AU2018101946A4 - Geographical multivariate flow data spatio-temporal autocorrelation analysis method based on cellular automaton - Google Patents

Geographical multivariate flow data spatio-temporal autocorrelation analysis method based on cellular automaton Download PDF

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AU2018101946A4
AU2018101946A4 AU2018101946A AU2018101946A AU2018101946A4 AU 2018101946 A4 AU2018101946 A4 AU 2018101946A4 AU 2018101946 A AU2018101946 A AU 2018101946A AU 2018101946 A AU2018101946 A AU 2018101946A AU 2018101946 A4 AU2018101946 A4 AU 2018101946A4
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Jiangping Chen
Zhipeng Xiong
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Abstract

A geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton is provided. The spatio-temporality and complexity of geographical data are expressed by adopting an improved cellular automaton dynamic model, and a transformation rule and spatial heterogeneity of asynchronous evolution of a cell (geographic region) are considered to analyze geographical multivariate flow data of a non-linear structure based on a complex network more accurately. A cellular automaton model parameter is obtained more accurately by analyzing a cellular unit and extracting a plurality of influence factors, and is accurate and high in efficiency; the transformation rule obtained by using an ANN algorithm is more dynamic than the fixed transformation rule of the whole model, more describable, and conforms to an actual cellular changing situation; the correlation between cells is expressed by Moran's I to reflect a spatio-temporal distribution situation of geographical data better and more clearly, thereby facilitating subsequent simulation and prediction of spatio-temporal data model , and achieving the simulation and prediction more accurately. Fig. 2 rule/transformation tie st function Cell attribute neighborhood ni oho celsae information state ifatiut geographical space Fig 1 land use data of hi storical years image data randomly sampled obtaining transformation rule | lasification training data based on ANN algorithm influence factor data transformation rule data of distance at fdsac tatistical unit quantity of cell from city of cel fro - - - - (btaining through Cellular automatonfas downtown mirodneighborhood window) modelfas actual land use precision simulation result data assessment lan suang precision complies? yes spati-temoral Improved Moran's I -A ST I prediction result - data of future land use change Fig 2

Description

SPECIFICATION
GEOGRAPHICAL MULTIVARIATE FLOW DATA SPATIO-TEMPORAL
AUTOCORRELATION ANALYSIS METHOD BASED ON CELLULAR AUTOMATON
TECHNICAL FIELD [0001] The present disclosure belongs to a geographical spatial statistical analysis method, and particularly to the fields of cellular automata and geographical multivariate flow data processing, geographic spatial correlation analysis, and the like.
BACKGROUND [0002] In recent years, with the continuous development and popularization of geographical information technology, remote sensing technology, Internet of Things and mobile terminals, multivariate geographical data with a spatial reference is rapidly evolved over decades and becomes massive geographical multivariate flow data. The flow data features sequentiality, large quantity, rapidness and continuous arrival, may be aggregated into a dynamic data set that grows infinitely over time. The flow data may also be referred to as spatio-temporal flow data, such as traffic data and real-time temperature monitoring data.
[0003] At present, the spatial autocorrelation analysis technology can better reveal inherent spatial characteristics of research objects, and is widely applied to analyze and monitor spatial distribution characteristics of environments and disasters. However, it may be found from research literatures of scholars in different countries that a model of geographical multivariate flow data is mainly constructed based on a time serial model, which only takes into account time autocorrelation, and does not consider the geographical spatial heterogeneity and correlation of different multivariate variables. As shown in the relevant literatures, in Patent Application No.
CN201410529971.5 (Publication No. CN104298743A) entitled “DISTRIBUTED THREEDIMENSIONAL (3D) DYNAMIC SPACE DATA ANALYZING METHOD” of Inspur Group Co., Ltd., collecting spatial data of dynamic bodies in a particular time period and storing data information of a particular time point at a specified time interval may be used for behavior analysis and behavior determination of dynamic bodies; in Patent Application No. CN201711403609.3 (Publication No.
