CN106126918A - A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force - Google Patents

Abstract

The invention discloses a kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, comprise the following steps: build Space Lorentz Curve matrix based on the Spatial Adjacency type selected；Use the action intensity between spatial interactive mode l tolerance adjacent object；Contiguous object based on depth scan mode or range scan mode continuous selection maximum intensity joins in candidate aggregate district, until the likelihood ratio LR/ log-likelihood ratio LLR value that likelihood ratio LR/ log-likelihood ratio LLR value no longer increases or Low value anomaly gathering is corresponding of high-value sector gathering correspondence no longer reduces or candidate aggregate district reaches stopping during maximum specified size；The multiple candidate aggregate districts formed are carried out Monte Carlo simulation, thus detects the abnormal aggregation district by nonrandomness hypothesis testing.The present invention is higher to the detectivity in irregularly shaped abnormal aggregation district, is more easy to detect the abnormal aggregation district comprising Weak link, and will not non-abnormal geographic object be included in the abnormal aggregation district of detection.

Description

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force

Technical field

The present invention relates to geospatial information processing technology field, a kind of geographical space based on interaction force Abnormal aggregation domain scanning statistical method.

Background technology

Geographical space scan statistics belongs to geographical space clustering method.Space clustering refers to geographic object special according to space If seeking peace, attribute character is grouped into Ganlei so that between homogeneous object, between similarity maximum, class, between object, difference is maximum, different The object of class has significantly differentiation in spatial distribution.The purpose of space clustering is to find geographic space distribution pattern, and Mutual relation potential between geographic object.Traditional spatial clustering method can be divided into partition clustering, hierarchical clustering, density poly- The polytype such as class, Grid Clustering.

Being different from traditional spatial clustering method, geographical space scan statistics is detection geographical space abnormal area Method.Free air anomaly district refers to reference to other geographic object, it is intended that the geographic object aggregation zone that attribute character is dramatically different. Free air anomaly district can be divided into attribute high-value sector district, attribute Low value anomaly district two types.Spacescan statistical method is to research Geographic object in district is scanned/searches for, according to inside and outside sweep limits between geographic object property value in scanning process Difference, detects whether the excessive risk accumulation regions existing in statistical significance, and determines the position of aggregation zone, scope and assemble journey Degree, provides foundation for early warning and decision-making.

The scan statistics based on circular window that the Kulldorff M. of Harvard University in 1997 proposes is classics side One of method, the method using each geographic object in study area as scanning start element, i.e. using this spatial object center as The center of circle of circular scan window, is scanned surrounding space unit with radius variable, according to attribute inside and outside window overlay area Actual ratio and random distribution assume that lower theoretical ratio calculates scan statistics log-likelihood ratio LLR (Log Likelihood Ratio), until statistic no longer changes, choose in the candidate aggregate window generated statistic maximum/ Little gathering window (corresponding high-value sector gathering/Low value anomaly is assembled), and carry out hypothesis testing to assembling window, verify its point The nonrandomness of cloth, so that it is determined that the area of space that aggregation extent is the highest, referred to as most probable cluster MLC (Most Likely Or most probable accumulation regions Cluster).

On this basis, within 2006, Kulldorff M. proposes oval spacescan statistical method, and scanning window is The ellipse that shape, angle are continually changing, simultaneously in order to retrain the accumulation regions shape detected, introduces non-compact (non- Compactness) penalty factor [4s/ (s+1)²]^a, whereinBeing determined by oval eccentricity e, parameter a >=0 is certainly Determining strength of punishment, be worth the biggest degree of irregularity to accumulation regions shape and punish the strongest, shape more tends to compact.

Geographical space abnormal aggregation district in reality is different, most is irregular, therefore, based on Kulldorff Circular, oval-shaped scan statistical method, existing research focuses on the detectivity aspect improving irregular area, i.e. to sweeping Retouching mode, window shape etc. to be optimized, it is thus possible to detect various erose free air anomaly accumulation regions, but these grind Study carefully and all do not account for interaction impact intrinsic between geospatial object.

It practice, the entity in geographical space is not isolated existence, there is relatedness each other.As Tobler The viewpoint that First Law of Geography illustrates, spatial object presents the spatial framework that is mutually related, and this relatedness along with The increase of the spacing of spatial object and weaken.Relatedness determines to exist between spatial object and interacts.Certainly, though right In identical operating distance, it is assumed that interaction strength is the most identical in survey region is also unpractical, shows as in office The high level (" focus ") in region, portion and low value (" cold spot ") are assembled or abnormal.

Summary of the invention

For solving the deficiency that prior art exists, the invention discloses a kind of geographical space based on interaction force abnormal Accumulation regions scan statistics method, it is contemplated that interaction impact intrinsic between geographic object, compared to classical Kulldorff circle Shape, oval-shaped scan method, the method (the especially range scan mode) detectivity to irregularly shaped abnormal aggregation district Higher, it is more easy to detect the abnormal aggregation district comprising Weak link, and non-abnormal space object will not be included in detect different Often in accumulation regions.

For achieving the above object, the concrete scheme of the present invention is as follows:

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, comprises the following steps:

Judge the abnormal aggregation district type of detection, if attribute Low value anomaly accumulation regions, then by right to the geography detected It is attribute high-value sector accumulation regions as property value carries out shift conversion；

For attribute high-value sector accumulation regions, build Space Lorentz Curve matrix based on the Spatial Adjacency type selected；

Use the action intensity between spatial interactive mode l tolerance adjacent object；

Contiguous object based on depth scan mode or range scan mode continuous selection maximum intensity joins time Select in accumulation regions, until high-value sector is assembled corresponding likelihood ratio LR/ log-likelihood ratio LLR value and no longer increased or candidate aggregate district Reach to stop during maximum specified size；

The multiple candidate aggregate districts formed are carried out Monte Carlo simulation, thus detects by nonrandomness hypothesis testing Abnormal aggregation district.

