A method for measuring heterogeneity of spatial point data based on ensemble learning

Abstract

The present invention provides a spatial point data heterogeneity measurement method based on ensemble learning, comprising: generating training data for spatial point data heterogeneity measurement; measuring point data heterogeneity using multivariate statistical indicators and performing significance tests; constructing an ensemble learning evaluation model by acquiring model parameters; pre-judging the distribution pattern of its test data, and weighted fusion of the calculation results of incompleteness indicators in the ensemble framework to obtain a heterogeneity measurement index I based on the test data of the evaluation model, which is used to achieve heterogeneity measurement of spatial point data under different prior distributions in the same dimension; the present invention innovatively draws on parameter learning algorithms driven by data, and proposes an ensemble learning evaluation model for sampling point heterogeneity; driven by training data, a robust evaluation and horizontal comparison of the heterogeneity of arbitrary spatial point data is achieved, which has the dual advantages of application effectiveness and horizontal comparison under a unified dimension for different sampling point data.

Description

Technical Field

[0001] The present invention relates to the field of geostatistics, and in particular to a spatial point data heterogeneity measurement method based on ensemble learning. Background Art

[0002] The object described by spatial point data is a discrete point in geographic space, with longitude and latitude coordinates, but no size. The more common spatial point data is sampling point data. For ecological and environmental monitoring, the reasonable selection of sampling points is helpful to obtain accurate monitoring data. Therefore, the precise quantitative evaluation of spatial sampling point heterogeneity is an important research issue to achieve the transformation and upgrading of ecological and environmental improvement from "quantitative change" to "qualitative change" under the background of the new normal of ecological and environmental monitoring. Its scientific and reliable evaluation report is of great significance for monitoring and predicting the environment, improving disaster prevention and resistance capabilities, and maintaining the ecological environment. In the process of environmental monitoring, ideally, the more evenly and densely the sampling points can cover the entire target monitoring area, the more complete the environmental information monitored will be. However, objectively, due to the limitations of construction costs and terrain environment, the spatial layout of actual sampling points will deviate from the ideal uniform and dense distribution, that is, there is a certain degree of spatial heterogeneity.

[0003] In the actual production process of engineering measurement and environmental testing, the spatial distribution of various monitoring sites does not present a uniform distribution state, and due to the influence of artificial manipulation and various geographical factors, the spatial distribution of various points often deviates from a completely random distribution. The geographical theory corresponding to this uneven distribution of points in space is a manifestation of heterogeneity, and this deviation phenomenon can be described by spatial heterogeneity.

[0004] Most of the existing spatial point data heterogeneity measurement methods are based on statistical ideas, and are further divided into methods based on geographic processes and methods based on spatial point distribution characteristics statistics according to the different modeling objects.

[0005] The method based on geographic process modeling is mainly derived from the idea of ​​random fields, and describes heterogeneity by establishing a suitable variogram. Shi Zhongjie et al. combined classical statistical methods with geostatistical methods and proposed to use the semivariance model to measure the heterogeneity of leaf area index based on the consideration of fractal dimension. This method is mainly suitable for spatial differentiation research in ecology and for research with a smaller sampling scale. Li Habin and other scholars proposed to use geostatistical knowledge such as nugget variance and sill value to quantitatively describe the spatial heterogeneity of forest stands. This method relies on the division of heterogeneity scales. With the transformation of spatial point data, the classification heterogeneity of the method also increases. Liu Chang et al. used the variogram to study the spatial heterogeneity of carbon content in Pinus sylvestris and explored its causes. In addition to the study of spatial point heterogeneity in ecological forestry, there are also many methods based on geographical processes in the study of meteorological monitoring. For example, Xu et al. proposed a method based on Kriging and entropy theory to design the precipitation monitoring network in Shanghai. Under the conditions of combining the minimum Kriging standard error (KSE) and the maximum net information (NI), the heterogeneity of precipitation spatial points was reduced, thereby obtaining the best sampling network and the best precipitation information. Bayat et al. used ordinary Kriging (OK) and Bayesian maximum entropy (BME) combined with genetic algorithms to measure the heterogeneity of precipitation monitoring sites in time and space, effectively saving the cost of setting up precipitation sites and improving efficiency.