2018101946 04 Dec 2018
CN108133291A) entitled “METHOD OF ANALYZING CORRELATION BETWEEN SOCIAL
EVENTS AND PASSENGER TRANSPORT TRAFFIC DEMANDS” of Beijing Jiaotong University, a fusion model is respectively constructed based on a design attribute for different types of events by using a machine learning algorithm to predict a changing amount of traffic demands caused by the events. The spatial autocorrelation analysis method is mainly applied to discrete spatio-temporal data, in which the spatio-temporal data is split into spatial data and time serial data, and the correlation analysis is separately performed for the two types of data while an interaction between time and space is neglected.
[0004] Therefore, the present disclosure innovatively discloses a solution for geographical multivariate flow data spatio-temporal autocorrelation analysis based on a cellular automaton, in which the spatio-temporality and complexity of geographic data are expressed by adopting an improved cellular automaton dynamic model, and a transformation rule and spatial heterogeneity of asynchronous evolution of a cell (geographical region) are considered to analyze geographical multivariate flow data of a non-linear structure based on a complex network more accurately.
[0005] Any discussion of the prior art throughout the specification should in no way be considered as an admission that such prior art is widely known or forms part of common general knowledge in the field.
SUMMARY [0006] It is an object of the present invention to overcome or ameliorate at least one of the disadvantages of the prior art, or to provide a useful alternative.
[0007] An object of the preferred embodiments described in the present disclosure is to implement spatio-temporal autocorrelation analysis of geographical multivariate flow data. Based on characteristics of time dimension and continuous arrival of data, an expression model of geographical multivariate flow data based on a cellular automaton is constructed, and a spatiotemporal autocorrelation analysis method of improving Moran’s I exponent is provided. The present disclosure can reveal spatio-temporal evolution characteristics of geographical multivariate flow data, and provide a solution with consideration of continuous expression of spatio-temporal
2018101946 04 Dec 2018 dimension for predictive analysis on real-time temperature monitoring, traffic monitoring, and the like, which is of great significance for geographical data processing.
[0008] According to one aspect of the present invention, there is provided a geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton, comprising:
Block 1: obtaining grid data containing a plurality of categories by classifying raw geographical multivariate flow data;
Block 2: building a cellular automaton model that conforms to characteristics of geographical multivariate flow data by improving the cellular automaton model;
Block 3: defining each grid in the grid data as one cellular unit, and extracting influence factors from each cellular unit;
Block 4: determining a state situation of cells and a neighbourhood relationship between the cells;
Block 5: randomly extracting attribute data from several cells as training sampled data;
Block 6: considering data multiplicity and spatio-temporality, repeatedly training the training sampled data by using an ANN algorithm in machine learning until an optimal solution is obtained, and taking the obtained output result as a parameter required in the cellular automaton model;
Block 7: taking the extracted influence factors as an input layer, adopting the result obtained by training as an initial weight value, mining a transformation rule in each cell by using the ANN algorithm, and obtaining an initial transformation probability that the category of the cell is transformed to another category;
Block 8: extracting a maximum value by using output layer data, i.e., transformation probability data, which is obtained by training, and determining whether the category of the cell at a next moment changes and which category to which the transformation tends;
Block 9: calculating a spatio-temporal weight value between cells by adopting a Moore neighbourhood of the cellular model;
2018101946 04 Dec 2018
Block 10: improving a spatio-temporal structure of a spatio-temporal Moran’s I analysis variable according to a continuous characteristic of geographical multivariate flow data and model expression forms at three levels of a spatial position, an attribute, and time;
Block 11: considering the correlation between cells, performing simulation analysis and prediction for a spatio-temporal weight matrix calculated at block 9 and Moran’s I exponents improved at block 10 in combination with the cellular automaton model built based on geographical multivariate flow data to form a combination model having a spatiotemporal autocorrelation analysis function based on the cellular automaton model.
