CN102222313A - Urban evolution simulation structure cell model processing method based on kernel principal component analysis (KPCA) - Google Patents

Abstract

The invention relates to an urban evolution simulation structure cell model processing method based on kernel principal component analysis (KPCA). The method comprises the following steps of: (1) outputting a remote sensing image twenty years before of a selected region to a KPCA spatial data processing module, performing data processing on the remote sensing image twenty years before with the module and establishing a geographical CA (Cellular Automata) conversion rule; (2) classifying a current remote sensing image of the selected region by using remote sensing image processing software to obtain an urban development classification chart of the researched region, wherein the urban development classification chart is taken as a reference for evaluating a simulation result; (3) performing simulation and prediction of a KPCA-CA (Kernel Principal Component Analysis-Cellular Automata) model on the researched region by using a geographical CA simulation frame to obtain a simulation and prediction chart; and (4) comparing the simulation and prediction chart obtained in the step (3) with the urban development classification chart obtained in the step (2) to obtain a simulation result and an evaluation report of model performance. Compared with the prior art, the method has the advantage of obtaining more reasonable conversion rule and simulation result and the like on the cost of reasonable computation.

Description

City evolution simulation cellular models treated method based on core principle component analysis

Technical field

The present invention relates to a kind of city evolution analogy model disposal route, especially relate to a kind of city evolution simulation cellular models treated method based on core principle component analysis.

Background technology

(Cellular Automata, CA) since the complicacy of recognition system, CA has obtained using comparatively widely at natural science and social science numerous areas to propose to utilize cellular automaton from Wolfram.In the urban geography field, cellular automaton is used to simcity form evolution and the soil utilization changes, the possibility sight in future in city under the different planning of the prediction restrictive conditions.At present, the cellular automaton simulation has become the effective means of being familiar with and understanding city complex space general layout and evolutionary process.

In geographical CA simulation, to NextState, institute is based on the transformation rule that reflects the city growth mechanism to urban morphology from last state evolution.Therefore, the definition of transformation rule just becomes the core of geographical CA city simulation.In the research, several different methods is used to the analysis space variable, thereby obtains the rule of geographical CA both at home and abroad, and these methods mainly comprise: (1) spatial statistics method, as least square method and logistic homing method etc.; (2) artificial intelligence and machine learning are as fuzzy logic, genetic algorithm, neural network, immunity intelligence, and support vector machine etc.; (3) system dynamics method, etc.But, influence between the space variable that urban development and soil utilization change and often have serious correlativity, traditional spatial statistics method can't be eliminated the adverse effect that the multiple conllinear of variable brings, and can not portray the nonlinear kinetics process in city well, so the true form in the difficult reflection of analog result city; And research thinks that some intelligent Modeling methods but can obtain analog result preferably, but its parameter physical significance and indeterminate.Therefore, we need explore the non-linear process of a kind of correlativity that can eliminate space variable, reflection urban development, simultaneously its parameter transformation rule of having clear and definite physical significance again.

Summary of the invention

Purpose of the present invention be exactly provide in order to overcome the defective that above-mentioned prior art exists a kind of can be with rational calculation cost, obtain comparatively reasonably transformation rule and analog result, and its simulation cellular models treated method that can develop for the city based on core principle component analysis that city planning and decision-making provide the reference of usefulness that predicts the outcome also.

Purpose of the present invention can be achieved through the following technical solutions:

A kind of city based on core principle component analysis develops and simulates cellular models treated method, it is characterized in that, may further comprise the steps:

1) will select the remote sensing image before 20 years of zone to output in the core principle component analysis spatial data processing module, this module is carried out data processing to the remote sensing image before 20 years, sets up the transformation rule of geographical CA;

2) by the remote sensing image process software to selecting the present classification of remote-sensing images in zone, obtain the urban development classification chart of survey region, as the benchmark of estimating analog result;

3) by geographical cellular automaton phantom frame, survey region is carried out the simulation and the prediction of the geographical cellular model (KPCA-CA) of core principle component analysis, obtain simulation and prognostic chart;

4) with the simulation in the step 3) and prognostic chart and step 2) in the urban development classification chart compare, obtain the appraisal report of analog result and model performance;

5) output and preservation analog result.