[0006] The statistical method based on spatial point features is to describe the heterogeneity of spatial points by studying the probability distribution of point patterns and borrowing the measurement method model of spatial heterogeneity. With the continuous development of spatial analysis, the study of point heterogeneity level was first proposed by Ripley, who used the K function to qualitatively describe the scale of a single biological species, that is, the degree of aggregation, and could not quantitatively describe the spatial heterogeneity of points. Schilcher tried to combine the inhomogeneity measurement method with the sample Pearson correlation coefficient to measure heterogeneity based on the classical sample method, but because this method is limited by personal experience, the measurement results of heterogeneity are biased. Baddeley et al. proposed a kernel density estimation method to observe spatial heterogeneity by studying the density changes of local points on a continuous density surface. Although this method has more specific quantitative information than the previous method. The nearest neighbor distance proposed by Diggle and Dixon et al. can effectively evaluate the state of spatial distribution patterns, but the real geographical scene is very complex, and the method of measuring heterogeneity by calculating a single statistical indicator is not suitable. Considering that a single indicator is biased in evaluating heterogeneity, and the reliability of different indicators is not easy to compare due to different measurement perspectives, Shu et al. summarized previous studies and used simulated data experiments, crime incidents, earthquakes, OD flow and other data to evaluate 17 classic heterogeneity measurement indicators. These indicators are calculated based on the distance between spatial points and between spatial points and generated random event points, or the second-order and higher distances. The study found that Clark and Evans' statistic (Aw) and Byth and Ripley's statistic (H-xw) are robust, and the study innovatively proposed a standardized indicator LH*.

[0007] In summary, the existing spatial point data heterogeneity assessment methods have the following main shortcomings:

[0008] 1. Different methods have different degrees of bias in terms of perceiving data distribution characteristics. A single model or indicator cannot robustly evaluate spatial point data under different prior distributions, resulting in low credibility and usability of its evaluation results.

[0009] 2. The existing methods are easily affected by data and model parameters, making it impossible to achieve horizontal comparison of the degree of heterogeneity of multiple spatial point data under the same dimension, and have great application limitations. Summary of the invention

[0010] The present invention provides a spatial point data heterogeneity measurement method based on ensemble learning. Its purpose is to propose an ensemble learning evaluation model for sampling point heterogeneity based on the overall framework of ensemble learning and innovatively draw on parameter learning algorithms driven by data. Driven by training data, a robust evaluation and horizontal comparison of the heterogeneity of arbitrary spatial point data can be achieved, which has the dual advantages of application effectiveness and horizontal comparison under a unified dimension for data from different sampling points.

[0011] In order to achieve the above object, the present invention provides a spatial point data heterogeneity measurement method based on ensemble learning, comprising:

[0012] Step 1, generating training data for measuring heterogeneity of spatial point data;

[0013] Step 2: Use multivariate statistical indicators to measure the heterogeneity of point data and conduct significance tests;

[0014] Step 3, constructing an integrated learning evaluation model by obtaining model parameters;

[0015] Step 4: pre-judge the distribution pattern of the test data of the integrated learning evaluation model, and perform weighted fusion on the calculation results of the incompleteness index in the integrated framework under the current distribution pattern pre-judgment scenario to obtain the heterogeneity measurement index I based on the test data of the evaluation model, which is used to realize the heterogeneity measurement of spatial point data under different prior distributions in the same dimension.

[0016] The generation of training data for spatial point data heterogeneity measurement specifically includes:

[0017] 1) Build Hierarchical structure training dataset;

[0018] 2) Generate the non-homogeneous Poisson point distribution pattern P1 using the point distribution pattern probability density function. The point distribution pattern probability density function is:

[0019]

[0020] Among them, the intensity function λ(x,y) represents the distribution density and homogeneity of points in space τ;

[0021] 3) Generate the Poisson cluster point distribution pattern P2 using the point distribution pattern probability density function. The point distribution pattern probability density function is:

[0022]

[0023] Among them, λ p represents the intensity of the Poisson point process;

[0024] 4) Generate the COX point distribution pattern P3 using the point distribution pattern probability density function. The point distribution pattern probability density function is:

[0025]

[0026] Among them, λ p represents the intensity of the Poisson point process;

[0027] 5) Generate the Gaussian-Poisson superposition point distribution pattern P4 using the point distribution pattern probability density function, the point distribution pattern probability density function is:

[0028]

[0029] Among them, N(μ, σ) and λ are density-related parameters that control the density of the generated point results;

[0030] 6) Generate the Markov point distribution pattern P5 using the point distribution pattern probability density function, the point distribution pattern probability density function is:

[0031]

[0032] Among them, τ represents the point set within a unit area, the constant ω represents the normalization coefficient, the parameter λ represents the point process intensity, and the parameter The parameter n represents the size of the mutual influence of random points, the parameter m represents the number of different neighboring point pairs within the set threshold r.