[0009] In some embodiments, wherein the cellular automaton model that conforms to characteristics of geographical multivariate flow data at block 2 is defined as follows:
A = {F,L,G,S,N,R} Formula (2);
in the above formula, F = {f} refers to quantitatively expressible attribute information data; L = {/} refers to distribution of a geographic phenomenon; G refers to cellular division in a geographic space; N = {cj,c2,...,c„} refers to a cellular neighbour; 5 = refers to a state variable of a cell; R = {r} refers to a rule set, or is referred to as an evolutional function set.
[0010] In some embodiments, wherein a maximum value and a minimum value are normalized in such a way that all obtained training sampled data are between 0 and 1 in block 5.
[0011] In some embodiments, wherein a calculation formula used for determining whether the category of the cell at the next moment changes and which category to which the transformation tends in block 8 is as follows:
/(/,7) = (1+(-In χ)α)χpg'Acon(St(i,j}')'Aklt(i,j') Formula (5);
in the above formula, p(i,j) refers to a transformation probability of a category of a cell; l+(-ln/)“ refers to a random item that enables a simulation result to better conform to an actual situation; pg refers to a global transformation probability; con(S‘(i,jy) refers to a constraint condition of a cellular unit; Q‘(i,j) refers to a neighbourhood function representing an influence ofthe neighbourhood on the cellular transformation probability.
2018101946 04 Dec 2018 [0012] In some embodiments, wherein the Moran’s I exponents improved at block 10 are expressed in two manners with specific formulas being as follows:
a Moran’s I exponent OSTIk in a global spatio-temporal flow form and a Moran’s I exponent PSTIk in a local spatio-temporal flow form,
OSTIk = ί
PSTZ* =
L η n __ __
- ^,t-k)(A. t - Aj,t) i=l J=l
Figure AU2018101946A4_D0001
__ n __
J=i
Formula (6);
Figure AU2018101946A4_D0002
- Λ.,..)2 ./Σ(4,-Α<)2 in the above formula, n refers to the number of cellular units; wt_kk refers to a time weight value from a moment t-k to a moment t; wkj is one element of a spatial weight matrix w, and W refers to a spatial weight matrix with row normalization for quantifying the proximity between surrounding regions; Aitk refers to a normalized attribute value of a cellular unit / at the moment t-k; A^-k refers to an average value ofthe normalized attribute values of all cellular units at the moment t-k; Ajt refers to a normalized attribute value of a cellular unit j at the moment t; Aj,t refers to an average value of normalized
2018101946 04 Dec 2018 attribute values of all cellular units at the moment t; a changing range of the Moran’s I exponents OSTIk and PSTIk based on geographical multivariate flow data is (-1, 1).
[0013] In some embodiments, wherein a spatial-temporal statistical quantity Z that follows
OSTI PSTI normal distribution is constructed based on obtained values k and k in block 10 to verify the significance of spatial-temporal autocorrelation, and the spatial-temporal statistical quantity is expressed as follows:
7_ OSTIk-E[OSTIk} 7_ PSTIk-E[PSTIk] ]VAR[OSTlk] °Γ ]VAR[PSTIk] wherein, , £[0^1=--3(«-!) , ^E47?[OS77J = £[(OS77J2] - £[OS77J2
E[PSTIk] =--— (h-1) .
\vAR[PSTIk] = E[(PSTIk)2]- E[PSTIk]2 [0014] Beneficial effects of the present disclosure are as follows: a cellular automaton model parameter may be obtained more accurately by analyzing a cellular unit and extracting different influence factors. When being used, the parameter is smaller in error, better in accuracy and higher in efficiency than the parameter determined manually; the transformation rule obtained by using an ANN algorithm is more dynamic than the fixed transformation rule of the whole model, more describable, and conforms to an actual transformation situation of a cell; the correlation between cells expressed by Moran’s I may reflect a spatio-temporal distribution of geographical data better and more clearly, thereby facilitating subsequent simulation and prediction of a spatio-temporal data model and making the simulation and prediction more accurate.