Described 1) data handling procedure in is as follows:

11) from remote sensing image, extract the space length variable data, data are carried out standardization;

12) choose kernel function f (xij), and obtain the matrix K that kernel function is formed as element,

Wherein,

In the formula, f (x _Ij) be kernel function,

Be x _i(j=1,2 ..., expectation value m), σ is the standard deviation of DS;

13) utilize this kernel function to shine upon, obtain the new matrix K under the high-dimensional feature space ^*, K ^*=K-AK-KA+AKA, wherein A is the matrix that all elements is 1/m, and compute matrix K ^*The eigenwert μ of/m _i(i=1 ..., m) with proper vector v _i(i=1 ..., m);

14) extract major component, find out l major component characteristic of correspondence value μ _j(i=1 ..., l) with proper vector v _j(i=1 ..., l);

15) ask for cellular under the area variable effect at t transition probability constantly:

$P_k^{t,l}=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}$

16) consider cellular neighbours' influence, constraints limit and enchancement factor, soil cellular k at t development probability constantly is:

$P_k^t=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}\×\frac{\underset{3\×3}{\mathrm{\Σ}}\mathrm{con}(S_k=\mathrm{urban})}{3\×3-1}\×\mathrm{con}({\mathrm{cell}}_k^t=\mathrm{suitable})\×(1+{(-\ln \mathrm{\γ})}^{\mathrm{\β}})$

Wherein, P _k ^tBe cellular k at t joint development probability constantly, con (cellkt=suitable) is a limiting factor, and 1+ (ln γ) β is an enchancement factor;

17) calculate after the probability of each cellular development, itself and pre-set threshold compared, if the urban development probability of cellular more than or equal to this threshold value, then this cellular is converted to urban land, otherwise this cellular is not converted to urban land.

Space length variable in the described step 11) is included in intown distance, to the distance at center, town, to the distance of main roads, to the distance in vegetable garden, to the distance in arable land.

It is as follows that data in the described step 11) are carried out standardized method:

Wherein,

s _jIt is its standard deviation.

Compared with prior art, the present invention has the following advantages:

(1) core principle component analysis can carry out dimension-reduction treatment to space variable under the prerequisite of information loss minimum, and can realize that the non-linear major component of space variable is extracted in the geographical CA modeling with kernel method.Therefore, the geographical cellular rule based on KPCA can reflect urban development complex nonlinear process better.

(2) utilize geographical cellular automaton phantom frame, can extract the geographical space variable easily, obtain the space sample data, and carry out otherwise pre-service; This framework can be carried out multiple cellular model (as the KPCA-CA of this paper) easily simultaneously, and analog result is carried out accuracy assessment.

(3) the KPCA-CA model conforms to better with actual conditions to the analog result that Jiading District 1989-2006 city, Shanghai City develops.The calculating of simulation precision and the analysis showed that, the overall accuracy of KPCA-CA model is 80.67%, the Kappa coefficient is 61.02%, the geographical cellular model that is better than linear principal component analysis (PCA) cellular model (PCA-CA), latter's overall accuracy are 76.55%, the Kappa coefficient is 52.58%.From analog result and actual count relatively, the result of KPCA-CA model also more meets the truth that the city develops.This studies show that, utilizes the core principle component analysis method to obtain comparatively reasonably transformation rule and analog result with rational calculation cost, and it predicts the outcome also and can provide the reference of usefulness for city planning and decision-making.

Description of drawings

Fig. 1 is a process flow diagram of the present invention;

Fig. 2 be in the KPCA method each major component contribution rate of accumulative total with the situation of change of nuclear parameter;

Fig. 3 be KPCA-CA and PCA-CA analog result ratio of precision.

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Embodiment

With the test site of Shanghai City Jiading District as the KPCA-CA model.Jiading District is positioned at the northwestward, Shanghai City, adjoins with the Kunshan City, Jiangsu Province, belongs to the outer suburbs on the region, and administrative area under one's jurisdiction area is 463.6km ²Past 20 years was the fast-developing period of Jiading District, and soil utilization/covering changes constantly and changes, and the completed region of the city continues to enlarge.With the test site of so quick urbanized area, can check the validity of this model preferably as the KPCA-CA model.The data that this test is adopted are mainly two groups of remote sensing images in Landsat-5 TM on August 6th, 1989 and on April 30th, 2006.

