CN115757664B - Causal relation mining method between SDG indexes of coupling transfer entropy and HITS algorithm - Google Patents

Causal relation mining method between SDG indexes of coupling transfer entropy and HITS algorithm Download PDF

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CN115757664B
CN115757664B CN202310037126.5A CN202310037126A CN115757664B CN 115757664 B CN115757664 B CN 115757664B CN 202310037126 A CN202310037126 A CN 202310037126A CN 115757664 B CN115757664 B CN 115757664B
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CN115757664A (en
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曹敏
白煜颖
李悦
王小川
郭雅琪
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Shenzhen Planning And Natural Resources Data Management Center Shenzhen Spatial Geographic Information Center
Nanjing Normal University
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Abstract

The invention discloses a causal relation mining method between SDG indexes of a coupling transfer entropy and HITS algorithm, which comprises the following steps: screening specific indexes of sustainable development targets (Sustainable Development Goals, SDG) of united nations, and establishing a regional sustainable development index system; adopting correlation analysis to explore the synergy and trade-off relation among multiple indexes of the SDG; calculating transfer entropy values among SDG indexes based on a transfer entropy algorithm in the field of information theory, and determining causal transfer directions among the SDG indexes; based on a Hyperlink-topic search (HITS) algorithm in a complex network, calculating relative independent relevance indexes, and screening obvious causal relationship SDG index pairs. The invention researches the causal relationship of the synergy and the trade-off effect among the SDG multiple indexes, has the capability of realizing causal relationship data products among the SDG indexes in the production area, provides method assistance for researching the causal relationship in the synergy and the trade-off effect among the SDG multiple indexes, and promotes the area to accelerate the sustainable development process.

Description

Causal relation mining method between SDG indexes of coupling transfer entropy and HITS algorithm
Technical Field
The invention relates to the field of causal relation mining among targets (Sustainable Development Goal, SDG) of united nations sustainable development, in particular to a causal relation mining method among SDG targets of a coupling transfer entropy and Hyperlink topic search algorithm (Hyperlink-Induced Topic Search, HITS).
Background
The peak of sustainable development of united nations passes the resolution draft "change our world: the sustainable development agenda of 2030, which is a more universal and comprehensive sustainable development goal that the united nations pass after the "thousand years development goal" (Millennium Development Goals, MDGs). The "sustainable development goal" (Sustainable Development Goals, SDGs) in the 2030 development agenda contains 17 sustainable development goals and 169 specific goals. The goal of sustainable development is to balance the economic, social and environmental aspects of sustainable development. The action taken to achieve one goal (i.e., sustainable development goal, specific goal or index) may enhance or attenuate the performance of the other goal, respectively, defined as a synergistic effect or tradeoff between sustainable development goals. According to the consensus of previous studies, solving the trade-off problem and promoting synergy is still critical to achieving a sustainable development goal by 2030.
Currently, existing research on SDG interactions can be largely divided into qualitative evaluation by expert knowledge or official document and quantitative correlation analysis, including pearson correlation coefficient, spearman rank correlation analysis, multi-factor analysis, and auto-regression correlation. Meanwhile, some researches have discussed causal relationship in SDG interactive networks. However, most causal relationship researches, such as judging causal relationship among SDG indexes based on expert opinion, have strong subjectivity, and the Grandis causal analysis is a linear analysis method, and only the causal direction can be judged, so that causal relationship strength can not be obtained. The transfer entropy is a non-parametric measurement method for estimating the directional information flow in a random process. The method is based on the concepts of shannon entropy and mutual information in the field of information theory, can be used for linear and nonlinear systems, and does not need prior knowledge of system model mechanisms. In particular, transfer entropy is an efficient way to quantify causal coupling strength and asymmetry in a system, from which the transfer relationship between variables can be found.
A Hyperlink topic search algorithm (Hyperlink-Induced Topic Search, HITS) in a complex network can more fully analyze causal relationships between data with transitive relationships. The method is mainly applied to the field of network centrality calculation, and aims to improve the result of general topic retrieval, and the most valuable webpage aiming at a certain retrieval question is obtained through a certain calculation method. The algorithm idea can be migrated to node centrality analysis among interlinking vectors, has the characteristics of simple calculation and high efficiency, and can be used for further selecting variables with strong causal relationship for prediction. The research combines nonparametric spearman rank correlation analysis, transfers an entropy algorithm and an HITS algorithm, and explores causal relationship in synergy and trade-off among multiple SDG indexes.