[0033] Among them, the use of multivariate statistical indicators to measure point data heterogeneity and conduct significance tests specifically includes:

[0034] Select the multivariate heterogeneity measure F = {f h}(h∈[1,17]);

[0035] Using the incompleteness statistic index {f h}(h∈[1,17]) for the heterogeneous sequence of distribution pattern P1 The data is calculated to obtain a set of heterogeneity measurement results Right now

[0036] Repeat the calculation of the heterogeneous sequence data of distribution pattern P1, and count the sequences The data are respectively in the incompleteness statistical index f h Ranking of experimental results under measurement The number of times is recorded as

[0037] Monte Carlo simulation method is used to analyze the multivariate statistical index f hThe ranking results of the distribution pattern P1 under the metric were tested for significance and the p-value was corrected.

[0038] Among them, building an integrated learning evaluation model specifically includes: during the training process, multivariate statistical indicators obtain the confidence parameter matrix U and the pattern recognition parameter matrix M by calculating the heterogeneity of the training data set, and building an integrated learning evaluation model.

[0039] In the testing phase of the ensemble learning evaluation model, the voting mechanism based on ensemble learning is used to pre-judge the distribution pattern that meets the test data and to evaluate the incompleteness statistical index {f h The calculation results of}(h∈[1,17]) are weighted fused to obtain the heterogeneity index I based on the test data of the evaluation model;

[0040] The heterogeneity index I measures the test data and the multivariate heterogeneity index F = {f h The heterogeneity index I can robustly evaluate spatial point data under different prior distributions and realize horizontal comparison of the heterogeneity degree of multiple spatial point data under the same dimension.

[0041] Among them, the non-homogeneous Poisson point distribution mode P1, Poisson cluster point distribution mode P2, COX point distribution mode P3, Gaussian-Poisson superposition point distribution mode P4 and Markov point distribution mode P5 all generate N groups of heterogeneous sequences by adjusting the parameters of the probability density function of their respective point distribution modes.

[0042] The above-mentioned multivariate statistical index calculation includes:

[0043] Using the statistical indicator f1 to analyze the sequence The data is calculated;

[0044] Calculate the statistical index f1 for 100 sets of sequences Sorting results of

[0045] Calculate statistical series In the incompleteness statistic f h Ranking of experimental results under measurement The number of times is recorded as

[0046] The process of significance testing includes:

[0047] The ranking results of the distribution pattern P1 measured by the statistical indicator f1 are tested for significance using the Monte Carlo simulation method to obtain the data set The correction result of the p value under the statistical indicator f1 measurement is statistically Get the dataset by repeating The correction result of the p value under the statistical index f1 measurement is used to obtain the distribution mode p under the statistical index f1 measurement. j , j∈[1,5], and finally obtain the incompleteness statistical index f h Correction results of each distribution mode under measurement.

[0048] The confidence parameter matrix is Among them uh j It represents the ability of the hth indicator to quantify the degree of incompleteness of the jth pattern; the pattern recognition parameter matrix Where m hj It represents the ability of the hth indicator to identify the jth pattern.

[0049] The testing phase of the integrated learning evaluation model includes:

[0050] Randomly thin the test data Px of the sampling point to obtain the thinning sequence in Represent the test data P r And the data obtained after thinning by 15%, 30%, 45%, and 60%.

[0051] Using the incompleteness statistic f h Measure and get statistical results

[0052]

[0053] Get the test vector R = [r1, r2, ..., r 17 ] T , define r h Incompleteness statistic f h For the test data P r Quantitative identification of the situation, statistical results sorting Design sequence with test data The sorting is consistent, indicating the incompleteness statistical index f h Quantifiable identification test data P r , remember r h =1; otherwise, r h =0, use r h Make up the test vector.

[0054] Pre-judge the distribution pattern of the test data, check the column vector m of the vector R and the pattern recognition parameter matrix M jPerform Hadamard product calculation to obtain the point distribution pattern type discrimination result b of the test data set j :

[0055] b j =R⊙m j

[0056] Where b j Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j The pattern recognition result; ⊙ is the Hadamard product; m j Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j pattern recognition ability, and b j Composition mode proportion B = [b1, ..., b5];

[0057] The test vector R is combined with the column vector u of the confidence parameter matrix U j Perform Hadamard product calculation to obtain the incompleteness statistical index [f h}(h∈[1,17]) in the context of pre-discrimination mode j :

[0058] c j =R⊙u j

[0059] In the formula, c j Indicates the measurement ability under the corresponding discrimination mode, u j Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j The measurement capability of j Composition confidence ratio C = [c1, ..., c5];

[0060] Under the current distribution mode pre-identification scenario, the calculation results of the incomplete statistical indicators in the integrated framework are weighted and fused to obtain the heterogeneity index value I based on the test data of the evaluation model:

[0061]

[0062] In the formula, ∑b j ,∑c j Represents the column vector b j and c j The sum of ∑B and ∑C represent the sum of all elements of matrices B and C respectively, n * The multivariate heterogeneity measure F = {f h The effective number of}(h∈[1,17]).

