p target variable y1,y2,…ypAs p principal component, instead of original 7 target variables, so as to enter to p principal component
Row comprehensive analysis；
Step 6.2, comprehensive score is calculated：
In formula (7)：bjFor the information contribution rate of j-th of principal component, can be carried out evaluating according to comprehensive score value；
Correlation matrix is sought with MATLAB softwares, obtains t principal component：
Respectively principal component comprehensive evaluation model is built by weight of the contribution rate of t principal component：
Further, in step 7,
Step 7.1：Calculate elementary loading matrix；
According to the eigenvalue λ of the correlation matrix R obtained by step 51≥λ2≥…≥λn>=0, and corresponding feature to
Measure u1,…,un, wherein uj=[u1j,…,unj]T, elementary loading matrix is
Step 7.2：Scoring function is so as to judging evaluation index impact effect after calculating factor loading estimation and rotation；
According to the contribution rate of each common factor, k main gene is selected；The Factor load-matrix of extraction is rotated,
Obtain matrix(whereinFor Λ1Preceding k row, T is orthogonal matrix), structure requirement model
Scoring function after trying to achieve factor loading estimation and rotating, so as to judge evaluation index impact effect.
Compared with the prior art, beneficial effects of the present invention are embodied in：
1. obtaining the correlation matrix between data using different types of data, and evaluation is worth to based on correlation matrix feature
The index contribution weight coefficient of model, i.e. evaluation index weight coefficient are from data in itself and independent of artificial experience
Science and accurate and effective.
2. utilizing factor analysis and elementary loading matrix, score of each index in common factor is obtained, so as to
The index of the livable degree ranking in city can most be significantly affected by picking out, and lifted Livable City level for city manager and specified and exert
Power and improved direction and approach.
Embodiment
The present invention is described in further detail below.
In order to verify the validity of proposed Livable City evaluation model, 8 be applied in the economic zone of Huai-Hai
The livable property analysis of individual city (Suqian, Lianyun Harbour, Suzhou, Shangqiu, Jining, Zaozhuang, Xuzhou, the Huaibei), the seven of this eight cities
Individual achievement data is as shown in table 2, then evaluation model index number n=7, evaluation object number m=8.
Case-study step is：
Eight, 2 Huai-Hai economic zone of table, seven, city achievement data table
Evaluation model and the data of table 2 based on principal component analysis, tried to achieve using MATLAB softwares 7 before correlation matrix
Individual characteristic root and its contribution rate are as shown in table 3：
The principal component analysis result of table 3
As can be seen that the contribution rate of accumulative total of preceding four characteristic roots just reaches more than 90%, principal component analysis effect is fine, because
Four principal components carry out overall merit, characteristic vector such as table 4 corresponding to preceding four characteristic roots before this chooses.
Characteristic vector corresponding to preceding 4 principal components of the standardized variable of table 4
It can thus be concluded that four main are respectively into composition:
By weight of the contribution rate of three principal components, the comprehensive evaluation model of structure principal component is respectively：
Z=0.4435y1+0.2116y2+0.1612y3+0.1028y4 (12)
By formula (12) and table 2, city good for habitation's ranking is obtained, such as table 5,
The ranking of table 5 and comprehensive evaluation result
Calculate correlation matrix R eigenvalue λ1≥λ2≥…≥λ7>=0, and corresponding characteristic vector u1,…,u7, its
Middle uj=[u1j,…,u7j]T, elementary loading matrix is
The characteristic root being calculated and the contribution such as table 6 below of each factor.
The contribution of the characteristic root of table 6 and each factor
According to the contribution rate of each common factor, 4 main genes are selected.The Factor load-matrix of extraction is rotated,
Obtain matrix(whereinFor Λ1It is preceding four row, T is orthogonal matrix), structure requirement model, as shown in formula (14)
Scoring function after trying to achieve factor loading estimation and rotating, as shown in table 7.