Disclosure of Invention
The invention aims to: in order to more accurately and effectively explore the causal relationship between SDG indexes, a causal relationship mining method between the SDG indexes of a coupling transfer entropy and HITS algorithm is provided, and a correlation analysis, a transfer entropy algorithm and a hyperlink topic search algorithm are integrated, so that a new idea is provided for the synergy and trade-off causal relationship mining between multiple indexes of SDGs.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a causal relation mining method between a coupling transfer entropy and an SDG index of a hyperlink topic search algorithm, comprising the following steps:
s1: screening the indexes of sustainable development targets (Sustainable Development Goals, SDG) of the united nations, establishing a regional sustainable development index system, and carrying out reduction treatment on the SDG indexes;
s2: obtaining the synergy and trade-off relation among the SDG multiple indexes by utilizing nonparametric Szelman rank correlation analysis;
s3: obtaining probability estimation among SDG indexes according to a maximum information coefficient binning method;
s4: determining causal transition directions and transition entropy values among SDG indexes according to probability estimation;
s5: constructing an asymmetric matrix of transfer entropy causal relationship among multiple SDG indexes;
s6: based on a Hyperlink topic search (Hyperlink-Induced Topic Search, HITS) algorithm in a complex network, calculating an authoritative value and a link value of an SDG causal index pair, and reflecting the importance degree of the SDG index on the causal relationship;
s7: calculating relative independent correlation indexes of the SDG indexes according to the authoritative value and the link value of the SDG causal index pair, and measuring the causal relation significance of the SDG indexes;
s8: binding correlation analysisChecking and relatively independent correlation indexes, screening SDG synergy and weighting obvious causal relation pairs, repeating the steps S2-S8, and selecting the SDG synergy and weighting obvious causal relation pairs from
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To->
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Carrying out dynamic iteration by taking k years as an interval and 1 year as a step length;
s9: visualizing SDG synergies with and trades off causal networks.
Further, after establishing the SDG index system suitable for the research area in step S1, in order to laterally compare the development conditions of different SDG indexes, the indexes are classified into three types, namely, a positive index, a neutral index and a negative index according to the attribute of the index, and then the three types of SDG indexes are subjected to reduction treatment.
Further, in the step S2, a non-parameter spearman rank correlation analysis is used to obtain correlation coefficients between different SDG indexes, and according to the spearman correlation coefficient size, the correlation coefficients are divided into three types of strong positive correlation, strong negative correlation and insignificant correlation, wherein the strong positive correlation is a synergistic effect between the SDG indexes, the strong negative correlation is a trade-off effect between the SDG indexes, and weak correlation indicates that the interaction between the SDG indexes is insignificant.
Further, the method adopted for calculating the probability among the SDG indexes in the step S3 is a maximum information coefficient histogram estimation method based on non-parametric exploration of information.
Further, the variables required by the nonlinear transfer entropy calculation method in the step S4 are an independent variable time sequence, a dependent variable time sequence and a time lag number. Substituting the appropriate hysteresis variable into our conditional mutual information equation represents the transfer entropy. By considering one hysteresis dimension at a time, we can describe the slave by conditional mutual entropy
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To->
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Is delayed->
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。
The transfer entropy calculation method is shown in formula (1):
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，
wherein the method comprises the steps of
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For the variables->
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To the variables->
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Entropy value of transfer->
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For time (I)>
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The time of the lag is indicated as such,
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is shown at lag->
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Time->
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Under the condition->
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Probability of->
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Is shown at lag->
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Time->
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Under the condition->
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And hysteresis->
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Time->
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The probability of the occurrence of the simultaneous occurrence,
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is indicated at->
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Time->
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Probability of (2), hysteresis->
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Time->
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And hysteresis->
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Time->
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Probability of simultaneous occurrence, ++>
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Indicating hysteresis->
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Time->
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The probability of the occurrence of this is,
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at lag->
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Time->
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And hysteresis->
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Time->
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The probability of the occurrence of the simultaneous occurrence,
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is indicated at->
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Time->
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And hysteresis->
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Time->
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Probability of occurrence.
Further, the step S5 of constructing the causal relationship asymmetric matrix between the multiple indexes of the SDG specifically includes: the magnitude of the value in the causal relationship matrix represents the magnitude of the causal relationship strength of a certain SDG indicator to another SDG indicator.
Further, in the step S6, the authority value and the link value calculation core continuously update the two vector authority values and the link value until convergence through iterative operation of the matrix and defining a convergence threshold.
Further, in the step S7, three vectors are required for the relative independent correlation coefficient, which are respectively: an initial authority value vector, an authority value vector, and a link value vector.
Further, the screening of the SDG synergy and the weighting of the significant causal relationship pairs in step S8 is specifically implemented as follows: and dividing the causal relation asymmetric matrix between the SDG indexes into a synergy and trade-off transfer entropy causal matrix according to the two types of synergy and trade-off obtained by the correlation test. And repeating the steps S2-S8, and carrying out dynamic iteration on the Szellman rank correlation analysis, the transfer entropy and the HITS algorithm to obtain a matrix of the synergy and trade-off causality between SDG indexes in different time periods.
The beneficial effects are that: the transfer entropy algorithm is an effective method for quantifying causal relationship coupling strength and causal direction in a complex system, and the HITS algorithm can obtain the most important SDG index. The method combines the methods of correlation analysis, entropy algorithm transfer, HITS algorithm transfer and the like, can accurately and effectively dynamically iterate the causal relationship in the synergy and trade-off effect among the SDG indexes under different time scales, has the capability of realizing causal relationship data products among the SDG indexes in the production area, and provides method assistance for researching the causal relationship in the synergy and trade-off effect among multiple SDG indexes.