[0063] The above scheme of the present invention has the following beneficial effects: based on the overall framework of ensemble learning, innovatively drawing on parameter learning algorithms driven by data, an ensemble learning evaluation model for sampling point heterogeneity is proposed; driven by training data, a robust evaluation and horizontal comparison of data heterogeneity at any spatial point is achieved, which has the dual advantages of application effectiveness and horizontal comparison under a unified dimension for data from different sampling points.

[0064] Other beneficial effects of the present invention will be described in detail in the subsequent specific implementation section. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 It is a schematic diagram of the process of the present invention;

[0066] Figure 2 A schematic diagram of multivariate distance parameters according to an embodiment of the present invention;

[0067] Figure 3 This is a graph showing the visualization of sampling points and the measurement result of heterogeneity index I in an embodiment of the present invention;

[0068] Figure 4 This is a comparison chart of indicator measurement results of an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to make the technical problems, technical solutions and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0070] In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship, are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance.

[0071] In the description of the present invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a locking connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0072] In addition, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0073] like Figure 1 As shown, a spatial point data heterogeneity measurement method based on ensemble learning includes:

[0074] Step 1, generating training data for measuring heterogeneity of spatial point data;

[0075] Step 2: Use multivariate statistical indicators to measure data heterogeneity and conduct significance tests;

[0076] Step 3, constructing an integrated learning evaluation model by obtaining model parameters;

[0077] Step 4: pre-judge the distribution pattern of the test data of the integrated learning evaluation model, and perform weighted fusion on the calculation results of the incompleteness index in the integrated framework under the current distribution pattern pre-judgment scenario to obtain the heterogeneity measurement index I based on the test data of the evaluation model, which is used to realize the heterogeneity measurement of spatial point data under different prior distributions in the same dimension.

[0078] Specifically, the training data for generating spatial point data heterogeneity metrics include:

[0079] 1.1 Build The hierarchical structure training data set enables the ensemble learning evaluation model to fully fit the underlying data heterogeneity discrimination principle during the training process;

[0080] 1.2 Generate the non-homogeneous Poisson point distribution pattern P1 using the point distribution pattern probability density function shown in formula (1),

[0081]

[0082] Among them, the intensity function λ(x,y) represents the distribution density and homogeneity of points in space τ;

[0083] By adjusting the parameters λ and s in formula (1), the actual parameters are combined to determine the value of λ(x s +ys ) Take 1500(x 2 +y 2 )、2000(x 3 +y 3 )、2500(x 4 +y 4 )、3000(x 5 +y 5 ) and 3500(x 6 +y 6 ), generating an incomplete sequence containing 5 non-homogeneous Poisson point distribution patterns P1 data Right now The heterogeneity increases gradually from 1 to 5. Repeat the above operation to generate 100 sets of sequences.

[0084] 1.3 Use the point distribution pattern probability density function shown in formula (2) to generate the Poisson cluster point distribution pattern P2,

[0085]

[0086] Among them, λ p represents the intensity of the Poisson point process;

[0087] Under the same sampling scale, set λ p By adjusting the thresholds r = 0.2, 0.18, 0.16, 0.14 and 0.12, an incomplete sequence containing five Poisson cluster point distribution patterns P2 is generated. Right now The heterogeneity increases gradually from 1 to 5. Repeat the above operation to generate 100 sets of sequences.

[0088] 1.4 Generate the COX point distribution pattern P3 using the point distribution pattern probability density function shown in formula (3),

[0089]

[0090] Among them, λ p represents the intensity of the Poisson point process;

[0091] Under the condition of ensuring the consistency of sampling scale, by setting the parameter λ = 2000, 2500, 3000, 3500 and 4000, an incomplete sequence containing 5 COX point distribution pattern P3 data is generated. Right now The heterogeneity increases gradually from 1 to 5. Repeat the above operation to generate 100 sets of sequences.

[0092] 5) Generate the Gaussian-Poisson superposition point distribution pattern P4 using the point distribution pattern probability density function shown in formula (4),

[0093]

[0094] Among them, N(μ, σ) and λ are density-related parameters that control the density of the generated point results;

[0095] Specifically, by adjusting the parameters N(μ, σ) and λ, that is, setting (N, λ) to (200, 800), (300, 700), (400, 600), (500, 500) and (600, 400) respectively, an incomplete sequence containing 5 Gaussian-Poisson superposition point distribution patterns P4 data is generated. Right now The heterogeneity increases gradually from 1 to 5. Repeat the above operation to generate 100 sets of sequences.