[0015] Unless the context clearly requires otherwise, throughout the description and the claims, the words “comprise”, “comprising”, and the like are to be construed in an inclusive sense as
2018101946 04 Dec 2018 opposed to an exclusive or exhaustive sense; that is to say, in the sense of “including, but not limited to”.
BRIEF DESCRIPTION OF DRAWINGS [0016] A preferred embodiment of the invention will now be described, by way of example only, with reference to the accompanying drawings in which:
FIG. 1 is a schematic diagram illustrating a standard cellular automaton model.
FIG. 2 is a flowchart illustrating an example of the present disclosure.
FIG. 3 is a schematic diagram illustrating three cellular neighbourhood relationships.
FIG. 4 is a schematic diagram illustrating a model parameter obtained by neural network training.
DETAILED DESCRIPTION [0017] When implementing the technical solution of the present disclosure, those skilled in the art may operate the technical solution by adopting computer software technology. Descriptions will be made with land use data as an example below through the following specific blocks of examples of the present disclosure in combination with FIG. 2.
[0018] Block (1): multiplicity and spatio-temporality of data are analyzed by adopting geographical multivariate flow data, and the data adopted in this example is remote sensing image data of land use changes in different periods.
[0019] Block (2): a pre-processing operation is performed for raw data, and images are classified by ArcGIS software to obtain grid data containing a plurality of land types, such as urban land, woodland, grassland, garden, wetland, water body, and undeveloped land.
[0020] Block (3): a cellular automaton model is constructed. A cellular automaton model that conforms to characteristics of geographical multivariate flow data is built by improving the cellular automaton model in combination with example data. A standard cellular automaton is a quadruple (as shown in FIG. 1) including a cell, a cell state, a neighbourhood and a state updating rule, which may be expressed by a mathematical symbol as follows.
2018101946 04 Dec 2018
A = {L,d,S,N,f} Formula (1) [0021] Full expression and description of geographical multivariate flow data are required to have rich and accurate semantics, but transformation rules and the spatial heterogeneity of asynchronous evolution of different cells (geographical regions) are neglected in the traditional cellular automaton. Therefore, by improving the cellular automaton model, a cellular automaton model based on geographical multivariate flow data is constructed to express complicated, dynamic and interrelated geographic information elements. The improved model is defined as follows.
A = {F,L,G,S,N,R} Formula (2) [0022] In the above formula, ~ refers to attribute information data which can be quantitatively expressed; _ refers to distribution of a geographical phenomenon which cannot
N — ic c cl be quantitatively expressed; G refers to cell division in a geographic space; 1 *’ 2’·’ n> refers to a cellular neighbour; $ ~ refers to a cellular state variable; _ refers to a rule set, or is referred to as an evolutional function set.
[0023] According to a principle of a time serial model, the state of a cell m at a moment t+k is determined by the state of the cell at a moment t and the cellular neighbor, and an iteration process is expressed as follows.
st+k=r(Nm’st) Formula (3) [0024] Block (4): a cellular unit is defined, and each grid in grid data is defined as one cellular unit.
[0025] Block (5): a plurality of attribute characteristics (i.e., influence factors) exist in each (x X X } cellular unit, a plurality of influence factors z1’ z·2......’ ζ β may be extracted by using a spatial analysis tool in the ArcGIS software, where Q refers to the number of influence factors. For land
2018101946 04 Dec 2018 use data, the mainly extracted influence factors may include data of a distance from a city downtown, data of a distance from a road, the number of statistical units of different land types extracted in a neighbourhood window form, and the like.
[0026] Block (6): the state situation of the cell is determined and a land type is indicated with the state in which the cell is. In image classification, different land types are represented by multi-color rendering so that the distribution of land types can be clearly known .
[0027] Block (7): a neighbourhood relationship between cells is determined. At present, the main neighborhood relationship models mainly include a von Neumann model, a Moore model, a Margoles model, and the like. A Moore neighbourhood relationship model is adopted according to example data (as shown in FIG. 3).