Drawings
FIG. 1 is a schematic view of a basic framework structure of the method of the present invention;
FIG. 2 is a diagram of a data format after SDG index reduction;
FIG. 3 is a 2011-2020 collaborative causal network;
FIG. 4 is a 2011-2020 tradeoff causal network;
FIG. 5 is an enlarged view of a portion of a collaborative causal network;
FIG. 6 is a partial enlarged view of a tradeoff causal network;
FIG. 7 is a 2011-2020 collaborative causal matrix;
FIG. 8 is a 2011-2020 tradeoff cause and effect matrix.
Detailed Description
The invention is further elucidated below in connection with the drawings and the specific embodiments.
The invention provides a causal relation mining method between SDG indexes of a coupling transfer entropy and hyperlink topic search algorithm, which comprises four parts, wherein the first part is SDG index data screening and preprocessing, a regional sustainable development index system is established, the second part is correlation analysis between SDG indexes, the third part is causal transfer entropy between SDG indexes calculated based on the transfer entropy algorithm, and the fourth part is relative independent correlation index calculated by using the hyperlink topic search algorithm, and obvious causal SDG index pairs are screened.
Combining four parts, the method for mining causal relationship between the coupling transfer entropy and the SDG index of the hyperlink theme search algorithm in the embodiment comprises the following steps:
s1: screening the indexes of sustainable development targets (Sustainable Development Goals, SDG) of the united nations, establishing a regional sustainable development index system, and carrying out reduction treatment on the SDG indexes;
s2: obtaining the synergy and trade-off relation among the SDG multiple indexes by utilizing nonparametric Szelman rank correlation analysis;
s3: obtaining probability estimation among SDG indexes according to a maximum information coefficient binning method;
s4: determining causal transition directions and transition entropy values among SDG indexes according to probability estimation;
s5: constructing an asymmetric matrix of transfer entropy causal relationship among multiple SDG indexes;
s6: based on a Hyperlink topic search (Hyperlink-Induced Topic Search, HITS) algorithm in a complex network, calculating an authoritative value and a link value of an SDG causal index pair, and reflecting the importance degree of the SDG index on the causal relationship;
s7: calculating relative independent correlation indexes of the SDG indexes according to the authoritative value and the link value of the SDG causal index pair, and measuring the causal relation significance of the SDG indexes;
s8: screening SDG synergy and trade-off significant causal relationship pairs by combining correlation analysis and inspection with relative independent correlation indexes, and repeating S2-S8, thereby obtaining the product
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To->
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The dynamic iteration is carried out by taking k years as an interval and 1 year as a step length,
s9: visualizing SDG synergies with and trades off causal networks.
The method comprises the following steps:
(1) Constructing a regional SDG index system integrating the SDG index;
(11) Combining with the framework of the SDGs index system of the united nations, adopting four methods of direct selection, improvement, expansion or substitution to carry out localization research on the existing index system.
(12) The time span of the sustainable development index system of the construction area is 2000-2020, 16 SDG targets and 65 indexes are total, and specific indexes and sources are shown in table 1.
(2) Correlation analysis among SDG indexes;
(21) And calculating the correlation coefficient between the SDG indexes by utilizing the Szelman rank correlation analysis.
(22) The obtained correlation coefficient is divided into a threshold value, and the relation among SDG indexes is divided into three major categories of synergy, trade-off and insignificant.
(3) Calculating causal relationship among SDG indexes by using a transfer entropy algorithm;
(31) Calculating the state probability of the SDG indexes by using a maximum information coefficient histogram estimation method, and further obtaining a conditional probability entropy value and a joint entropy value of each SDG index pair;
(32) Calculating according to a nonlinear transfer entropy formula to obtain variables of different time periods
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To the variables->
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Is used for transferring entropy values.
(4) Screening obvious causal pairs among multiple SDG indexes;
(41) And calculating the authority value of the SDG index and calculating the link value between the SDG index pairs.
(42) And calculating a relative independent correlation index of the SDG index pair according to the initial authority value vector, the authority value vector and the link value vector, and screening an SDG synergy and balance significant causal relationship index pair by combining correlation analysis, transfer entropy value and relative independent correlation index results. And (3) dynamically iterating the steps S2-S8 to obtain correlation analysis results, transfer entropy values and relative independent correlation index results in different time periods, wherein the iteration step length is 1 year.
The first part is SDGs index data screening and preprocessing, and a regional sustainable development index system is established, and the specific implementation steps comprise the following steps:
SDGs are a set of sustainable development evaluation index systems proposed by the united nations aiming at the global scale, and the characteristics of each country and region are difficult to fully develop. Therefore, it is necessary to perform localization analysis on the index system according to the characteristics of the research area, and to investigate the usability, coverage and quantitative calculation formula of the index. Combining with an SDGs index system, adopting four methods of direct selection, improvement, expansion or substitution to carry out localization research on the existing index system. The present example constructs a total of 65 indices for SDG index system in Jiangsu province, as shown in table 1.