The factorial analysis table of table 7
It can be seen from Table 7 that having obtained four factors, first factor is x5The factor, represents road mileage, and second
The individual factor is x6The factor, contribution rate of the tertiary industry to economic growth is represented, the 3rd factor is x3The factor, room rate is represented,
4th factor is x2The factor, represent cities and towns per capita disposable income.This illustrates x5, x6, x3And x2Representative evaluation refers to
Mark, in Livable City assessment of levels, has important influence power, it is therefore desirable to be improved in terms of these, so as to have
Effect lifting Livable City is horizontal.
Step 1：Model basic assumption and model symbol explanation
Step 1.1 model hypothesis are established
Appropriate hypothesis is advantageous to model and accurately and effectively describes Livable City level.
1) all data all true and accurates are assumed.
2) assume that influence of each index to Livable City is independent.
3) assume that eight studied cities are separate, do not influence each other.
4) social equilibrium's development is assumed.
Step 1.2 models symbol description
For the needs of modeling, related symbol is illustrated, as shown in table 1.
Table 1 models symbol description
Step 2：Important feasible evaluation index is determined by index analysis on its rationality
The livable degree index system in city is description and the set for the mensurable parameter for evaluating human settlement environment in city livable-in
It assessment indicator system, should set about from humanistic environment and the broad aspect of natural environment two, come from economic, ecology, society, life etc.
Evaluate satisfaction of the resident to occupied city.Economy is the basis of urban development, and influences the important of Living consumption
Factor.GDP per capita, city dweller's disposable income and room rate more can intuitively show the economic level of city dweller.Environment
Graceful degree and urban green coverage rate have a major impact to the livable property in city.The traffic in city and road mileage determine resident trip
Convenient degree；And the horizontal contribution rate increased with tertiary industry prosperity degree to urban economy of business development in a city is then
Reflect the development degree in city.National urban crime rate seniority among brothers and sisters then embodies the safe coefficient in city, is to influence livable property
Key factor.
Referred to based on above-mentioned analysis and documents and materials, choose GDP per capita, controlled income of each urban resident, room rate, green
Rate, road mileage, the tertiary industry rank this seven indexs on contribution rate, the National urban crime rate of economic growth as influence
The index of the livable degree in city.
Use x1,x2,x3…xn(n=7) GDP per capita, cities and towns per capita disposable income, room rate, urban landscape are represented respectively
Contribution rate, the National urban crime seniority among brothers and sisters of (green percentage), road mileage, the tertiary industry to economic growth.With i=1,2,3 ..., m
M cities to be evaluated, i-th of j-th of city target variable x are represented respectivelyjValue be denoted as aij, structural matrix A=(a)m×n。
Step 3：The processing of initial data data normalization.
By each index aijChange into standardized indexI.e.
Wherein：
That is μj、sjThe sample average and sample standard deviation of j-th of index.Accordingly, claim
For standardized index variable.
Step 4：Calculate correlation matrix R.
Shown in correlation matrix such as formula (3)
R=(rij)n×n (3)
Wherein
In formula (3)：rii=1, rij=rji, rijIt is the coefficient correlation of i-th of index and j-th of index.
Step 5：Calculate characteristic value and characteristic vector.
Calculate correlation matrix R eigenvalue λ1≥λ2≥......≥λn>=0, and corresponding standardized feature vector
u1,u2,.....,un, wherein uj=(u1j,u2j,......,unj)T, n new target variables are formed by characteristic vector：
In formula (4)：y1It is the principal component of first index；y2It is the principal component ... of second index, ynIt is n-th of index
Principal component.
Step 6：P (p≤n) individual principal component is selected, calculates and establishes comprehensive evaluation value model.