The major component contribution rate that table 1 obtains according to various different IPs parameters

The space sample data matrix that obtains is implemented the KPCA conversion obtain K ^*/ m.Further to K ^*/ m carries out principal component analysis (PCA), obtains the irrelevant major component of corresponding linear.Different nuclear parameters can obtain different K ^*/ m matrix, therefore the major component of finally obtaining is also different.Table 1 has shown under the different IPs parameter, the contribution rate of each major component.Clearly, along with nuclear parameter increases, the contribution rate of first principal component obviously increases, and the contribution rate of accumulative total of first three major component also sharply increases simultaneously.When nuclear parameter greater than 10 the time, this variation is no longer obvious, each major component contribution rate of accumulative total is with variation such as Fig. 2 of nuclear parameter.

Because nuclear parameter is that 10 o'clock preceding two major components are D _Urbancenter, D _Towncenter, D _Mainroad, D _Plowland, D _Kaleyard: 0.917 ,-0.159,0.954 ,-0.872 ,-0.882;-0.121,0.982,0.689 ,-0.487 ,-0.444, its contribution rate of accumulative total is 97.526%, and wherein the 1st major component is mainly represented the information based on city center and road, and the 2nd major component is mainly represented the information based on center, town and road.The accuracy of the ca parameter of considering calculated amount and obtaining is used for explaining the version space variable with these two major components.Nuclear parameter is 10 o'clock, and the geographical CA rule of utilizing the KPCA method to obtain is as follows:

$P_k^t=\frac{1}{1+\exp [-(0.5330*D_{\mathrm{urbancenter}}+0.2421*D_{\mathrm{towncenter}}+0.7314*D_{\mathrm{mainroad}}-0.7164*D_{\mathrm{plowland}}-0.7077*D_{\mathrm{kaleyaed}})]}$

$\×\frac{\underset{3\×3}{\mathrm{\Σ}}\mathrm{con}(S_k=\mathrm{urban})}{3\×3-1}\×\mathrm{con}({\mathrm{cell}}_k^t=\mathrm{suitable})\×(1+{(-\ln \mathrm{\γ})}^{\mathrm{\β}})$

The 1st cellular local transitions probability in the formula for obtaining by KPCA,

Be the cellular neighborhood, con (cell _k ^t=suitable) be the development restriction condition, 1+ (ln γ) ^βBe the development enchancement factor.Turnpike road (D in the rule of obtaining by KPCA _Mainroad) and city center (D _Urbancenter) weight is bigger, and is consistent with preceding two meanings that major component contained.

As a kind of nonlinear principal component analytical method (PCA), KPCA relates to nonlinear computation aspect dimension-reduction treatment, and is therefore longer with respect to its time consumption for training of linear PCA; Under the identical calculations environment, this research space sample to be trained, surpass the logistic homing method computing time of KPCA to a certain extent, but the ca parameter that KPCA obtains can reflect the complex nonlinear essence of urban development better.

Threshold value is determined

In the CA simulation process, need to be provided with what kind of threshold value P actually _Threshold, and how long each dry run (Iteration) represent the real time, be need be in the middle of model calibration problem repeatedly.Simultaneously, P _ThresholdSetting and the time span of Iteration representative confidential relation is arranged.For calibration model, expand the threshold value range of choice to 0.40～0.92, each test is finished, and threshold value is increased by 0.02 test next time.Each threshold value correspondence repeatedly circulates (Iteration), and wherein must existing once, simulation is that precision is the highest.Model tuning just is based on simulation urban development in 2006, with simulation drawing that obtains and the urban development classification chart that obtains by the remote sensing classification, utilizes confusion matrix to compare, and selects wherein overall accuracy maximal value corresponding threshold P _ThresholdAnd the best of breed of number of run (Iteration).Utilize Jiading District history image data that the KPCA-CA model is proofreaied and correct, obtain P _ThresholdBe 0.62, Iteration is 17, overall accuracy is 80.67%.Simultaneously, for comparative studies, we also proofread and correct the cellular model based on PCA, obtain P _ThresholdBe 0.64, Iteration is 17, overall accuracy is 76.55%.