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/>
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The completion of the SDGs target is a space-time process, and if the realization process is to be monitored and evaluated, quantitative calculation is needed to be carried out on the indexes, and the time sequence development change condition of each index is quantized. In the constructed index system, part of indexes can be counted by adopting a simple counting method, and the indexes are counted year by the existing related institutions, such as the indexes of GDP, grain unit yield and the like, and can be directly obtained by referring to the related counting annual inspection. Part of the index needs to be analyzed and processed by the collected data.
In order to measure the development and change conditions of each index along with the time change, normalization processing is required to be carried out on the numerical value of each index. In this embodiment, the data of each index from 2000 to 2020 are sorted, and each value is adjusted to an index between 0 and 100, wherein 0 represents the worst development condition and 100 represents the best development condition. Since the normalization process is very sensitive to the selection of extrema, the extremum of the data is processed by the following steps, with reference to the papers Untangling the interactions among the Sustainable Development Goals in China by the united states, sustainable Development Report 2020 (SDR 2020) and Zhang Junze et al, published by month 6 of the united states 2020:
(1) For absolute targets such as popularity requirements of popularity rate and the like in indexes, an index 100 is corresponding to the popularity rate of 100%, the sustainable target is completed, an index 0 is corresponding to the popularity rate of 0, the sustainable target completion degree is 0, and the value range of the index is 0-100.
(2) Other indexes are classified into three types, and the larger the forward index representing value is, the higher the sustainable degree is, such as popularization of primary and secondary education and the like; the larger the negative index is, the lower the sustainable degree is, such as neonatal mortality rate and the like; the neutral index has an optimal value, and the higher the sustainability degree is when the optimal value is reached, the lower the sustainability degree is when the neutral index is far away from the optimal value, such as the education gender difference is eliminated. If the index is a forward index, the index 100 corresponds to the maximum value in all data; if the index is a negative index, the index 100 corresponds to the minimum value in all data; if neutral, the index 100 corresponds to the optimal value achieved in all data.
(3) To reduce the effect of the minimum on the index, 2.5% of the worst sustainable data was removed, see SDR 2020. The minimum value of the forward index after 2.5% of the minimum value is removed is
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Data smaller than this value are all converted to 0; the maximum value after the negative index is removed by 2.5% of the maximum value is +.>
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Data above this value has an index of 0; the neutral index does not need to be removed.
After the upper and lower data limits are determined, the indices are linearly converted to index indices between 0 and 100 using the following formula. The positive index is reduced by using the formula (2), the negative index is reduced by using the formula (3), and the neutral index is reduced by using the formula (4). The reduction formula is as follows:
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，
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，
wherein, the liquid crystal display device comprises a liquid crystal display device,
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values before data normalization, +.>
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Is the index value corresponding to the index value after standardization,
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maximum and minimum, respectively, determined by the above>
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Maximum and minimum values of the original data representing the neutral index,/->
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Is the optimal value of the neutral index. After data normalization, the obtained index indexes are all positive, and the larger the index value is, the higher the sustainable degree is represented. The data used in this study were normalized and the results are shown in figure 2.
Wherein the second part is the correlation analysis among SDG indexes. The specific implementation steps comprise the following steps:
the data used in the study are SDG time sequence data in 2000-2020 of Jiangsu province, the study takes 10 years as an example, takes 2000 as the initial year and 2020 as the final year, the correlation results among SDG indexes in every 10 years can be dynamically and iteratively calculated, the transfer entropy among the SDG indexes and the relative independent correlation index are calculated, and the dynamic iteration times are 12 times.
At present, the existing interaction research among SDG indexes is mainly the synergic and trade-off research among SDGs indexes. The synergistic effect among SDG indexes means that the realization of one index can promote the improvement of the other index at the same time, namely the mutual promotion relation among indexes; an index trade-off refers to the implementation of one index at the expense of another index, i.e., the conflicting relationship between the indices. The trade-off and synergistic effects of SDG are mostly understood as statistically significant negative and positive correlations between SDG index pairs.
The spearman rank correlation coefficient evaluates the strength of the correlation between two variables and is used in several studies to evaluate the correlation between sustainable development goals or indicators to determine their synergistic and trade-off effects. Positive correlation coefficients represent synergy and negative correlation coefficients represent trade-offs. In order to avoid over-interpretation of the correlation coefficient values, SDG index pairs with strong correlation can be obtained by dividing the threshold values. Meanwhile, in order to determine that the correlation is not affected by accidental factors, a significance test is utilized to judge whether the correlation between the two is reliable. Therefore, the study utilizes the spearman rank correlation coefficient method to judge the synergy and trade-off relation between SDG indexes. If the correlation coefficient is greater than 0.6, the relationship between SDG indexes is considered to be synergy; if the correlation coefficient is less than 0.6, the relationship between the SDG indicators is considered as a trade-off. If the significance value among the SDG indexes is larger than 0.05, the correlation among the SDG indexes is not significant, and the correlation coefficient value is not reserved; conversely, if the significance value is less than 0.05, the correlation between the SDG indexes is considered to be significant and has interpretability.