Step 6.1 calculates eigenvalue λj(j=1,2 ... information contribution rate 7) and accumulation contribution rate, claim
For principal component yjInformation contribution rate；
For principal component y1,y2,…ypAccumulation contribution rate, work as αpClose to 1 (αp=0.85,0.90,0.95) when, then select
Preceding p target variable y1,y2,…ypAs p principal component, instead of original 7 target variables, so as to enter to p principal component
Row comprehensive analysis.
Step 6.2 calculates comprehensive score：
In formula (7)：bjFor the information contribution rate of j-th of principal component, can be carried out evaluating according to comprehensive score value.
Correlation matrix is sought with MATLAB softwares, obtains t principal component：
Respectively principal component comprehensive evaluation model is built by weight of the contribution rate of t principal component：
Step 7：Influence power analysis is carried out to evaluation index using factorial analysis.
Step 7.1：Calculate elementary loading matrix.
According to the eigenvalue λ of the correlation matrix R obtained by step 51≥λ2≥…≥λn>=0, and corresponding feature to
Measure u1,…,un, wherein uj=[u1j,…,unj]T, elementary loading matrix is
Step 7.2：Scoring function is so as to judging evaluation index impact effect after calculating factor loading estimation and rotation.
According to the contribution rate of each common factor, k main gene is selected.The Factor load-matrix of extraction is rotated,
Obtain matrix(whereinFor Λ1Preceding k row, T is orthogonal matrix), structure requirement model, as shown in (11) formula.
Scoring function after trying to achieve factor loading estimation and rotating, so as to judge evaluation index impact effect.
By specific embodiment and its result, the Livable City evaluation model based on principal component analysis can be direct
The various data of different dimensions are handled, by the characteristic value and characteristic vector of dependency relation matrix, determine the combination of each index
Weight coefficient, so as to obtain the Livable City of linear combination evaluation scoring model, essence is to utilize achievement data itself
Dependency relation obtain each index evaluation contribution weight, without artificial experience judge.It is additionally based on characteristic value and feature
Vector, elementary loading matrix is constructed, thus obtains Factor Analysis Model, it is determined that each evaluation index is in common factor
The contribution rate of common factor.The Livable City evaluation model construction that is itd is proposed is succinct directly perceived, result of calculation is simply clear and definite, not only
The livable rational ranking analysis of degree in city can be given, can also determine to significantly affect the index of the livable degree in city.It can help
City manager makees science to Livable City development level and accurately judged, while is the lifting livable horizontal improved route in city
Effective guidance is done, so as to which the management for the livable property of Chinese Urbanization and construction provide scientific basis.
In summary, the invention discloses a kind of Livable City evaluation model based on principal component analysis, its feature letter
Breath is shown as follows：1. a pair problem modeling proposes reasonable assumption and symbol description；2. determined by index analysis on its rationality
Important feasible evaluation index；3. data normalization is handled；4. calculate correlation matrix R；5. calculate characteristic value and feature to
Amount；6. selecting p principal component, comprehensive evaluation model is established；7. influence power analysis is carried out to evaluation index using factorial analysis.This
Invention effectively utilizes comprehensive evaluation analysis ability of the PCA when handling many factors, and it is livable to be applied to city
Property problem analysis, and evaluation index influence power is judged based on factorial analysis.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention.All essences in the present invention
All any modification, equivalent and improvement made within refreshing and principle etc., should be included in the scope of the protection.
Claims (9)
1. the Livable City evaluation model based on principal component analysis, it is characterised in that：By directly handling each of different dimensions
Kind of data, and by the characteristic value and characteristic vector of dependency relation matrix, the combined weight number of each index is determined, so as to obtain
The Livable City of linear combination is taken to evaluate scoring model.
2. the Livable City evaluation model according to claim 1 based on principal component analysis, it is characterised in that：According to such as
Lower step is carried out：
Step 1：Problem is modeled and proposes reasonable assumption and symbol description；
Step 2：Important feasible evaluation index is determined by index analysis on its rationality；
Step 3：Data normalization processing；
Step 4：Calculate correlation matrix R；
Step 5：Calculate characteristic value and characteristic vector；
Step 6：P principal component is selected, establishes comprehensive evaluation model；
Step 7：Influence power analysis is carried out to evaluation index using factorial analysis.
3. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 1
In,
The modeling symbol includes：I is the i-th city；J is jth index；Z is characteristic vector；aijIt is target variable；It is standard
Change index；μjIt is j-th of index sample average；sjIt is i-th of index sample standard deviation；rijIt is i-th of index and index
Coefficient correlation；λ is matrix R characteristic value；U is standardized feature vector；yjIt is principal component；bjIt is the information contribution rate of principal component；
apIt is the accumulation contribution rate of principal component；Z is comprehensive score；bizIt is z-th of characteristic vector of i-th of index；T is principal component
Number；C is principal component contributor rate.
4. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 2
In,
Choose and use x1,x2,x3…xn(n=7) GDP per capita, controlled income of each urban resident, room rate, greening are represented respectively
Rate, road mileage, the tertiary industry rank this seven indexs on contribution rate, the National urban crime rate of economic growth as influence city
The index of the livable degree in city；M cities to be evaluated, i-th of j-th of city target variable x are represented respectively with i=1,2,3 ..., mj
Value be denoted as aij, structural matrix A=(a)m×n。
5. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 3
In,
I-th of j-th of city target variable xjValue aijChange into standardized indexI.e.
Wherein：That is μj、sjThe sample average and sample of j-th of index
This standard is poor；Accordingly, claim
For standardized index variable.
6. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 4
In,
Correlation matrix such as formula (3)
R=(rij)n×n (3)
Wherein
In formula (3)：rii=1, rij=rji, rijIt is the coefficient correlation of i-th of index and j-th of index.
7. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 5
In,
Calculate correlation matrix R eigenvalue λ1≥λ2≥......≥λn>=0, and corresponding standardized feature vector u1,
u2,.....,un, wherein uj=(u1j,u2j,......,unj)T, n new target variables are formed by characteristic vector：
In formula (4)：y1It is the principal component of first index；y2It is the principal component ... of second index, ynIt is the master of n-th of index
Composition.
8. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 6
In,
P principal component is selected, wherein, p≤n, calculate and establish comprehensive evaluation value model；
Step 6.1, eigenvalue λ is calculatedj(j=1,2 ... information contribution rate 7) and accumulation contribution rate, claim
For principal component yjInformation contribution rate；
For principal component y1,y2,…ypAccumulation contribution rate, work as αpClose to 1 (αp=0.85,0.90,0.95) when, then p before selecting
Individual target variable y1,y2,…ypAs p principal component, instead of original 7 target variables, so as to be carried out to p principal component
Comprehensive analysis；
Step 6.2, comprehensive score is calculated：
In formula (7)：bjFor the information contribution rate of j-th of principal component, can be carried out evaluating according to comprehensive score value；
Correlation matrix is sought with MATLAB softwares, obtains t principal component：
Respectively principal component comprehensive evaluation model is built by weight of the contribution rate of t principal component：
9. the Livable City evaluation model according to claim 2 based on principal component analysis, it is characterised in that：Step 7
In,
Step 7.1：Calculate elementary loading matrix；
According to the eigenvalue λ of the correlation matrix R obtained by step 51≥λ2≥…≥λn>=0, and corresponding characteristic vector
u1,…,un, wherein uj=[u1j,…,unj]T, elementary loading matrix is
Step 7.2：Scoring function is so as to judging evaluation index impact effect after calculating factor loading estimation and rotation；
According to the contribution rate of each common factor, k main gene is selected；The Factor load-matrix of extraction is rotated, obtained
Matrix(whereinFor Λ1Preceding k row, T is orthogonal matrix), structure requirement model
Scoring function after trying to achieve factor loading estimation and rotating, so as to judge evaluation index impact effect.
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