[0096] 6) Generate the Markov point distribution pattern P5 using the point distribution pattern probability density function shown in formula (5),

[0097]

[0098] Among them, τ represents the point set within a unit area, the constant ω represents the normalization coefficient, the parameter λ represents the point process intensity, and the parameter Indicates the magnitude of the mutual influence of random points, parameter n indicates the number of random points, and parameter m indicates the number of different neighboring point pairs within the set threshold r;

[0099] Specifically, by setting Based on the fixed value, the parameters r = 0.02, 0.04, 0.06, 0.08 and 0.1 are set to generate an incomplete sequence containing 5 Markov point distribution patterns P5 data Right now The heterogeneity increases gradually from 1 to 5. Repeat the above operation to generate 100 sets of sequences.

[0100] Specifically, using multivariate statistical indicators to measure data heterogeneity and conduct significance tests includes:

[0101] 2.1 Selecting the multivariate heterogeneity measure F = {f h}(h∈[1,17]).

[0102] Among them, Figure 2As shown, d, x1, x2, y, and z represent different nearest neighbor distances. The distance from a sampling point to its nearest sampling point is defined as d, the distance from a random point to its nearest sampling point is defined as x1, the distance from a random point to the second nearest sampling point is defined as x2, the distance from the sampling point closest to the random point to the nearest sampling point to the sampling point is defined as y, and the distance from the sampling point closest to the random point to the nearest sampling point SP3 (sampling point SP3 is not in the half-plane of sampling point SP1) is defined as z.

[0103] Table 1 Metrics and statistics

[0104]

[0105]

[0106] 2.2 Using the incompleteness statistical indicators {f h}(h∈[1,17]) for the heterogeneous sequence of distribution pattern P1 The data is calculated to obtain a set of heterogeneity measurement results Right now

[0107] The details are as follows:

[0108] 2.2.1 Using the statistical indicator f1 to analyze the sequence The data is calculated; the heterogeneity measurement results are combined into a set Right now

[0109]

[0110] The heterogeneity measurement result set Sort in ascending order to get the sorting result statistics The frequency of occurrence of each sort in the sequence, and the sort with the highest number of occurrences is used as the 100 groups of sequences Ranking of experimental results under the statistical indicator f1 measurement The number of times is recorded as

[0111] 2.2.2 Repeat the above operation to obtain the statistical index f1 for 100 groups of sequences Sorting results of

[0112] 2.2.3 Repeat steps 2.2.1 and 2.2.2 to count the sequence In the incompleteness statistic f h Ranking of experimental results under measurement The number of times is recorded as

[0113] 2.3 Repeat the above 2.2 operation to count each sequence The data are respectively in the incompleteness statistical index f h Ranking of experimental results under measurement The number of times is recorded as

[0114] 2.4 In order to obtain significant ranking results, a significance test was performed and the p-value was corrected using the FDR method.

[0115] 2.4.1 The ranking results of the distribution pattern p1 measured by the statistical indicator f1 are tested for significance using the Monte Carlo simulation experiment method.

[0116] Among them, the method of Monte Carlo simulation experiment, the specific steps are as follows:

[0117] Generate n sets of random data MC1 = {MC1(t)}, t = 1, 2, ..., n. The data is consistent with the scale and area of ​​the integrated training data set; use the statistical index f1 to analyze the random data D MC Measure and get the statistical result f1[D MC ], that is, f1[D MC ]={f1[D MC (1)],f1[D MC (2)],…,f1[D MC (n)]).

[0118] Among them, the statistical results {f1[D MC (1)],f1[D MC (2)],…,f1[D MC (t)]} Sort in ascending order and get the result Rank({f1[D MC (t)],t=1,2,..,n});

[0119] Next, calculate The value of .

[0120] Recalculate In Rank({f h [D MC (t)], t=1,2,..,n}), denoted as Rank * .

[0121] The next step is to calculate the p-value, which is

[0122]

[0123] The significance level was set to α=0.05 and a significance test was performed.

[0124] Remember the dataset Repeat the above steps to get the data set The data in Values ​​and results of significance tests.

[0125] By Sort in ascending order, and the sorting result is

[0126] Calculate the q value, Set the false discovery rate level β = 0.05, i∈[1,100]:

[0127]

[0128] Among them, k represents the significance test calculation Value Ranking in .