[0028] Block (8): attribute data is randomly extracted from several cells as training sampled data. Training data is mainly obtained by randomly extracting data of each grid and a plurality of types of influence factor data therein. Considering that the obtained training data is different in size and numerical values between different pieces of data are greatly different, a maximum value and a minimum value are normalized, so that the obtained training sampled data is all between 0 and 1.
[0029] Block (9): considering the multiplicity and spatio-temporality of data, the training sampled data is repeatedly trained by using an ANN algorithm in machine learning until an optimal solution is obtained, and the obtained output result is used as a parameter required in the cellular automaton model (as shown in FIG. 4).
(x X X } [0030] Block (10): the extracted influence factors z1’ ......’ ζ β are used as an input layer, and the result obtained by training is used as an initial weight value.
[0031] Block (11): the transformation rule in each cell is mined by using the same ANN algorithm again to enter a hidden layer based on information of the input layer and the weight value and obtain an initial transformation probability that the land type of the cell is transformed to another land type by activating a Sigmoid function, and then, a particular threshold is selected to
2018101946 04 Dec 2018 ίο return to the input layer and perform repeated training until the optimal transformation probability is obtained. The activated Sigmoid function selected in the ANN algorithm is as follows.
Sigmoid(y) =---2---- Formula (4) / ,w„ + e ’ [0032] In the above formula, Wp'q refers to a weight value between nerve cells p and q; X,'q refers to a normalized attribute value of the q-th nerve cell (i.e., influence factor) at the moment t.
[0033] Block (12): the maximum value is extracted by using output layer data, that is, transformation probability data, which is obtained by training, to determine whether the land type of the cell at the next moment changes and which land type to which the transformation tends. The calculation formula is as follows.
/ (z, y) = (1 + (-In/)a)xpgxcon(S‘(i,jy)xQ.‘(i,j) Formula (5) [0034] In the above formula, P (z,2) refers to a transformation probability of a land type of a cell; 1 + (—ln z) refers to a random item that enables a simulation result to better conform to an actual situation; Pg refers to a global transformation probability; conF 0,7)) refers to a constraint condition of a cellular unit; 0’7) refers to a neighbourhood function representing an influence of the neighbourhood on the cellular transformation probability.
H’ W- [0035] Block (13): spatio-temporal weight values ' * 'and ' ' between cells are calculated by w , w , using the Moore neighbourhood of the cellular model. ‘ k'‘ refers to a time weight value of ‘ k'‘
W- .
from a moment t-k to the moment t; PJ refers to one element of a spatial weight matrix W. W is a spatial weight matrix with row normalization for quantifying the proximity between surrounding regions.
STI [0036] Block (14): a spatio-temporal structure of a Spatio-Temporal Moran’s I ( k) analysis variable proposed by the scholar Wartenberg is improved according to the continuous characteristic of geographic multivariate flow data and a model expression forms at three levels of a spatial position, an attribute and time to perform the spatio-temporal autocorrelation analysis for the geographical multivariate flow data. Because the spatio-temporal heterogeneity exists when the analysis is performed for global and local regions, there are two expression manners: a
2018101946 04 Dec 2018
OSTI
Moran’s I exponent k in a global spatio-temporal flow form and a Moran’s I exponent in a local spatio-temporal flow form. The Moran’s I exponents temporal flow form are expressed by the following formula.
OSTI, =
BSTQ =
L η n __ __
- Ai,t-k)(Aht - Aj,t) i=l J=l
Figure AU2018101946A4_D0003
__ n __ nW-k/Ay-k ~ A’A
J=i
Figure AU2018101946A4_D0004
PSTIk
OSTI. .
k and
PSTIk in the spatioFormula (6) [0037] In the above formula, n refers to the number of cellular units; ! Z A refers to a normalized attribute value of a cellular unit i at the moment t-k; Akl~k refers to an average value of the normalized attribute values of all cellular units at the moment t-k; jk refers to a normalized attribute value of a cellular unit j at the moment t; Aj,t refers to an average value of the normalized attribute values of all cellular units at the moment t.