Analog result and analysis

Analog result figure and reference map are pursued cellular relatively, obtain confusion matrix (table 2) based on the KPCA-CA model result.From producer's angle, at the remote sensing image reference map is in the cellular in non-city, have 84.09% in analog result also right and wrong city cellular, but have 15.91% in analog result, to belong to other types, promptly omitted 15.91% city cellular in the analog result; And from user's angle, in all are modeled as the cellular in non-city, have 80.61% in reference map also right and wrong city cellular, but 19.39% cellular that is modeled as non-city is arranged, in reference map, belong to other types, promptly mistakenly the cellular of other types is modeled to for non-city cellular.

For the city cellular, from producer's angle, in the remote sensing image reference map, be the city class, and also be that the ratio of city class is 76.73% in analog result, this means that 23.27% belongs to other types in analog result, promptly omitted 23.27% city cellular in the analog result; And from user's angle, in being modeled as the cellular in city, all have 80.74% also to be the city cellular in reference map, but 19.26% cellular that is modeled as the city is arranged, in reference map, belong to other types, promptly mistakenly the cellular of other types is modeled to for the city cellular.And overall accuracy shows, has 80.67% cellular to be carried out correct simulation; From whole consistance, KPCA-CA modeling result's Kappa coefficient is 61.02%.

The confusion matrix of table 2 KPCA-CA simulation Jiading District urban development

Suppose that the Shanghai City Jiading District keeps present urban development mechanism, and city planning, policy wind direction etc. do not develop great change,, can predict its city space general layout in 2010 years then according to this KPCA-CA model.From analog result, the future development of Jiading District city is (Jiading town), zone, the southeast (near center, Shanghai City) and turnpike road and extend mainly along the central area, promptly is basically outwards to expand on original basis of building up zone (Jiading new city, manufacturing district, Jiading, Jiang Qiao town and very new street); And, be from the Jiading District center along turnpike road radial southeastward, a plurality of directions such as northeast, northwest, southwest develop; Simultaneously, along with the construction in international automobile city, Shanghai, this distinguish southern Huang Du, peace booth two towns have formed new city development zone.

Clearly, the KPCA-CA model is syncaryon method, PCA and cellular Automation Model and set up, therefore can by accuracy assessment detect it than the improvement (table 3 and Fig. 3) of PCA cellular model.As known from Table 3, for cellular unconverted situation in soil in the practical development of city, promptly non-city cellular, producer's ratio of precision PCA-CA model of KPCA-CA model is high nearly 2.05%, and user's precision is high by 4.59%; And the soil cellular that changes has taken place for reality, i.e. city cellular, user's ratio of precision PCA-CA model of KPCA-CA model is high by 6.50%, and producer's precision is high by 3.47%; The property ignored mistake and substituting mistake be respectively by producer's precision and user's accuracy computation and, its numerical value is with afterwards both equate, but opposite in sign.

The ratio of precision of table 3 KPCA-CA and PCA-CA analog result

The KPCA-CA model is higher by 4.12% than PCA-CA model on the overall accuracy, and the former is higher by 8.44% than the latter in Kappa coefficient aspect.This shows, utilize KPCA under high-dimensional feature space, to extract ca parameter, promoted the precision of analog result to a certain extent, make that analog result is also reasonable more and approach the actual evolution situation in city.

Simultaneously, this paper has calculated area control accuracy and area discrepancy index, portray model owing to having added the uncertainty influence that random factor produces, if model can be controlled the harmful effect that uncertain factor produces better, then its performance also just good (table 4) more.

Table 4 compares based on the cellular modeling result's of KPCA and PCA area controlling index

As shown in Table 4, the KPCA-CA model aspect the area controlling index of city cellular than PCA-CA model height, wherein the area control accuracy of KPCA-CA model is 95.59%, the simulation area is less than statistics area 4.41%, and the area control accuracy of the city cellular of PCA-CA model is 91.43%, and the simulation area is greater than actual count area 8.57%.Aspect the area controlling index of non-city cellular, the KPCA-CA model is equally than PCA-CA model height, wherein KPCA-CA model area control accuracy is 96.21%, the simulation area is greater than statistics area 3.79%, and the area control accuracy of the non-city cellular of PCA-CA model is 92.63%, and the simulation area is less than actual count area 7.37%.Aspect area control accuracy and area discrepancy index, the KPCA-CA model all increases than PCA-CA model, and this has proved that from another angle KPCA has played effect preferably to the improvement of PCA method.