The spearman rank correlation coefficient may be defined as the pearson correlation coefficient between the rank statistics of two variables, which applies only to linear correlation variables, whereas spearman correlation coefficients may be used for linear and nonlinear variables. Sisi (Chinese character)Pi Erman rank correlation coefficient calculation principle is that if there are n groups of observation samples
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We rank the set of observation samples to get the rank statistic +.>
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Then->
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The calculation formula of (2) is:
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，
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is the correlation coefficient of the SDG index pair, +.>
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Representing the difference of the two ranks. />
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The closer the absolute value is to 1, the stronger the correlation between SDG indexes is, and the synergy or trade-off is shown; />
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The closer the absolute value is to 0, the weaker the correlation between the SDG indices is.
Correlation coefficient significance test
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The value judges whether the correlation coefficient is obvious or not, and the formula is as follows:
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，
in the middle of
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Is a standard normal distribution. If->
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A value greater than 0.05, there is no significant difference, that is, there is no reason to consider that there is a significant difference, that is, there is no correlation. If->
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A value less than 0.05, a significant difference is considered.
The third part is that the transfer entropy algorithm calculates the causal relationship between SDG indexes. The specific implementation steps comprise the following steps:
(1) Calculation of information entropy
20. Since century 70, along with the development of information entropy theory, a method for judging causal relationship by transmitting information measurement indexes such as entropy gradually rises. The information theory-based method can measure the strength of the causal relationship, and has higher precision in causal inference of the high-dimensional time sequence. Such methods are based on the concept of "uncertainty" (probability distribution), which is considered if the variables are
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Can reduce the variable->
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Is considered +.>
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Is->
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Cause of (1),>
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is->
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Is a "fruit" of (a). Information entropy is a basic index of information theory, is a measure of system confusion, and is also a quantification of uncertainty. For some discrete random variables->
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Suitable functions for these constraints are defined as follows:
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，
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is a variable->
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Is a time series value of +.>
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Is the information entropy->
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Is representative of->
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Probability density function of (a). />
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The maximum information coefficient histogram method is used to calculate the maximum information coefficient histogram method, in which the sample space is divided into a limited discrete bin, and all data points are assigned to one bin according to their values. The probability is then estimated by counting the proportion of samples located in each bin, which is achieved by simply dividing the number of samples in each bin by the total number of samples. This naturally extends to vector data, where each element of the vector corresponds to +.>
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One dimension in a dimension histogram. The measurement such as entropy can be better calculated through a histogram method, so that the causality can be detected by using the transfer entropy more successfully.
(2) Calculation of the transfer entropy of the data,
early information theory methods describing the behavior of the coupling process involved the concept of mutual information. This shannon entropy derived metric describes whether the information stored in a given time sequence is shared by another time sequence. In particular, whether the coding of two time sequences requires less information than the sum of the individual codes. Conceptually we can consider that if one process shares some information with a second process, then the information already encoded by the first process can be used to efficiently describe the second process. This can be expressed as:
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denoted as->
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And->
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Mutual information of->
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Representation->
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Entropy of->
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Representation->
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Entropy of->
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Is indicated at->
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Under the condition->
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Entropy of->
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Is indicated at->
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Under the condition->
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Entropy.
The transition entropy is an asymmetric index of the metric causality, which can be interpreted if
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And->
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Is determined by historical information of (a)>
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Uncertainty of (2) is smaller than by +.>
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Is determined by historical information of (a)>
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Uncertainty of (2), then->
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Namely +.>
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See formula (1):
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，/>
wherein the method comprises the steps of
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For the variables->
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To the variables->
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Entropy value of transfer->
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For time (I)>
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The time of the lag is indicated as such,
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is shown at lag->
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Time->
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Under the condition->
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Probability of->
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Is shown at lag->
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Time->
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Under the condition->
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And hysteresis->
Figure 398549DEST_PATH_IMAGE011
Time->
Figure 198009DEST_PATH_IMAGE016
The probability of the occurrence of the simultaneous occurrence,
Figure 566674DEST_PATH_IMAGE017
is indicated at->
Figure 726260DEST_PATH_IMAGE010
Time->
Figure 231190DEST_PATH_IMAGE014
Probability of (2), hysteresis->
Figure 700087DEST_PATH_IMAGE011
Time->
Figure 821626DEST_PATH_IMAGE013
And hysteresis->
Figure 394690DEST_PATH_IMAGE011
Time of
Figure 144340DEST_PATH_IMAGE016
Probability of simultaneous occurrence, ++>
Figure 410237DEST_PATH_IMAGE018
Indicating hysteresis->
Figure 363280DEST_PATH_IMAGE011
Time->
Figure 5614DEST_PATH_IMAGE014
The probability of the occurrence of this is,
Figure 609771DEST_PATH_IMAGE019
at lag->
Figure 46569DEST_PATH_IMAGE011
Time->
Figure 976654DEST_PATH_IMAGE013
And hysteresis->
Figure 157100DEST_PATH_IMAGE011
Time->
Figure 615763DEST_PATH_IMAGE016
The probability of the occurrence of the simultaneous occurrence,
Figure 489041DEST_PATH_IMAGE020
is indicated at->
Figure 416677DEST_PATH_IMAGE010
Time->
Figure 135234DEST_PATH_IMAGE014
And hysteresis->
Figure 713983DEST_PATH_IMAGE011
Time->
Figure 492583DEST_PATH_IMAGE013
Probability of occurrence. The causal transition direction and the transition entropy value of the SDG index pair can be obtained through the formula (1), wherein the larger the transition entropy value is, the stronger the causal relationship of the SDG index pair is, and the smaller the transition entropy value is, the weaker the causal relationship of the SDG index pair is.