[0129] Recalculate the data set Correction statistical results under the statistical indicator f1 measurement

[0130]

[0131] In the formula Indicates the number of times the q-value test is passed.

[0132] Repeat the above steps to obtain the data set The correction result under the statistical index f1 is measured and the statistics are

[0133] 2.4.2 By repeating the above operations, we can obtain the distribution pattern p measured by the statistical index f1. j , significance test results of j∈[1,5].

[0134] 2.4.3 Repeat the above steps and finally obtain the incompleteness statistical index f h Correction results of each distribution mode under measurement.

[0135] Specifically, we build an integrated learning evaluation model, which includes:

[0136] During the training process, multivariate statistical indicators obtain the parameters of the integrated learning evaluation model, namely the confidence parameter matrix U and the pattern recognition parameter matrix M, by calculating the heterogeneity of the training data set.

[0137] Among them, the confidence parameter matrix Its u hjIt represents the ability of the h-th indicator to quantify the degree of incompleteness of the j-th pattern.

[0138] Comparative experiment results sorting with sequence Whether the order of is consistent, and then determine u 11 Value

[0139]

[0140] Repeat the above steps to obtain u hj The value of .

[0141] Obtain the pattern recognition parameter matrix of the ensemble learning evaluation model Where m hj It represents the ability of the hth indicator to identify the jth pattern.

[0142] Then calculate m by the following formula: 11 Values:

[0143]

[0144] in, Representation dataset The corrected statistical results under the statistical index f1 are calculated by repeating the above operations to obtain m hj The value of .

[0145] Specifically, in the test phase of the ensemble learning evaluation model, the distribution pattern that the test data conforms to is pre-judged based on the ensemble learning voting mechanism, so as to analyze the incompleteness statistical index {f h}(h∈[1,17]) is used to measure the ability of the pre-judgment mode. Finally, the voting results are fused to comprehensively evaluate the degree of incompleteness of the test data.

[0146] 4.1 The test data selected is as follows Figure 3 PM2.5 sampling point data in the Yangtze River Delta region shown in D c =(D c1 , D c2 ) and PM2.5 station data in Beijing-Tianjin-Hebei region H =(D H1 , D H2 ) is an embodiment of the present invention. Wherein D c1 , D c2 They represent the existing PM2.5 sampling point data and the original PM2.5 sampling point data (including the suspended sampling points) in the Yangtze River Delta region. Figure 3 (a) as shown, D H1 , D H2They represent the existing PM2.5 sampling point data and the original PM2.5 sampling point data (including the suspended sampling points) in the Bohai Rim area respectively. Figure 3 (b) as shown.

[0147] The specific steps are as follows:

[0148] 4.1.1 Test data D for sampling points c1 Perform random thinning to obtain the thinning sequence D c1 ={D c1 (1),D c1 (2),…,D c1 (5)}, where D c1 (1) D c1 (2), ..., D c1 (5) respectively represent data D c1 And the data obtained after thinning by 15%, 30%, 45%, and 60%.

[0149] 4.1.2 Using the incompleteness statistic f h Measure and get the statistical result f h [D c1 ]:

[0150] {f h [D c1 ]}={f h [D c1 (1)],f h [D c1 (2)],…,f h [D c1 (5)]}.

[0151] 4.1.3 Through the above steps, we can obtain the test vector R = [r1, r2, ..., r 17 ] T .

[0152] Definition h Incompleteness statistic f h For the test data P r Quantitative recognition of the situation, statistical results ranking Rank ({{f h [D c1 ]}}) and test data design sequence D c1 The sorting is consistent, indicating the incompleteness statistical index f h Quantifiable identification test data D c1 , remember r h =1; otherwise, r h =0, then R=[0,1,0,0,0,0,0,0,0,0,0,1,0,0,1,0,0,1].

[0153] 4.1.4 Pre-judge the distribution pattern of the test data; check the column vector m of the vector R and the pattern recognition parameter matrix M j Perform Hadamard product calculation to obtain the point distribution pattern type discrimination result b of the test data set j :

[0154] b j =R⊙m j (11)

[0155] Where b k Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j The pattern recognition result; ⊙ is the Hadamard product; m j Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j pattern recognition ability. j Composition mode proportion B = [b1, ..., b5].

[0156] 4.1.5 Substitute the test vector R with the column vector u of the confidence parameter matrix U j Calculate the Hadamard product and obtain the incompleteness statistical index {f h}(h∈[1,17]) in the context of pre-discrimination mode j :

[0157] c j =R⊙u j (12)

[0158] In the formula, c j Indicates the measurement ability under the corresponding discrimination mode; u j Incompleteness statistic index {f h}(h∈[1,17]) for the distribution mode P j The measurement capability of j Composition confidence weight C = [c1, ..., c5].