Core principle component analysis

The basic thought of core principle component analysis is that kernel method is applied in the principal component analysis (PCA).Realize the mapping of input space X to high-dimensional feature space F, i.e. the sample point x of the input space by transforming function transformation function Φ () ₁, x ₂..., x _m, be transformed to the sample point Φ (x of feature space ₁), Φ (x ₂) ..., Φ (x _m), in feature space, use principal component analysis (PCA) to find the solution its eigenvalue problem then.In new higher dimensional space, it is as follows to obtain new covariance matrix:

$C=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Φ}\left(x_i\right)\mathrm{\Φ}{\left(x_i\right)}^T---\left(1\right)$

In order to obtain first principal component, need to solve Cv=μ v, μ is designated as the eigenwert in new space, v is the pairing proper vector of μ.C in this problem to be solved is replaced with formula (1), obtains down establishing an equation:

$\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Φ}\left(x_i\right)\left({\mathrm{\Φ}}^T\left(x_i\right)v\right)=\mathrm{\μv}---\left(2\right)$

This is the equation that needs solution, but we do not wish to solve in higher dimensional space.Because v is Φ (x _i) linear combination, must have one group of α _iMake

Set up.

Expression formula above utilizing is replaced the v in the formula (2), then has:

$\mathrm{\μ}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_i\mathrm{\Φ}\left(x_i\right)=\frac{1}{m}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\mathrm{\Φ}\left(x_i\right){\mathrm{\Φ}}^T\left(x_i\right)\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_i\mathrm{\Φ}\left(x_i\right)---\left(3\right)$

But not all transform function () all in inner product, therefore need be taken advantage of Φ (x together in formula (3) both members _n), n=1:m does inner product, obtains:

$\mathrm{\μ}\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\Φ}}^T\left(x_n\right)\mathrm{\Φ}\left(x_i\right)=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_j\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\left({\mathrm{\Φ}}^T\left(x_n\right)\mathrm{\Φ}\left(x_i\right)\right)\left({\mathrm{\Φ}}^T\left(x_i\right)\mathrm{\Φ}\left(x_j\right)\right)---\left(4\right)$

Like this, can therefore need not directly in higher dimensional space, resolve by replacing inner product with kernel function.

The note kernel function is:

K _ij＝Φ ^T(x _i)Φ(x _j)＝K(x _i，x _j) (5)

According to the definition of K, can again formula (4) be expressed as:

$\mathrm{\μK\α}=\frac{1}{m}{K}^2\mathrm{\α}---\left(6\right)$

Therefore, only need obtain eigenwert just can finish solution procedure.In order to extract major component, have simply:

y _i＝v ^tx (7)

For all i, v is the relevant proper vector of major component.At last, former data are rebuild:

$y_i=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_i{(\mathrm{\Φ}}^T\left(x_j\right)\mathrm{\Φ}\left(x_i\right)=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x_i,x_j)---\left(8\right)$

Cellular model based on KPCA

Based on above-mentioned KPCA theory, we can obtain the transformation rule of geographical CA.At first obtain the space variable data set, and with its standardization.Utilization is extracted space length variable data (a certain proportion of sample point is as 20%) at the cellular automaton phantom frame SimUrban of independent development from remote sensing image, comprising: to intown distance (D _Urbancenter), to the distance (D at center, town _Towncenter), to the distance (D of main roads _Mainroad), to the distance (D in vegetable garden _Kaleyard), to the distance (D that ploughs _Plowland) wait 5 kinds apart from variable.The gained data are carried out standardization, the information distortion of avoiding the dimension difference to cause, method is:

$x_{\mathrm{ij}}^{*}=(x_{\mathrm{ij}}-{\stackrel{\‾}{x}}_j)/s_j---\left(9\right)$

Wherein,

s _jBe its standard deviation, then new sample data collection is $X^{*}={\left(x_{\mathrm{ij}}^{*}\right)}_{n\×p}=(x_1^{*},...,x_p^{*}).$

Choose suitable kernel function, obtain matrix K.Generally speaking, K is kernel function f (x _Ij) matrix formed as element., can represent the coverage of urban development characteristic according to the regional space variable with Gaussian radial basis function with range attenuation.General Gaussian radial basis function is:

$f\left(x_{\mathrm{ij}}\right)=\exp (-{(x_{\mathrm{ij}}-{\stackrel{\‾}{x}}_j)}^2/2{\mathrm{\σ}}^2)---\left(10\right)$

In the formula, f (x _Ij) be x _IjGaussian radial basis function,

Be x _i(j=1,2 ..., expectation value m), σ is the standard deviation of DS.Gaussian radial basis function shows that this basis function f (x) is in central value

The place reaches maximal value, from

F far away more (x) is more little.This speed of successively decreasing is relevant with radially basic width parameter σ, and σ is big more, and the speed that f (x) successively decreases is more little; σ is more little, shows x _iDistributing concentrates on central value more, and radially Ji width is more little.