Further, for attribute Low value anomaly accumulation regions, by geospatial object S_iThe property value c of detection_iIt is transformed to c_i', c_i' it is all geographic object property value { c₁,c₂,…,c_NMaximum deduct c_i, formula is:

c_i'=max{c₁,c₂,…,c_N}-c_i

Wherein N is spatial object number, by above-mentioned conversion, the detection of Low value anomaly accumulation regions is converted into high-value sector and gathers Ji Qu.

Further, building Space Lorentz Curve matrix is binary type matrix W, w_ij=1 representation space object S_iWith S_j Adjacent, w_ij=0 represents non-conterminous, and Space Lorentz Curve uses geospatial object to have the form of public boundary, public vertex.

Further, spatial interactive mode l is referred to as SIM model, particularly as follows: two spatial object S_iAnd S_jBetween exist Active force, its directed force F_ijBeing directly proportional to the example incidence rate of object, and the distance between them is inversely proportional to, active force is the biggest then Object S_i、S_jBetween spatial correlation the strongest, formula is:

$F_{ij}=k\frac{{\left(r_i\·r_j\right)}^b}{d_{ij}^a}=k\frac{{\left(\frac{c_i}{b_i}\·\frac{c_j}{b_j}\right)}^b}{d_{ij}^a}$

Wherein, k is constant, can be taken as 1；r_i、r_jIt is respectively spatial object S_i、S_jExample rate, i.e. example number and overall number Ratio；c_iFor the attribute of detection, referred to as example；b_iFor the primary attribute relevant to detection attribute, it is referred to as overall；d_ijFor S_i、S_jIt Between distance；A, b are constant.

Further, from N number of spatial object { S after building Space Lorentz Curve matrix₁, S₂..., S_NSky is selected in } Between object S_iAs the start element of candidate aggregate district Z, by S_iJoin in candidate aggregate set Z,

Further, described depth scan mode: be newly added candidate aggregate district Z spatial object for current active list Unit, obtains all of its neighbor unit of active cell, but does not comprise the unit added in set Z according to adjacency matrix W；Foundation SIM model formation calculates the steric interaction intensity between active cell and these adjacent units, selects SIM maximum intensity Adjacent unit S_jJoin in candidate aggregate set Z,

Further, described range scan mode: obtain each spatial object in candidate aggregate district Z according to adjacency matrix W Adjacent unit, but do not comprise the unit added in set Z；Calculate each object in Z according to SIM model formation and be adjacent unit Between SIM intensity, select SIM maximum intensity adjacent unit S_jJoin in candidate aggregate set Z,

Further, the statistic LR/LLR value of Z overlay area is calculated；When the sky that statistic no longer increases or comprises in Z Between object number when reaching the maximum cluster size set, then stop scanning, gather ZXing Chengyige candidate aggregate district.

Further, spacescan statistic LR/LLR building process is:

Select probability model, if p is spatial object S in scanning window i.e. candidate aggregate district Z_kExample c_kThe probability occurred And obeying this probabilistic model, q is the probability of window Z outer example generation and obeys this probabilistic model, and null hypothesis is H₀: p=q represents Assuming that the example probability of happening inside and outside window Z not there are differences, alternative hypothesis is H_Z: assembling for high level, p > q represents hypothesis window Example probability of happening in mouth Z is higher than the probability of happening outside window, if H_Z、H₀Assume the likelihood function of lower candidate aggregate district Z respectively For L (Z), L₀, then statistic LR=L (Z)/L₀Being referred to as likelihood ratio, LLR=ln (LR) is referred to as log-likelihood function ratio.

Further, also need to candidate aggregate district before the multiple candidate aggregate districts formed being carried out Monte Carlo simulation Screen: according to LR/LLR value, N number of candidate aggregate district is sorted from big to small；Screen the most successively: if The spatial object that the spatial object that the candidate aggregate district of current screening comprises and the candidate aggregate district retained comprise repeats, then pick Except current candidate accumulation regions, otherwise retain current candidate accumulation regions.

Further, if remaining the candidate aggregate district of M non-overlapping copies after Shai Xuan, M≤N, the most successively to respectively Candidate aggregate district carries out Monte Carlo simulation hypothesis testing.

Further, when each candidate aggregate district is carried out Monte Carlo simulation hypothesis testing, specifically include:

(1) for the distributional pattern of current candidate accumulation regions, the parameter value of selected probabilistic model is calculated；

(2) premised on null hypothesis i.e. random distribution, whole region is produced N_SimThe individual simulation meeting corresponding probability distribution Data set；

(3) utilize depth scan mode or range scan mode, obtain the most probable abnormal aggregation district of each simulated data sets And corresponding LR/LLR value；

(4) by current candidate accumulation regions and N_SimThe abnormal aggregation district of individual simulated data sets is according to LR/LLR value from big to small It is ranked up, determines that current candidate accumulation regions is at N_SimPosition sequence Rank in+1 LLR, counting statistics significance value P=Rank/ (N_Sim+1)；

(5) when P is less than level of significance α, then null hypothesis H of random distribution is refused₀, accept the attribute in candidate aggregate district High level probability of happening is higher than alternative hypothesis H outside accumulation regions_Z, show that current candidate accumulation regions is false by Monte Carlo nonrandomness If inspection.

Further, by each candidate aggregate district foundation LR/LLR of nonrandomness hypothesis testing after Monte Carlo simulation Value is followed successively by intensity of anomaly abnormal aggregation district from high to low from big to small.

Beneficial effects of the present invention:

The present invention considers interaction impact intrinsic between geographic object, circular, ellipse compared to classical Kulldorff Circular scan method, the present invention overcomes the deficiency not considering that geographic object influences each other, the method (especially range scanning side Formula) higher to the detectivity in irregularly shaped abnormal aggregation district, it is more easy to detect the abnormal aggregation district comprising Weak link, and not Non-abnormal space object can be included in the abnormal aggregation district detected.