The fourth part is to screen obvious causal pairs among multiple SDG indexes through an HITS algorithm. The specific implementation steps comprise the following steps:
(1) Authoritative value and link value calculation
The HITS algorithm is commonly referred to as "Hyperlink-based topic search" (Hyperlink-Induced Topic Search). The algorithm was proposed by Jon Kleinberg in 1999 as an algorithm for ranking web pages. The results after the web page ordering help people get the information of interest more conveniently. This algorithm idea can be migrated to node centrality analysis between interlinked vectors and can be used to further select variables with strong causal relationships for prediction. The basic idea of the HITS algorithm is: the importance of each web page is characterized by two indexes, namely an Authority value (Authority) and a link value (Hub), wherein the Authority value represents the importance of the web page, and the link value represents the link relation between the web pages.
Suppose a set of web pages
Figure 406051DEST_PATH_IMAGE055
Is a directed graph, then the graph +.>
Figure 928299DEST_PATH_IMAGE056
Is->
Figure 361554DEST_PATH_IMAGE057
Is +.>
Figure 311056DEST_PATH_IMAGE058
An asymmetric 0-1 matrix of (c), see equation (9):
Figure 947704DEST_PATH_IMAGE059
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure 539223DEST_PATH_IMAGE060
representing a directed graph->
Figure 702351DEST_PATH_IMAGE056
A pair of nodes in->
Figure 947387DEST_PATH_IMAGE061
Representing a collection of edges, when->
Figure 461545DEST_PATH_IMAGE062
When the value of (1) is 1, it indicates the node +.>
Figure 702427DEST_PATH_IMAGE063
And node->
Figure 720062DEST_PATH_IMAGE064
There is a link between->
Figure 401579DEST_PATH_IMAGE065
When the value of (2) is 0, then it indicates the node +.>
Figure 137454DEST_PATH_IMAGE063
And node->
Figure 414982DEST_PATH_IMAGE064
There is no link between them.
And authority value
Figure 411757DEST_PATH_IMAGE066
Link value->
Figure 405121DEST_PATH_IMAGE067
And link matrix->
Figure 362713DEST_PATH_IMAGE057
The following relationship is shown in formula (10): />
Figure 208047DEST_PATH_IMAGE068
，
According to the formula (10), the Authority value and the pivot value are interdependent and mutually influenced, the Hub page and the Authority page are mutually and iteratively enhanced, and the two weights of each page are updated by each round of iterative calculation until the weights are stable and no obvious change occurs.
By recursion formula (11), an authority vector can be obtained
Figure 200273DEST_PATH_IMAGE069
And a link value vector +.>
Figure 958014DEST_PATH_IMAGE070
：
Figure 668481DEST_PATH_IMAGE071
，
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure 553391DEST_PATH_IMAGE057
for the link matrix +.>
Figure 400125DEST_PATH_IMAGE072
Is->
Figure 594346DEST_PATH_IMAGE057
Transposed link matrix, ">
Figure 526530DEST_PATH_IMAGE073
For a set convergence threshold, when
Figure 716596DEST_PATH_IMAGE074
In this case, the authority value and the link value in the steady state can be obtained.
(2) SDG significant causal relationship mining coupling the transition entropy and the hyperlink topic search algorithm,
in order to find the influence of other variables on a specific variable in a complex nonlinear system, we combine the transition entropy with a hyperlink topic search algorithm, and input the transition entropy value between SDG indexes obtained by calculation of the transition entropy into formula (9), thus obtaining a causal link matrix of SDG asymmetry
Figure 948994DEST_PATH_IMAGE075
See formula (12):
Figure 48537DEST_PATH_IMAGE076
，
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure 733596DEST_PATH_IMAGE077
is a dependent variable, the other n-1 variables are independent variables of the dependent variable, +.>
Figure 960310DEST_PATH_IMAGE078
Expressed as the transition entropy of one variable over another.