Utilize this kernel function to shine upon, obtain the new matrix K under the high-dimensional feature space ^*, K ^*=K-AK-KA+AKA, wherein A is the matrix that all elements is 1/m.

Compute matrix K ^*The eigenwert μ of/m _i(i=1 ..., m) with proper vector v _i(i=1 ..., m).Extract major component, find out l major component characteristic of correspondence value μ _j(i=1 ..., l) with proper vector v _j(i=1 ..., l).

Each is estimated sample obtain composite evaluation function, carry out comprehensive evaluation.Preceding two major components of finding the solution out by KPCA just can be expressed the most information of sample point generally speaking, and its dimensionality reduction effect is obvious, and this also is one of reason of using in geographical cellular Automation Model KPCA.

Satisfactory major component is carried out Comprehensive Assessment, and then the cellular automaton based on the local space variable can be expressed as at t transition probability constantly:

$P_k^{t,l}=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}---\left(11\right)$

Consider cellular neighbours' influence, constraints limit and enchancement factor, soil cellular k at t development probability constantly is:

$P_k^t=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}\×\frac{\underset{3\×3}{\mathrm{\Σ}}\mathrm{con}(S_k=\mathrm{urban})}{3\×3-1}\×\mathrm{con}({\mathrm{cell}}_k^t=\mathrm{suitable})\×(1+{(-\ln \mathrm{\γ})}^{\mathrm{\β}})---\left(12\right)$

Wherein, P _k ^tBe that cellular k is at t joint development probability constantly, con (cell _k ^t=suitable) be limiting factor, 1+ (ln γ) ^βIt is enchancement factor.

Calculate after the probability of each cellular development, itself and pre-set threshold are compared, if the urban development probability of cellular is more than or equal to this threshold value P _Threshold, then this cellular is converted to urban land, otherwise this cellular is not converted to urban land.Analyze in conjunction with KPCA, the final criterion that we can obtain the KPCA-CA model is:

With other kernel methods similar (Fisher differentiates as nuclear), KPCA can reflect the non-linear nature of complicated geographical phenomenon, but there is bigger difference in its realization mechanism.It is that urban development complicated phenomenon in the lower dimensional space is mapped to higher dimensional space that nuclear Fisher differentiates, and realizes its linear separability, thereby obtains the transformation rule of geographical CA; KPCA extracts the bigger major component of city evolution contribution amount by the Nonlinear Dimension Reduction mode, thereby obtains geographical ca parameter.The geographical ca parameter that obtains by KPCA has comparatively clear physical meaning.

The KPCA-CA structure of models

As shown in Figure 1, comprising two modules based on the geographical CA model of KPCA, is respectively core principle component analysis spatial data processing module and geographical cellular automaton phantom frame.(1) the KPCA algoritic module of developing based on Matlab.This module is used for handling and analysis space sample points certificate, thereby sets up the transformation rule of geographical CA.(2) based on the geographical cellular automaton phantom frame of ArcGIS Engine 9.2 and Visual Studio.NET exploitation.Make up on the basis of the geographical simulation prototype system that the author once proposed, this framework can be used for extracting the space sample point data, simulation and the dynamically evolution of demonstration urban morphology, and estimate simulation precision etc.Simultaneously, SimUrban not only can carry out KPCA cellular model, geographical CA transformation rule that also can integrated other types.

At first by the TM image classification of remote sensing image process software, obtain the urban development classification chart of survey region in the simulation process, as the benchmark of estimating analog result to obtaining.Comprehensive existing document utilizes ArcGIS Analyst analysis and extracts aforementioned five kinds of space variables, and obtain the respective sample point data the analysis that the utilization of soil, Shanghai City changes.Utilize KPCA algoritic module analyzing samples data, obtain the transformation rule of geographical CA.By geographical cellular automaton phantom frame, survey region is carried out the KPCA-CA model obtain simulation and prognostic chart.At last, utilize confusion matrix, Kappa coefficient and area controlling index etc. to estimate this analog result.