For attribute Low value anomaly accumulation regions detection problem in the application, entered by the property value that each spatial object is detected Line translation, thus problem is converted into attribute high-value sector accumulation regions detection problem, it is possible to realize Low value anomaly accumulation regions Accurately detection.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention；

Fig. 2 (a)-Fig. 2 (c) is that the Rook of Space Lorentz Curve is adjacent, Bishop adjacent and Queen adjoins respectively；

Fig. 3 (a) chooses scanning start element S_i；

Fig. 3 (b) chooses the adjacent unit S of SIM maximum intensity_jJoin in candidate aggregate district Z；

Fig. 3 (c) depth scan: continue to choose and be newly added object S_jThe adjacent unit of SIM maximum intensity join in Z；

Fig. 3 (d) range scans: the adjacent unit continuing to choose the SIM maximum intensity of all spatial objects in Z joins Z In；

Fig. 4 (a)-Fig. 4 (d) is the banding cluster of simulated data sets I, S-shaped cluster, O shape cluster and cross cluster respectively True shape；

Fig. 5 (a) is the true shape containing concave units banding cluster data collection of simulated data sets II；

Fig. 5 (b) is the result of detection of SIM depth scan；

Fig. 5 (c) is the result of detection of SIM range scanning；

Fig. 5 (d) is the result of detection of Kulldorff circular scan；

Fig. 6 (a) is the true shape containing concave units cross cluster data collection of simulated data sets II；

Fig. 6 (b) is the result of detection of SIM depth scan；

Fig. 6 (c) is the result of detection of SIM range scanning；

Fig. 6 (d) is the result of detection of Kulldorff circular scan；

Fig. 7 (a) is O shape and the true shape of I shape cluster of simulated data sets III；

Fig. 7 (b) is L-shaped and the true shape of S-shaped cluster of simulated data sets III；

Fig. 8 is SIDS2 data set SIDS mortality rate spatial distribution map.

Fig. 9 (a) is that SIDS2 data set SIM depth scan MLC clusters result of detection；

Fig. 9 (b) is that SIDS2 data set SIM range scanning MLC clusters result of detection；

Figure 10 (a) is that SIDS2 data set Kulldorff circular scan MLC clusters result of detection；

Figure 10 (b) is that the Kulldorff oval-shaped scan MLC of a=0 clusters result of detection；

Figure 10 (c) is that the Kulldorff oval-shaped scan MLC of a=0.5 clusters result of detection；

Figure 10 (d) is that the Kulldorff oval-shaped scan MLC of a=1 clusters result of detection.

Detailed description of the invention:

The present invention is described in detail below in conjunction with the accompanying drawings:

1. related definition:

(1) set study area G and have N number of spatial object G={S₁, S₂..., S_N, spatial object S_iPosition be { x_i, y_i, right In wire and planar object, position can be barycenter, geometric center etc..

(2) for spatial object S_iIf the attribute of detection is c_i, such as number of patients, crime number etc., frequently referred to example , and set the primary attribute relevant to detecting attribute as b (cases)_i, such as population etc., it is frequently referred to overall (population), then Corresponding example rate is

(3) for study area G, spatial object number is N, and total example number isOverall number is Example rate isFor candidate aggregate district (i.e. scanning window region) Z, spatial object number is n_Z, example number isOverall number isExample rate is

(4) definition binary type Space Lorentz Curve matrix W, w_ij=1 representation space object S_iWith S_jAdjacent, w_ij=0 table Show non-conterminous, wherein i=1,2 ..., N, j=1,2 ..., N, and i ≠ j, w_ii=0.

2, spatial interactive mode l

Action intensity between adjacent space object is incorporated into sky as weighing the factor of correlation degree between spatial object Between in scan statistics method, between object, action intensity the biggest expression relatedness is the strongest.

Spatial interactive mode l is the model calculating steric interaction power improved based on Gravity Models, referred to as SIM Model (Spatial Interaction Model).The primitive form of Gravity Models represents: arbitrarily exist mutually between two articles The active force attracted, amount of force is directly proportional to the quality of object, and the distance between object is inversely proportional to.Gravity Mode after improvement Type, i.e. SIM model is shown in formula (1), and implication is: two spatial object S_iAnd S_jBetween there is active force, its directed force F_ijWith right The example incidence rate of elephant is directly proportional, and the distance between them is inversely proportional to, the biggest then object S of active force_i、S_jBetween space close Connection property is the strongest.

$F_{ij}=k\frac{{\left(r_i\·r_j\right)}^b}{d_{ij}^a}=k\frac{{\left(\frac{c_i}{b_i}\·\frac{c_j}{b_j}\right)}^b}{d_{ij}^a}---\left(1\right)$

Wherein, k is gravitational constant, can be taken as 1, r_i、r_jIt is respectively spatial object S_i、S_jExample rate (i.e. example number is with total The ratio of body number), d_ijFor S_i、S_jBetween distance, a, b are constant.For different types of application, r and d can have different tables Reaching form, r can be to be other form such as example number, example number density, and d can be European common distance, European Weighted distance, graceful The forms such as Hatton's distance (Manhattan distance), Chebyshev's distance (Chebyshev distance).

SIM model is incorporated in spacescan statistical method, considers during to irregularly shaped MLC scanning probe The interaction factor that geospatial object is intrinsic, reflects geographical spatial data and is different from the peculiar property of traditional data Spatial dependence.

Illustrate as a example by detection high-value sector accumulation regions:

As it is shown in figure 1, a kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, including following Step:

Step one: select Spatial Adjacency type, builds Space Lorentz Curve matrix W；According to problem types, select suitably Probability Distribution Model；Make cycle-index i=1.

Space Lorentz Curve uses geospatial object to have the form of public boundary, public vertex, specifically includes Rook Adjacent, Bishop adjoins, Queen adjoins three types, and Rook is adjacent when adjoining the same border of definition space object-sharing, Bishop is adjacent when adjoining the same summit of definition space object-sharing, and Queen adjoins the same border of definition space object-sharing Or be adjacent during summit, respectively as shown in Fig. 2 (a)～2 (c), the unit that colors in is the adjacent unit of center cell.