OSTI PSTI [0038] A changing range of the Moran’s I exponents k and k based on geographical
STI OSTI multivariate flow data is (-1, 1). If two cellular units are spatio-temporally uncorrelated, k ( k and k ) is expected to be close to 0. When the value k (OSTIk PSTIk jg g negafjve value that generally indicates spatio-temporal negative autocorrelation, the spatio-temporal
STI OSTI correlation of the change of the land type at the next moment is weak; when the value k ( k
2018101946 04 Dec 2018
Formula (7)
Formula (8)
PSTI and k) is a positive value that generally indicates spatio-temporal positive autocorrelation, the spatio-temporal correlation of the change of the land type at the next moment is strong.
STI [0039] Based on the obtained theoretical value k, a spatio-temporal statistical quantity Z that follows normal distribution may be constructed to verify the significance of the spatio-temporal autocorrelation (p<0.05). The spatio-temporal statistical quantity Z is expressed as follows.
v STlt-E[STlt} jVA^STIA where,
E\STI J =--— ] L (H-l) [EW77J = £[(S77J2] - £[S77J2
OSTI PSTI [0040] Similarly, k and k may also be used to verify the significance of the spatiotemporal autocorrelation by the formulas 7 and 8.
[0041] (15) Finally, considering the correlation between cells, simulation analysis and prediction are performed for the spatio-temporal weight matrix calculated at block (13) and the spatioOSTI PSTI temporal Moran’s I exponent k or k at block (14) in combination with the cellular automaton model built based on land use data to form a combination model having a spatiotemporal autocorrelation analysis function based on the cellular automaton model. According to the analysis and prediction results, non-urban land (grassland, woodland, water body, etc.) may be changed into urban land over time, and the area of change may be calculated, thereby providing good guidance for relevant departments to subsequently use predicted changing situation of land use in urban expansion or extension construction.
[0042] The specific examples described herein are merely illustrative of the spirit of the present disclosure. It should be noted that a plurality of modifications, supplementations or equivalents may be made to replace the described specific examples by those of ordinary skill in the art without departing from the spirit of the present disclosure or exceeding the scope defined in the appended claims.

Claims (6)

  1. CLAIMS:
    1. A geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton, comprising:
    Block 1: obtaining grid data containing a plurality of categories by classifying raw geographical multivariate flow data;
    Block 2: building a cellular automaton model that conforms to characteristics of geographical multivariate flow data by improving the cellular automaton model;
    Block 3: defining each grid in the grid data as one cellular unit, and extracting influence factors from each cellular unit;
    Block 4: determining a state situation of cells and a neighbourhood relationship between the cells;
    Block 5: randomly extracting attribute data from several cells as training sampled data;
    Block 6: considering data multiplicity and spatio-temporality, repeatedly training the training sampled data by using an ANN algorithm in machine learning until an optimal solution is obtained, and taking the obtained output result as a parameter required in the cellular automaton model;
    Block 7: taking the extracted influence factors as an input layer, adopting the result obtained by training as an initial weight value, mining a transformation rule in each cell by using the ANN algorithm, and obtaining an initial transformation probability that the category of the cell is transformed to another category;
    Block 8: extracting a maximum value by using output layer data, i.e., transformation probability data, which is obtained by training, and determining whether the category of the cell at a next moment changes and which category to which the transformation tends;
    Block 9: calculating a spatio-temporal weight value between cells by adopting a Moore neighbourhood of the cellular model;
    Block 10: improving a spatio-temporal structure of a spatio-temporal Moran’s I analysis variable according to a continuous characteristic of geographical multivariate flow data and model expression forms at three levels of a spatial position, an attribute, and time;
    Block 11: considering the correlation between cells, performing simulation analysis and prediction for a spatio-temporal weight matrix calculated at block 9 and Moran’s I
    2018101946 04 Dec 2018 exponents improved at block 10 in combination with the cellular automaton model built based on geographical multivariate flow data to form a combination model having a spatiotemporal autocorrelation analysis function based on the cellular automaton model.