The area controlling index is check analog result and the matching degree between the actual count result and the precision index of difference degree that this paper proposes." area discrepancy index " (Area Difference Index ADI) is used to weigh the difference degree of modeling result and real area, and ADI is defined as:

Wherein, S _{Actual_area}Be the actual count area of a certain class cellular, S _{Simulated_area}Be the simulation area of a certain class cellular, if ADI is on the occasion of then showing the simulation area greater than the actual count area, if negative value then shows the simulation area less than real area, unit is a number percent.In addition, (Area Control Accuracy ACA) is: ACA=1-|ADI| definition area control accuracy

Here, ACA is characterized in the matching degree of area total amount aspect analog result and statistics, and unit is a number percent.

Claims (4)

1. the city evolution simulation cellular models treated method based on core principle component analysis is characterized in that, may further comprise the steps:

1) will select the remote sensing image before 20 years of zone to output in the core principle component analysis spatial data processing module, this module is carried out data processing to the remote sensing image before 20 years, sets up the transformation rule of geographical CA;

2) by the remote sensing image process software to selecting the present classification of remote-sensing images in zone, obtain the urban development classification chart of survey region, as the benchmark of estimating analog result;

3) by geographical cellular automaton phantom frame, survey region is carried out the simulation and the prediction of the geographical cellular model (KPCA-CA) of core principle component analysis, obtain simulation and prognostic chart;

4) with the simulation in the step 3) and prognostic chart and step 2) in the urban development classification chart compare, obtain the appraisal report of analog result and model performance;

5) output and preservation analog result.

2. a kind of city based on core principle component analysis according to claim 1 simulation cellular models treated method that develops is characterized in that described 1) in data handling procedure as follows:

11) from remote sensing image, extract the space length variable data, data are carried out standardization;

12) choose kernel function f (xij), and obtain the matrix K that kernel function is formed as element,

Wherein,

In the formula, f (x _Ij) be kernel function,

Be x _i(j=1,2 ..., expectation value m), σ is the standard deviation of DS;

13) utilize this kernel function to shine upon, obtain the new matrix K under the high-dimensional feature space ^*, K ^*=K-AK-KA+AKA, wherein A is the matrix that all elements is 1/m, and compute matrix K ^*The eigenwert μ of/m _i(i=1 ..., m) with proper vector v _i(i=1 ..., m);

14) extract major component, find out l major component characteristic of correspondence value μ _j(i=1 ..., 1) and proper vector v _j(i=1 ..., 1);

15) ask for cellular under the area variable effect at t transition probability constantly:

$P_k^{t,l}=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}$

16) consider cellular neighbours' influence, constraints limit and enchancement factor, soil cellular k at t development probability constantly is:

$P_k^t=\frac{1}{1+\exp (-\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{a}_i{x}_i)}\×\frac{\underset{3\×3}{\mathrm{\Σ}}\mathrm{con}(S_k=\mathrm{urban})}{3\×3-1}\×\mathrm{con}({\mathrm{cell}}_k^t=\mathrm{suitable})\×(1+{(-\ln \mathrm{\γ})}^{\mathrm{\β}})$

Wherein, P _k ^tBe cellular k at t joint development probability constantly, con (cellkt=suitable) is a limiting factor, and 1+ (ln γ) β is an enchancement factor;

17) calculate after the probability of each cellular development, itself and pre-set threshold compared, if the urban development probability of cellular more than or equal to this threshold value, then this cellular is converted to urban land, otherwise this cellular is not converted to urban land.

3. a kind of city based on core principle component analysis according to claim 2 develops and simulates cellular models treated method, it is characterized in that the space length variable in the described step 11) is included in intown distance, to the distance at center, town, to the distance of main roads, to the distance in vegetable garden, to the distance in arable land.

4. a kind of city based on core principle component analysis according to claim 2 develops and simulates cellular models treated method, it is characterized in that it is as follows that the data in the described step 11) are carried out standardized method:

Wherein,

s _jIt is its standard deviation.

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