Conventional probabilistic model has: Poisson distribution model, binomial distribution model, normal distribution model etc., different probability Model is suitable for different types of data, and Poisson distribution is applicable to the sequential of unfiled discrete type random distribution, space and space-time number According to, binomial distribution is applicable to the discrete type random distribution data of two differential countings, and normal model is applicable to Normal Distribution Seriality sequential, space and space-time data.Other probabilistic model includes space-time arranged model (Space-time Permutation Model), multinomial distribution (Multinomial model), in order/series model (Ordinal model), exponential (Exponential model) etc..Table 1 lists the applicable situation of different probability model.

The applicable situation of table 1 different probability model

Step 2: i & lt is circulated, from { S₁, S₂..., S_NSpatial object S is selected in }_iAs candidate aggregate district Z's Start element, by S_iJoin in candidate aggregate set Z,As shown in Fig. 3 (a)；Selected depth scanning subsequently or wide Degree scan mode performs step 3 or step 4 respectively.

Step 3: depth scan mode: be newly added candidate aggregate district Z spatial object for current active unit, foundation Adjacency matrix W obtains all of its neighbor unit of active cell, but does not comprise the unit added in set Z；Public according to SIM model Formula (1) calculates the steric interaction intensity between active cell and these adjacent units, selects the adjacent list of SIM maximum intensity Unit S_jJoin in candidate aggregate set Z,As shown in Fig. 3 (b), 3 (c)；Repeat this step until meeting step The condition of rapid five.

Step 4: range scan mode: obtain the adjacent list of each spatial object in candidate aggregate district Z according to adjacency matrix W Unit, but do not comprise the unit added in set Z；According to SIM model formation (1) calculate each object in Z be adjacent unit it Between SIM intensity, select SIM maximum intensity adjacent unit S_jJoin in candidate aggregate set Z,Such as Fig. 3 Shown in (b), 3 (d)；Repeat this step until meeting the condition of step 5.

Step 5: calculate the statistic LR/LLR value of Z overlay area；When the space that statistic no longer increases or comprises in Z The maximum that object number reaches to set clusters size (such as: the spatial object number that accumulation regions comprises should be less than survey region space The 50% of object sum) time, then stop scanning, gather ZXing Chengyige candidate aggregate district.

Likelihood ratio LR (Likelihood Ratio) or log-likelihood ratio LLR (Log Likelihood Ratio) is used to Evaluate the statistic of candidate aggregate district Z aggregation extent.Assembling for high level, LR/LLR value is the biggest, the region outside thinking with window Comparing, in window, the aggregation of specified attribute is the strongest；Assembling for low value, LR/LLR value is the least, shows that aggregation is the strongest.Right Assembling in high level, the purpose of spacescan statistics is exactly under Space Lorentz Curve retrains, and finds and assumes inspection by nonrandomness The LR/LLR value maximized window tested, its region covered is maximum possible accumulation regions MLC.

1, the LR/LLR statistic of Poisson distribution

Spacescan statistic of test LR/LLR building process based on Poisson distribution is as follows:

If p is spatial object S in scanning window (candidate aggregate district) Z_kExample c_kThe probability and the obedience Poisson that occur are divided Cloth, q is the probability of window Z outer example generation and obeys Poisson distribution, and null hypothesis (null hypothesis) is H₀: p=q, table Showing and assume that the example probability of happening inside and outside window Z not there are differences, alternative hypothesis (alternative hypothesis) is H_Z: High level is assembled, p > q, represent that the example probability of happening assumed in window Z is higher than the probability of happening outside window, or H_Z: for Low value is assembled, p < q, represents that the example probability of happening assumed in window Z is less than the probability of happening outside window.

H_Z、H₀Assume that the likelihood function of lower scanning window Z is respectively as follows:

$L\left(Z\right)=\frac{e^{-C_G}}{C_G!}{\left(\frac{c_Z}{b_Z}\right)}^{c_Z}{\left(\frac{C_G-c_Z}{B_G-b_Z}\right)}^{C_G-c_Z}{\&Pi;}_{S_k\&Element;Z}{c}_k---\left(2\right)$

$L_0=\frac{e^{-C_G}}{C_G!}{\left(\frac{C_G}{B_G}\right)}^{C_G}{\&Pi;}_{S_k\&Element;Z}{c}_k---\left(3\right)$

L (Z) is the likelihood function of alternative hypothesis, L₀The likelihood function of null hypothesis, then the likelihood ratio LR of window Z For:

$LR=\frac{L\left(Z\right)}{L_0}=\frac{{\left(\frac{c_Z}{b_Z}\right)}^{c_Z}{\left(\frac{C_G-c_Z}{B_G-b_Z}\right)}^{C_G-c_Z}}{{\left(\frac{C_G}{B_G}\right)}^{C_G}}---\left(4\right)$

Taking the logarithm above formula, available log-likelihood function is than LLR:

$\begin{array}{c}LLR=\ln \left(\frac{L\left(Z\right)}{L_0}\right)=c_Z\left(\ln \left(c_Z\right)-\ln \left(b_Z\right)\right)+\left(C_G-c_Z\right)\left(\ln \left(C_G-c_Z\right)-\ln \left(B_G-b_Z\right)\right)-\\ G_G\left(\ln \left(C_G\right)-\ln \left(B_G\right)\right)\end{array}---\left(5\right)$

2, the LR/LLR statistic of binomial distribution

Similar with the spacescan statistic building process of Poisson distribution, available null hypothesis H₀Under spacescan likelihood Function L₀:

$L_0={\left(\frac{C_G}{B_G}\right)}^{C_G}{\left(1-\frac{C_G}{B_G}\right)}^{B_G-C_G}---\left(6\right)$

And alternative hypothesis H_ZUnder likelihood function L (Z):

$L\left(Z\right)={\left(\frac{c_Z}{b_Z}\right)}^{c_Z}{(1-\frac{c_Z}{b_Z})}^{b_Z-c_Z}{\left(\frac{C_G-c_Z}{B_G-b_Z}\right)}^{C_G-c_Z}{(1-\frac{C_G-c_Z}{B_G-b_Z})}^{(B_G-b_Z)-(C_G-c_Z)}---\left(7\right)$

Then can obtain likelihood ratio LR=L (Z)/L₀And log-likelihood function is than LLR=ln (LR).