[0159] 4.1.6 Based on the idea of ​​ensemble learning voting, the calculation results of incomplete statistical indicators in the ensemble framework are weighted and integrated under the current distribution mode pre-identification situation to obtain the heterogeneity indicator value of the test data based on the ensemble learning evaluation model

[0160]

[0161] In the formula, ∑b j ,∑c j Represents the column vector b j and cj The sum of; ∑B, ∑C represent the sum of all elements of matrix B, C respectively; n * The multivariate heterogeneity measure F = {f h}(h∈[1,17]). That is

[0162] 4.2 Repeat step 4.1 for data D c2 , D H1 , D H2 Perform the same process and obtain

[0163] 4.3 Compare the four groups of data and obtain data D H2 The heterogeneity is the highest, D H1 Secondly, the heterogeneity of D c1 The third heterogeneity, D c2 The heterogeneity is minimal.

[0164] 4.4 Compare the heterogeneity measure I on the test data with the multivariate heterogeneity measure F = {f h}(h∈[1,17]) to obtain the following measurement results: Figure 4 The comparison chart of the indicator measurement results is shown. Heterogeneity measurement index I can robustly evaluate spatial point data under different prior distributions and realize horizontal comparison of the degree of heterogeneity of multiple spatial point data under the same dimension.

[0165] Based on the overall framework of ensemble learning, the present invention innovatively draws on parameter learning algorithms driven by data to propose an ensemble learning evaluation model for sampling point heterogeneity. Driven by training data, it realizes robust evaluation and horizontal comparison of data heterogeneity at any spatial point, which has the dual advantages of application effectiveness and horizontal comparison under unified dimensions for data from different sampling points.

[0166] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A spatial point data heterogeneity measurement method based on ensemble learning, characterized in that: include: Step 1: Generate training data for spatial point data heterogeneity measurement, including: Build Hierarchical structure training dataset; The non-homogeneous Poisson point distribution pattern P1 is generated using the point distribution pattern probability density function, and the point distribution pattern probability density function is: Among them, the intensity function λ(x,y) represents the distribution density and homogeneity of points in space τ; The Poisson clustering point distribution pattern P2 is generated using the point distribution pattern probability density function, and the point distribution pattern probability density function is: Among them, λ p represents the intensity of the Poisson point process; The COX point distribution pattern P3 is generated using the point distribution pattern probability density function, where the point distribution pattern probability density function is: Among them, λ p represents the intensity of the Poisson point process; The Gaussian-Poisson superposition point distribution pattern P4 is generated using the point distribution pattern probability density function, and the point distribution pattern probability density function is: Among them, N(μ, σ) and λ are density-related parameters that control the density of the generated point results; The Markov point distribution pattern P5 is generated using the point distribution pattern probability density function, and the point distribution pattern probability density function is: Among them, τ represents the point set within a unit area, the constant ω represents the normalization coefficient, the parameter λ represents the point process intensity, and the parameter Indicates the magnitude of the mutual influence of random points, parameter n indicates the number of random points, and parameter m indicates the number of different neighboring point pairs within the set threshold r; Step 2: Use multivariate statistical indicators to measure the heterogeneity of point data and perform significance tests, including: Select the multivariate heterogeneity measure F = {f h }(h∈[1,17]); Using the incomplete statistical index {fh}(h∈[1,17]) to analyze the heterogeneous sequence of distribution pattern P1 The data is calculated to obtain a set of heterogeneity measurement results Right now Repeat the calculation of the heterogeneous sequence data of distribution pattern P1, and count the sequences The experimental results of data are sorted under the incomplete statistical index fh metric The number of times is recorded as The Monte Carlo simulation method is used to analyze the incompleteness statistical index f h The ranking results of the distribution pattern P1 under the measurement are tested for significance and the p-value is corrected; Step 3: construct an integrated learning evaluation model by obtaining model parameters, including: During the training process, multivariate statistical indicators measure the heterogeneity of the training data set to obtain the confidence parameter matrix U and the pattern recognition parameter matrix M, and construct an integrated learning evaluation model; The confidence parameter matrix is where u hj It represents the ability of the hth indicator to quantify the degree of incompleteness of the jth pattern; The pattern recognition parameter matrix Where m hj represents the ability of the hth indicator to identify the jth pattern; Step 4: pre-judge the distribution pattern of the test data of the integrated learning evaluation model, and perform weighted fusion on the calculation results of the incompleteness index in the integrated framework under the current distribution pattern pre-judgment scenario to obtain the heterogeneity measurement index I based on the test data of the evaluation model, which is used to realize the heterogeneity measurement of spatial point data under different prior distributions in the same dimension.