  2. 2. The geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton according to claim 1, wherein the cellular automaton model that conforms to characteristics of geographical multivariate flow data at block 2 is defined as follows:
    A = {F,L,G,S,N,R} Formula (2);
    in the above formula, F = {f} refers to quantitatively expressible attribute information data; L = {1} refers to distribution of a geographic phenomenon; G refers to cellular division in a geographic space; N={cx,c2,...,cn} refers to a cellular neighbour; 5 = (^} refers to a state variable of a cell; R = {r} refers to a rule set, or is referred to as an evolutional function set.
  3. 3. The geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton according to claim 1 or claim 2, wherein a maximum value and a minimum value are normalized in such a way that all obtained training sampled data are between 0 and 1 in block 5.
  4. 4. The geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton according to any one ofthe preceding claims, wherein a calculation formula used for determining whether the category ofthe cell at the next moment changes and which category to which the transformation tends in block 8 is as follows:
    />'(/,» = (1+(-In/)a)xpgxcon(S‘(i,j))x&(i,j) Formula (5);
    in the above formula, p‘(i,j) refers to a transformation probability of a category of a cell; l+(-ln/)“ refers to a random item that enables a simulation result to better conform to an actual situation; pg refers to a global transformation probability; con(S‘(i,j)) refers to
    2018101946 04 Dec 2018 a constraint condition of a cellular unit; Q'(z,y) refers to a neighbourhood function representing an influence of the neighbourhood on the cellular transformation probability.
  5. 5. The geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton according to any one of the preceding claims, wherein the Moran’s I exponents improved at block 10 are expressed in two manners with specific formulas being as follows:
    a Moran’s I exponent OSTIk in a global spatio-temporal flow form and a Moran’s I exponent PSTIk in a local spatio-temporal flow form,
    OSTIk = =
    L η n __ __
    ΣΣ W./A - A,t-k)(Aj t - Aj,t) /=1 J=1
    - Jzw, - Λ.<)2 __ η __ ™t-k,SAkt_k - Α^-ΑϊΣ ^j(Aht ~ Ajf)
    J=1
    Formula (6);
    in the above formula, n refers to the number of cellular units; wt_kk refers to a time weight value from a moment t-k to a moment t; wkj is one element of a spatial weight matrix w, and W refers to a spatial weight matrix with row normalization for quantifying the proximity between surrounding regions; Aitk refers to a normalized attribute value of a cellular unit / at the moment t-k\ Ai,t-k refers to an average value of the normalized attribute values of all cellular units at the moment t-k', Ajt refers to a normalized attribute value of a cellular unit j at the moment f; Aj,t refers to an average value of normalized attribute values of all cellular units at the moment t; a changing range of the Moran’s I exponents OSTIk and PSTIk based on geographical multivariate flow data is (-1, 1).
  6. 6. The geographical multivariate flow data spatio-temporal autocorrelation analysis method based on a cellular automaton according to claim 5, wherein a spatial-temporal statistical quantity Z that follows normal distribution is constructed based on obtained
    2018101946 04 Dec 2018 values OSTlk and PSTlk in block 10 to verify the significance of spatial-temporal autocorrelation, and the spatial-temporal statistical quantity is expressed as follows: 7_ OSTIk-E[OSTIk\ 7_ PSTIk-E[PSTIk] ]VAR[OSTIk] °Γ ]VAR[PSTIk] wherein, , £TOSTA] = --2—.
    («-!) , = £[(OS77J2] - £[OS77J2
    E[PSTIk] =--— (h-1) .
    \vAR[PSTIk] = E[(PSTI ,)2]- E(PSTIk]2
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