3, the LR/LLR statistic of normal distribution

For the spacescan window area Z of study area G, null hypothesis H₀Represent the example c inside and outside window_i(i=1,2 ..., N) probability of happening not there are differences, and (average is μ to obey same normal distribution_G, variance be), H₀The likelihood of lower window Z Function is:

$L_0={\&Pi;}_{S_k\&Element;Z}\frac{1}{{\mathrm{\&sigma;}}_G\sqrt{2\mathrm{\&pi;}}}{e}^{-\frac{{\left(c_k-{\mathrm{\&mu;}}_G\right)}^2}{2{\mathrm{\&sigma;}}_G^2}}---\left(8\right)$

Wherein,Above formula asks logarithm to obtain log-likelihood function:

${\mathrm{lnL}}_0=-N\ln \left(\sqrt{2\mathrm{\&pi;}}\right)-N\ln \left({\mathrm{\&sigma;}}_G\right)-{\&Sigma;}_{S_k\&Element;Z}\frac{{\left(c_k-{\mathrm{\&mu;}}_G\right)}^2}{2{\mathrm{\&sigma;}}_G^2}---\left(9\right)$

Alternative hypothesis H_ZRepresent that the example probability of happening inside and outside window Z is obeyed different normal distributions and has same variance Property, i.e. the average of two normal distributions is different, variance is identical, and in window, the average of normal distribution isVariance isWindow The average of the outer normal distribution of mouth isVariance isInside and outside window, the variance of normal distribution is all mutually:

${\mathrm{\&sigma;}}_Z^2={\mathrm{\&sigma;}}_{Z^c}^2=\frac{1}{N}\left({\&Sigma;}_{S_k\&Element;Z}{c}_k^2-2c_Z{\mathrm{\&mu;}}_Z+n_Z{\mathrm{\&mu;}}_Z^2+{\&Sigma;}_{S_k\&NotElement;Z}{c}_k^2-2\left(C_G-c_Z\right){\mathrm{\&mu;}}_{Z^c}+\left(N-n_Z\right){\mathrm{\&mu;}}_{Z^c}^2\right)---\left(10\right)$

H_ZThe log-likelihood function of lower window Z is:

$\begin{array}{c}\ln L\left(Z\right)=-N\ln \left(\sqrt{2\mathrm{\&pi;}}\right)-N\ln \left(\sqrt{{{\mathrm{\&sigma;}}_Z}^2}\right)-\frac{1}{2{\mathrm{\&sigma;}}_Z^2}({\&Sigma;}_{S_k\&Element;Z}{c}_k^2-2c_Z{\mathrm{\&mu;}}_Z+n_Z{\mathrm{\&mu;}}_Z^2+{\&Sigma;}_{S_k\&NotElement;Z}{c}_k^2-\\ 2\left(C_G-c_Z\right){\mathrm{\&mu;}}_{Z^c}+\left(N-n_Z\right){\mathrm{\&mu;}}_{Z^c}^2)\end{array}---\left(11\right)$

Abbreviation is:

$\ln L\left(Z\right)=-N\ln \left(\sqrt{2\mathrm{\&pi;}}\right)-N\ln \left(\sqrt{{{\mathrm{\&sigma;}}_Z}^2}\right)-N/2---\left(12\right)$

Then the log-likelihood function of window Z than LLR is:

$LLR=\frac{\ln L\left(Z\right)}{{\mathrm{lnL}}_0}=Nln\left({\mathrm{\&sigma;}}_G\right)+{\mathrm{\&Sigma;}}_{S_k\&Element;Z}\frac{{\left(c_k-{\mathrm{\&mu;}}_G\right)}^2}{2{\mathrm{\&sigma;}}_G^2}-\frac{N}{2}-N\ln \left(\sqrt{{{\mathrm{\&sigma;}}_z}^2}\right)---\left(13\right)$

Step 6: make i=i+1, as i≤N, from { S₁, S₂..., S_NSpatial object S is reselected in }_iAs new The start element of candidate aggregate district Z, for the scan mode of deep search, repeats above-mentioned step 2, step 3, step 5, For the scan mode of breadth first search, repeat above-mentioned step 2, step 4, step 5；Until all of spatial object all quilts Complete as start element search, thus define N number of candidate aggregate district.

Step 7: N number of candidate aggregate district is sorted from big to small according to LR/LLR value；Sieve the most successively Choosing: if the spatial object weight that the spatial object that the candidate aggregate district of current screening comprises comprises with the candidate aggregate district retained Multiple, then reject current candidate accumulation regions, otherwise retain current candidate accumulation regions.

Step 8: remain the candidate aggregate district of M (≤N) individual non-overlapping copies after setting screening, the most successively to each time Select accumulation regions to carry out Monte Carlo simulation hypothesis testing, concretely comprise the following steps:

(1) for the distributional pattern of current candidate accumulation regions, selected probability Distribution Model is calculated (such as Poisson distribution, binomial Distribution, normal distribution etc.) parameter value；

(2) premised on null hypothesis (i.e. random distribution), whole study area is produced N_SimIndividual meet corresponding probability distribution Simulated data sets, for ease of calculating, N_SimGenerally take with the numerals of 999 endings, such as 999,1999,9999,99999 etc.；

(3) utilizing aforesaid deep search or breadth first search's scan mode, the most probable obtaining each simulated data sets is assembled District MLC and corresponding LR/LLR value；

(4) by current candidate accumulation regions and N_SimThe MLC of individual simulated data sets arranges from big to small according to LR/LLR value Sequence, determines that current candidate accumulation regions is at N_SimPosition sequence Rank in+1 LLR, counting statistics significance value P=Rank/ (N_Sim+ 1)；

(5) as P < level of significance α, as α=0.05,0.01,0.001 etc., then refuse null hypothesis H of random distribution₀, connect It is higher than alternative hypothesis H outside accumulation regions by the attribute high level probability of happening in candidate aggregate district_Z, show that current candidate accumulation regions is passed through Monte Carlo nonrandomness hypothesis testing.