To obtain other n-1 variable pairs dependent variables
Figure 781635DEST_PATH_IMAGE077
Is to matrix->
Figure 52079DEST_PATH_IMAGE079
Deleting the related information of the dependent variable to obtain +.>
Figure 958855DEST_PATH_IMAGE080
. And will be dependent on the variable>
Figure 379472DEST_PATH_IMAGE077
The transfer entropy calculation result of (2) is input into a matrix to obtain an initial authority value matrix +.>
Figure 429206DEST_PATH_IMAGE081
See formula (13): />
Figure 11497DEST_PATH_IMAGE082
，
From equation (10) an authority vector can be obtained
Figure 530203DEST_PATH_IMAGE083
And a link value vector +.>
Figure 223352DEST_PATH_IMAGE084
An initial authority value vector +.>
Figure 894636DEST_PATH_IMAGE085
Further calculating to obtain n-1 independent variable pair dependent variable->
Figure 647829DEST_PATH_IMAGE077
Phase of (2)Index of independent relevance->
Figure 388252DEST_PATH_IMAGE086
See formula (14):
Figure 885092DEST_PATH_IMAGE087
，
the larger the index of a certain SDG indicator, the greater its relevance to a particular SDG indicator and less affected by other SDG indicators; conversely, if the index of a certain SDG index is smaller, it indicates that the index has a small correlation with a specific SDG index and is more affected by other SDG indexes.
Screening the SDG significant causal index pairs by using the relative independent correlation indexes, and dividing the SDG significant causal index pairs into the following steps by combining the synergistic balance results in the correlation analysis: the SDG collaborative causal index pair and the SDG balance causal index pair obtain a collaborative and balance SDG causal network at intervals of 10 years, for example, the SDG collaborative causal network in 2011-2020 is shown in FIG. 3, the SDG balance causal network in 2011-2020 is shown in FIG. 4, FIG. 5 is a local enlarged view of the collaborative causal network, and FIG. 6 is a local enlarged view of the balance causal network. Meanwhile, an SDG collaborative causal matrix and a balance causal matrix at intervals of 10 years can be obtained, for example, the SDG collaborative causal matrix in 2011-2020 is shown in fig. 7, and the SDG balance causal matrix in 2011-2020 is shown in fig. 8. In the SDG causal network (fig. 3-6), nodes are SDG indexes, connecting edges represent causal relationships among the SDG indexes, arrows represent causal directions, and thicker connecting edges represent stronger causal strength between two SDG indexes. In the SDG cause and effect matrix (figures 7-8), the blank in the matrix indicates that there is no significant cause and effect relationship between two indexes, and the larger the value in the matrix is, the stronger the cause and effect intensity between two SDG indexes is.
In order to evaluate the causal judgment result of the method, the method constructed by the method is compared with the Grandis causal analysis method, and the experiment comparison is carried out on the same data source in the same experimental area. The statistics of the causal relationship results found by the method and the Granges method are shown in the table 2, and the results show that the number of the causal relationship found by the method is larger than that of the causal relationship found by the Granges method, and the method is probably because the analysis of the Granges causal relationship method is a qualitative time sequence causal deducing method, only a linear model is adopted, only the linear causal relationship in the time sequence can be found, and the method is only applicable to two-variable, stable and linear time sequences, and the coupling transfer entropy and the HITS algorithm disclosed by the invention not only can judge the causal relationship direction, but also can measure the degree of causal relationship and is applicable to nonlinear, non-stable and multivariable time sequences.
Figure 912347DEST_PATH_IMAGE088
The causal relationships between the present method and the consistent typical SDG indicators found by the Granges causal method are shown in Table 3, for example, the wide use of clean energy (SDG7.2.1) can effectively reduce the energy intensity (SDG7.3.1), and the reduction of energy intensity (SDG7.3.1) can further promote the reduction of sulfur dioxide emissions (SD13.2.1). The causal relationships among typical SDG indexes which can be mined by the method are shown in table 4, and are causal relationships which cannot be mined by the Granges causal method, such as strengthening the management and construction of public facility departments (SDG 6. B.1), not only can promote the improvement of the comprehensive management capability of water resources (SDG6.5.1) and the popularization of the water resources (SDG6.1.1), but also can effectively urge the construction of harmless sanitary facilities to be in place (SDG6.2.1) and the normal and efficient operation of the industrial water discharge flow (SDG6.3.1).
Figure 836441DEST_PATH_IMAGE089
，/>
Figure 329739DEST_PATH_IMAGE090
。
It should be noted that the above-mentioned embodiments are not intended to limit the scope of the present invention, and equivalent changes or substitutions made on the basis of the above-mentioned technical solutions fall within the scope of the present invention as defined in the claims.