2. The spatial point data heterogeneity measurement method based on ensemble learning according to claim 1 is characterized in that: The step 4 comprises: In the testing phase of the ensemble learning evaluation model, based on the voting mechanism of ensemble learning, the distribution pattern of the test data is pre-judged and the incomplete statistical index {f h The calculation results of}(h∈[1,17]) are weighted fused to obtain the heterogeneity index value I based on the test data of the evaluation model; The measurement results of the heterogeneity index I on the test data are compared with the measurement results of the multivariate heterogeneity measurement index F = {fh} (h∈[1, 17]), which reflects the effectiveness of the spatial point data heterogeneity measurement method based on ensemble learning; the heterogeneity index I can robustly evaluate the spatial point data under different prior distributions and realize the horizontal comparison of the heterogeneity degree of multiple spatial point data under the same dimension.

3. The spatial point data heterogeneity measurement method based on ensemble learning according to claim 2 is characterized in that: The non-homogeneous Poisson point distribution mode P1, Poisson cluster point distribution mode P2, COX point distribution mode P3, Gaussian-Poisson superposition point distribution mode P4 and Markov point distribution mode P5 all generate N groups of heterogeneous sequences by adjusting the parameters of their respective probability density functions.

4. The spatial point data heterogeneity measurement method based on ensemble learning according to claim 3 is characterized in that: The multivariate statistical indicator calculation includes: Using the statistical indicator f1 to analyze the sequence The data is calculated; Calculate the statistical index f1 for 100 sets of sequences Sorting results of Calculate statistical series Ranking of experimental results under the incomplete statistical index fh metric The number of times is recorded as 5. The spatial point data heterogeneity measurement method based on ensemble learning according to claim 3 is characterized in that: The significance test process includes: The ranking results of the distribution pattern P1 measured by the statistical indicator f1 are tested for significance using the Monte Carlo simulation method to obtain the data set The correction result of the p value under the statistical indicator f1 measurement is statistically Get the dataset by repeating The correction result under the statistical index f1 measurement is used to obtain the distribution mode p under the statistical index f1 measurement. j , j∈[1,5], and finally obtain the incompleteness statistical index f h Correction results of each distribution mode under measurement.

6. The spatial point data heterogeneity measurement method based on ensemble learning according to claim 5 is characterized in that: The testing phase of the ensemble learning evaluation model includes: The test data P of the sampling point r Perform random thinning to obtain a thinning sequence in Represent the test data P r and the data obtained after thinning by 15%, 30%, 45%, and 60%; Using the incompleteness statistic f h Measure and get statistical results Get the test vector R = [r1, r2, ..., r 17 ] T , define r h Incompleteness statistic f h For the test data P r Quantitative identification of the situation, statistical results sorting Design sequence with test data The sorting is consistent, indicating the incompleteness statistical index f h Quantifiable identification test data P r , remember r h =1; otherwise, r h =O, use r h Composition of test vector; Pre-judge the distribution pattern of the test data, check the column vector m of the vector R and the pattern recognition parameter matrix M j Perform Hadamard product calculation to obtain the point distribution pattern type discrimination result b of the test data set j : b j =R⊙m j Where b j Incompleteness statistic index {f h }(h∈[1,17]) for the distribution pattern P j The pattern recognition result; ⊙ is the Hadamard product; m j Incompleteness statistic index {f h }(h∈[1,17]) for the distribution pattern P j pattern recognition ability, and b j Composition mode proportion B = [b1, ..., b5]; The test vector R is combined with the column vector u of the confidence parameter matrix U j Calculate the Hadamard product and obtain the incompleteness statistical index {f h }(h∈[1,17]) The measurement capability c in the pre-discrimination mode context j : c j =R⊙u ·j In the formula, c j Indicates the measurement ability under the corresponding discrimination mode, u j Incompleteness statistic index {f h }(h∈[1,17]) for the distribution pattern P j The measurement capability of j Composition confidence ratio C = [c1, ..., c5]; Under the current distribution mode pre-identification scenario, the calculation results of the incomplete statistical indicators in the integrated framework are weighted and fused to obtain the heterogeneity index value I based on the test data of the evaluation model: In the formula, ∑b j ,∑c j Represents the column vector b j and c j The sum of ∑B and ∑C represent the sum of all elements of matrices B and C respectively, n * The multivariate heterogeneity measure F = {f h The effective number of}(h∈[1,17]).

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