Step 9: by each accumulation regions of nonrandomness hypothesis testing according to LR/LLR value be sequentially output from big to small into: 1st MLC cluster, second highest 2nd MLC that abnormal aggregation is the highest cluster, 3rd MLC clusters ..., etc..

Illustrate below by comparative example:

Embodiment 1: simulated data sets I

Simulated data sets I includes 4 data sets, and each data set comprises a difform MLC cluster, and shape is respectively For banding, S-shaped, O shape, cross, as shown in Fig. 4 (a)～4 (d).

The space cell sum N=400 of each data set, bulk properties b of each unit_i=40, unit in cluster Example attribute c_i=20, cluster the example attribute c of outer unit_i=10.The Cluster space unit number of 4 data sets is respectively 40, 40,80,80, MLC cluster dimensional ratios (referring to the ratio of MLC cluster cell number and data set unit sum N) be followed successively by 0.1, 0.1、0.2、0.2。

Space Lorentz Curve uses public boundary and the Queen form of summit direct neighbor.Steric interaction SIM model Parameter k, b value be 1, a value is 2, and d uses the common Euclidean distance between units centre of mass.Statistic of test uses Poisson to divide The log-likelihood function ratio of cloth.Level of significance α=0.01 of Monte Carlo test, number realization N_Sim=99, work as statistically significant Property value P=α=0.01 time, it is believed that the abnormal aggregation district detected is to be clustered by the MLC of nonrandomness hypothesis testing.

Table 2 is 4 data set SIM depth scan of simulated data sets I, the scanning of SIM range, Kulldorff circular scan Cluster result of detection, by the MLC cluster result of inspection when in table, listed result is P=0.01.For truly clustering chi Very little be 0.1 banding cluster, S-shaped cluster, maximum cluster size is respectively set as 0.05,0.1,0.15；For truly clustering chi Very little be 0.2 O shape cluster, cross cluster, maximum cluster size is respectively set as 0.15,0.2,0.25.In table, each index contains Justice:

LLR ratio: the ratio of the LLR that the MLC cluster detected clusters with true MLC；

Accuracy: belong to the unit number of true cluster and the ratio of true MLC cluster cell sum in the cluster detected；

Error rate: the ratio of non-genuine cluster cell number and cluster cell sum in the cluster detected；

Maximum cluster size: one of end condition of cluster detection, refers to cluster the space cell maximum number allowing to comprise Ratio with data set unit sum N；

MLC dimensional ratios (MLC Size Ratio): true MLC clusters dimensional ratios, refers to true MLC cluster cell sum Ratio with data set unit sum N.

When LLR ratio is 1 and accuracy is 100%, represent that the accumulation regions detected clusters complete one with true MLC Cause.

The scanning of table 2 SIM depth scan, SIM range, Kulldorff circular scan are to 4 of simulated data sets I not similar shapes Shape MLC clusters result of detection

As can be seen from the table, SIM depth scan, the scanning of SIM range, the spy of three kinds of methods of Kulldorff circular scan Survey the result maximum cluster size all by specifying to be affected.When maximum cluster size is not less than true cluster size, SIM is wide Degree scanning can intactly detect 4 kinds of difform true clusters, and (LLR ratio is 1, accuracy is 100%, error rate is 0%).

Clustering inconsistent result of detection for other with true, the LLR ratio of SIM depth scan and range scanning is the biggest (sole exception occurs in O shape cluster maximum cluster and is dimensioned so as to 0.25 many LLR ratios higher than Kulldorff circular scan SIM depth scan result) and error rate be 0%.And Kulldorff circular scan result occurs in that degree is different mostly Error rate, error rate is (when O shape cluster maximum cluster is dimensioned so as to 0.15), error rate 0% only occur once up to To 54.55% (when O shape cluster maximum cluster is dimensioned so as to 0.25).

Scan method based on SIM does not relies on the scanning window of definite shape, during scanning according to space adjacent cells it Between directed force F_ijIntensity carries out the degree of depth or breadth first search, two object S_iAnd S_jBetween directed force F_ijAlways with its example rate r_i、r_jAmassing is directly proportional, and therefore, the example rate of spatial object serves conclusive effect of contraction to search procedure, makes example rate Low non-genuine cluster cell will not be added in result of detection, and SIM depth scan and range scanning error rate are 0% Cluster result also demonstrates this point, this be SIM scan method be different from Kulldorff circular, the one of oval-shaped scan method Individual good characteristic.

Embodiment 2: simulated data sets II

Simulated data sets II includes 2 data sets, and each data set comprises a MLC cluster that there is concave units, MLC Cluster shape is respectively banding, cross, and as shown in Fig. 5 (a), Fig. 6 (a), concave units (depression unit) is self-explanatory characters The cluster cell that example rate is more slightly higher than the example rate clustering outer unit but lower than other unit example rate in cluster, depression is single The existence of unit adds the detection difficulty of spacescan method, when scan method detectivity is more weak, may not measure because visiting Concave units and cause cluster result to interrupt herein.Banding cluster comprises 1 concave units, and cross clusters in the left and right sides Respectively comprise 3 adjacent concave units, if detection is less than concave units, the concave units a small amount of cluster cell isolated (band Shape cluster is spaced 1 unit, and the cross cluster left and right sides is spaced 7 and 6 unit respectively) spy will not be included in In the cluster result surveyed.

The space cell sum N=400 of each data set, bulk properties b of each unit_i=40, in cluster, depression is single The example attribute c of unit_i=13, other unit c_i=20, cluster the example c of outer unit_i=10.The space cell of banding cluster Number is 40, and MLC dimensional ratios is 0.1；The space cell number of cross cluster is 80, and MLC dimensional ratios is 0.2.

Space Lorentz Curve uses public boundary and the Queen form of summit direct neighbor.Steric interaction SIM model Parameter k, b value be 1, a value is 2, and d uses the common Euclidean distance between units centre of mass.Statistic of test uses Poisson to divide The log-likelihood ratio function of cloth.Level of significance α=0.01 of Monte Carlo test, number realization N_Sim=99.

Table 3 is 2 data set SIM depth scan of simulated data sets II, the scanning of SIM range, Kulldorff circular scan Result of detection, by the MLC cluster result of inspection when in table, listed result is P=0.01.

The MLC of table 3 simulated data sets II clusters result of detection

As can be seen from the table, banding is clustered, when the maximum cluster size specified is not less than true cluster size, The result of detection of SIM range scanning is completely the same, as shown in Fig. 5 (c) with true cluster.Clustering for cross, SIM range is swept The accuracy retouched reaches 96.25%, only has 3 adjacent unit of left side and is not detected out, shown in Fig. 6 (c).Further, for two Planting the cluster of shape, the scanning of SIM range all can detect the true cluster cell isolated by concave units.SIM depth scan Though result of detection scan not as SIM range, but as SIM range scan method, all non-genuine cluster cell will not be added Entering in the cluster result of detection, as shown in Fig. 5 (b), 5 (c), 6 (b), 6 (c), i.e. error rate is 0%.And Kulldorff circle Shape scan method can not accomplish this point, as shown in Fig. 5 (d), 6 (d).

Embodiment 3: simulated data sets III

Simulated data sets III includes 2 data sets III (a), III (b), each data set comprise respectively two difform MLC clusters, as shown in Fig. 7 (a), 7 (b).The space cell sum N=400 of each data set, bulk properties b of each unit_i =40, the example attribute c of unit in cluster_i=20, cluster the example attribute c of outer unit_i=10.

III (a) comprises O shape and I shape two cluster, and Cluster space unit number is respectively 80,40, and cluster cell sum is 120, cluster overall size ratio is 0.3.III (b) comprises L-shaped and S-shaped two cluster, Cluster space unit number is respectively 40, 40, cluster cell sum is 80, and cluster overall size ratio is 0.2.The two data set detects multiple difformity MLC from simultaneously The angle of cluster carries out contrast test to SIM depth scan, the scanning of SIM range, three kinds of methods of Kulldorff circular scan, if Fixed single cluster full-size is 0.2, the results are shown in Table 4, is gathered by the MLC of inspection when in table, listed result is P=0.01 Class result.

The MLC of table 4 simulated data sets III clusters result of detection

From table 4, it can be seen that the result of detection of SIM range scanning and III (a), III (b) truly cluster are completely the same.SIM Though the LLR ratio result of depth scan is not as the scanning of SIM range but it is better than Kulldorff circular scan, and error rate is 0%.Further, the degree of depth based on SIM and range method can detect real cluster number 2 exactly, and Kulldorff is circular The cluster number of scanning probe is not only inconsistent with true cluster number, and entirely without the L-shaped cluster (LLR detected in III (b) Ratio is 0).

Embodiment 4:SIDS2 data set

SIDS2 data set is that each county sudden infant death is comprehensive during North Carolina, USA 1974-1978,1979-1984 Disease SIDS (Sudden Infant Death Syndrome) death toll (Data Source:https:// geodacenter.asu.edu/sdata), data set comprises 100 counties (N=100), and natus total number of persons is 752354 people (B_G=752354), SIDS total toll is 1503 people (C_G=1503), general mortality rate R_G=1.9977 (units: every thousand people), The distribution situation of each county SIDS mortality rate is as shown in Figure 8.This data set is usually used in different spaces, space scanning statistical method Performance evaluation.

Kulldorff circle, oval-shaped scan method is used to contrast with the degree of depth based on SIM, range scan method, High aggregation zone abnormal to SIDS mortality rate detects.The shape penalty function of Kulldorff ellipse method is [4s/ (s+1)²]^a, whereinBeing determined by oval eccentricity e, parameter a determines strength of punishment, respectively value be 0,0.5, The punishment of the biggest degree in irregular shape to accumulation regions of 1, a value is the strongest.

Space Lorentz Curve uses the Rook form that public boundary is adjacent.Parameter k of SIM model, b value are 1, a value Being 2, d uses the common Euclidean distance between each county barycenter.Statistic of test uses the log-likelihood ratio function of Poisson distribution.Maximum Cluster is sized to the 50% of spatial object sum N.Monte Carlo simulation times N_Sim=9999.Each scan statistics method Result of detection is shown in Table 5 and Fig. 9 (a)-Fig. 9 (b), Figure 10 (a)-Figure 10 (d).

Table 5 SIDS2 data set MLC clusters result of detection

In table 5, the 1st MLC that what LLR value was the highest is aggregation that SIM range scan method detects is the highest, LLR value Reach 46.04, the MLC cluster detected far above other method.In Kulldorff series methods, the ellipse side of a=0 Method LLR value is the highest, is 28.57, but it only detects 1 MLC cluster, does not detects the MLC cluster of upper right comer region.

Comparison diagram 9 (a)-Fig. 9 (b), the MLC distribution situation of Figure 10 (a)-Figure 10 (d), it can be seen that the MLC of distinct methods Cluster is the most overlapping, illustrates that the MLC result of detection is stable.Specifically, the SIM depth scan detection of Fig. 9 (a) Result is completely the same with the Kulldorff ellipse method result of detection of Figure 10 (d) a=1.The SIM range scanning MLC of Fig. 9 (b) Cluster has completely included the SIM depth scan of Fig. 9 (a), the Kulldorff oval-shaped scan of Figure 10 (c) a=0.5, Figure 10 (d) a The MLC cluster of the oval-shaped scan of=1, also contains the Kulldorff circular method of Figure 10 (a) and the ellipse of Figure 10 (b) a=0 Most of unit in circular method MLC cluster.In conjunction with aforementioned to the result of detection containing concave units simulated data sets II, explanation Relative to other method, range scan method based on SIM clusters detectivity to the MLC that there is Weak link (i.e. concave units) Higher.

The analysis result of 4 embodiments of summary, it is believed that with SIM depth scanning method, Kulldorff circle Scan method, Kulldorff oval-shaped scan method are compared, range scan method shape irregular to geographical space based on SIM The detectivity in shape abnormal aggregation district is higher, and is more easy to detect the abnormal aggregation district comprising Weak link.SIM depth scanning method Though detection performance scans not as SIM range, but is not weaker than Kulldorff series methods, and the degree of depth based on SIM and range scan Non-abnormal space object all will not be included in the MLC result of detection by method.

Although the detailed description of the invention of the present invention is described by the above-mentioned accompanying drawing that combines, but not the present invention is protected model The restriction enclosed, one of ordinary skill in the art should be understood that on the basis of technical scheme, and those skilled in the art are not Need to pay various amendments or deformation that creative work can make still within protection scope of the present invention.

Claims (10)

1. a geographical space abnormal aggregation domain scanning statistical method based on interaction force, is characterized in that, including following step Rapid:

Judge the abnormal aggregation district type of detection, if attribute Low value anomaly accumulation regions, then by the geographic object of detection is belonged to It is attribute high-value sector accumulation regions that property value carries out shift conversion；

For attribute high-value sector accumulation regions, build Space Lorentz Curve matrix based on the Spatial Adjacency type selected；

Use the action intensity between spatial interactive mode l tolerance adjacent object；

Contiguous object based on depth scan mode or range scan mode continuous selection maximum intensity joins candidate and gathers In collection district, until the likelihood ratio LR/ log-likelihood ratio LLR value of high-value sector gathering correspondence no longer increases or candidate aggregate district reaches Stop during maximum specified size；

The multiple candidate aggregate districts formed are carried out Monte Carlo simulation, thus detect by nonrandomness hypothesis testing different Often accumulation regions.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, for attribute Low value anomaly accumulation regions, by geospatial object S_iThe property value c of detection_iIt is transformed to c_i', c_i' be institute There is geographic object property value { c₁,c₂,…,c_NMaximum deduct c_i, formula is:

c_i'=max{c₁,c₂,…,c_N}-c_i

Wherein N is spatial object number, by above-mentioned conversion, the detection of Low value anomaly accumulation regions is converted into high-value sector accumulation regions.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, building Space Lorentz Curve matrix is binary type matrix W, w_ij=1 representation space object S_iWith S_jAdjacent, w_ij=0 Representing non-conterminous, Space Lorentz Curve uses geospatial object to have the form of public boundary, public vertex.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, spatial interactive mode l is referred to as SIM model, particularly as follows: two spatial object S_iAnd S_jBetween there is active force, its Directed force F_ijIt is directly proportional to the example incidence rate of object, and the distance between them is inversely proportional to, the biggest then object S of active force_i、S_j Between spatial correlation the strongest, formula is:

$F_{ij}=k\frac{{\left(r_i\&CenterDot;r_j\right)}^b}{d_{ij}^a}=k\frac{{\left(\frac{c_i}{b_i}\&CenterDot;\frac{c_j}{b_j}\right)}^b}{d_{ij}^a}$

Wherein, k is constant, can be taken as 1；r_i、r_jIt is respectively spatial object S_i、S_jExample rate, i.e. the ratio of example number and overall number； c_iFor the attribute of detection, referred to as example；b_iFor the primary attribute relevant to detection attribute, it is referred to as overall；d_ijFor S_i、S_jBetween Distance；A, b are constant.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, from N number of spatial object { S after building Space Lorentz Curve matrix₁, S₂..., S_NSpatial object S is selected in }_iMake For the start element of candidate aggregate district Z, by S_iJoin in candidate aggregate set Z,

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, described depth scan mode: be newly added candidate aggregate district Z spatial object for current active unit, according to adjacent Matrix W obtains all of its neighbor unit of active cell, but does not comprise the unit added in set Z；According to SIM model formation meter Calculate the steric interaction intensity between active cell and these adjacent units, select the adjacent unit S of SIM maximum intensity_jAdd Enter in candidate aggregate set Z,

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, described range scan mode: obtain the adjacent unit of each spatial object in candidate aggregate district Z according to adjacency matrix W, but Do not comprise the unit added in set Z；The SIM that in Z, each object is adjacent between unit is calculated strong according to SIM model formation Degree, selects the adjacent unit S of SIM maximum intensity_jJoin in candidate aggregate set Z,

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, calculates the statistic LR/LLR value of Z overlay area；When the spatial object number that statistic no longer increases or comprises in Z When reaching the maximum cluster size set, then stop scanning, gather ZXing Chengyige candidate aggregate district.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, also needs to screen candidate aggregate district before the multiple candidate aggregate districts formed are carried out Monte Carlo simulation: According to LR/LLR value, N number of candidate aggregate district is sorted from big to small；Screen the most successively: if current screening The spatial object that the spatial object that candidate aggregate district comprises and the candidate aggregate district retained comprise repeats, then reject current candidate Accumulation regions, otherwise retains current candidate accumulation regions.

A kind of geographical space abnormal aggregation domain scanning statistical method based on interaction force, its Feature is, if remaining the candidate aggregate district of M non-overlapping copies after Shai Xuan, M≤N, the most successively to each candidate aggregate district Carry out Monte Carlo simulation hypothesis testing；By each candidate aggregate district of Monte Carlo nonrandomness hypothesis testing according to LR/LLR Value is followed successively by intensity of anomaly abnormal aggregation district from high to low from big to small.