Claims (8)

1. A causal relation mining method between SDG indexes of a coupling transfer entropy and HITS algorithm is characterized by comprising the following steps:
s1: screening the target index of sustainable development of the united nations, namely Sustainable Development Goals and SDG, establishing a regional sustainable development index system, and carrying out reduction treatment on the SDG index;
s2: obtaining the synergy and trade-off relation among the SDG multiple indexes by utilizing nonparametric Szelman rank correlation analysis;
s3: obtaining probability estimation among SDG indexes according to a maximum information coefficient binning method;
s4: determining causal transition directions and transition entropy values among SDG indexes according to probability estimation;
s5: constructing an asymmetric matrix of transfer entropy causal relationship among multiple SDG indexes;
s6: based on a Hyperlink topic search algorithm in a complex network, namely Hyperlink-Induced Topic Search, HITS, authority values and link values of SDG cause and effect index pairs are calculated, and the importance degree of the SDG indexes on the cause and effect relationship is reflected;
s7: calculating relative independent correlation indexes of the SDG indexes according to the authoritative value and the link value of the SDG causal index pair, and measuring the causal relation significance of the SDG indexes;
s8: screening SDG synergy and trade-off significant causal relationship pairs by combining correlation analysis and inspection with relative independent correlation indexes, and repeating S2-S8, thereby obtaining the product
Figure QLYQS_1
To->
Figure QLYQS_2
The dynamic iteration is carried out by taking k years as an interval and 1 year as a step length,
s9: visual SDG collaboration and tradeoff causal networks;
wherein step S3 is specifically as follows,
(31) Calculating the state probability of the SDG indexes by using a maximum information coefficient histogram estimation method, and further obtaining a conditional probability entropy value and a joint entropy value of each SDG index pair;
(32) Calculating according to a nonlinear transfer entropy formula to obtain variables of different time periods
Figure QLYQS_3
To the variables->
Figure QLYQS_4
Is an information transfer entropy value of (a);
in the step S4, the variables required by the nonlinear transfer entropy calculation method are independent variable time series, dependent variable time series and time lag number, the transfer entropy is represented by substituting proper lag variables into a conditional mutual information equation, and the following is described by conditional mutual entropy by considering one lag dimension at a time
Figure QLYQS_5
Is delayed->
Figure QLYQS_6
，
The transfer entropy calculation method is shown in formula (1):
Figure QLYQS_8
wherein the method comprises the steps of
Figure QLYQS_14
For the variables->
Figure QLYQS_20
To the variables->
Figure QLYQS_11
Entropy value of transfer->
Figure QLYQS_17
For time (I)>
Figure QLYQS_23
Indicating the time of hysteresis, +.>
Figure QLYQS_29
Is shown at lag->
Figure QLYQS_24
Time->
Figure QLYQS_30
Under the condition->
Figure QLYQS_10
Probability of->
Figure QLYQS_18
Is shown at lag->
Figure QLYQS_35
Time of
Figure QLYQS_40
Under the condition->
Figure QLYQS_38
And hysteresis->
Figure QLYQS_42
Time->
Figure QLYQS_31
Probability of simultaneous occurrence, ++>
Figure QLYQS_37
Is shown in
Figure QLYQS_34
Time->
Figure QLYQS_39
Probability of (2), hysteresis->
Figure QLYQS_7
Time->
Figure QLYQS_13
And hysteresis->
Figure QLYQS_19
Time->
Figure QLYQS_25
The probability of the occurrence of the simultaneous occurrence,
Figure QLYQS_21
indicating hysteresis->
Figure QLYQS_28
Time->
Figure QLYQS_9
Probability of occurrence, ++>
Figure QLYQS_15
At lag->
Figure QLYQS_26
Time->
Figure QLYQS_32
And hysteresis->
Figure QLYQS_36
Time->
Figure QLYQS_41
Probability of simultaneous occurrence, ++>
Figure QLYQS_22
Is indicated at->
Figure QLYQS_27
Time->
Figure QLYQS_12
And hysteresis->
Figure QLYQS_16
Time->
Figure QLYQS_33
Probability of occurrence.
2. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: in the step S2, a non-parameter spearman rank correlation analysis is used to obtain correlation coefficients between different SDG indexes, the spearman correlation coefficient results are classified into three categories, a strong positive correlation is classified into a synergistic effect between the SDG indexes, a strong negative correlation is classified into a trade-off effect between the SDG indexes, and a weaker correlation indicates that the interaction between the SDG indexes is not significant.
3. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: in the step S3, a maximum information coefficient histogram estimation method is adopted to calculate transition probabilities between SDG indexes.
4. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: the magnitude of the causal relation asymmetric matrix value among the multiple SDG indexes constructed in the step S5 represents the magnitude of the causal relation strength of one SDG index to the other SDG index.
5. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: in the step S6, the authority value and the link value calculation core continuously update the two vector authority values and the link value until convergence through iterative operation of the matrix and defining a convergence threshold.
6. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: in the step S7, three vectors are required for the relative independent correlation coefficient, which are an initial authority value vector, an authority value vector and a link value vector.
7. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: in the step S8, the screening of the SDG synergy and the weighting of the significant causal relationship pairs are specifically implemented as follows: dividing the causal relation asymmetric matrix among the SDG indexes into a collaborative transfer entropy causal matrix and a trade-off transfer entropy causal matrix according to two types of collaboration and trade-off obtained by correlation test, repeating the steps S2-S8, and carrying out dynamic iteration on the Szelman rank correlation analysis, the transfer entropy and the HITS algorithm to obtain the collaborative and trade-off causal relation matrix among the SDG indexes in different time periods.
8. The method for mining causal relationship between the coupled transfer entropy and the SDG index of the HITS algorithm of claim 1, wherein: the key of the visual SDG synergy and trade-off causal network in step S9 is to visualize the SDG synergy and trade-off transition entropy causal matrix, wherein the causal direction is represented by an arrow, and the magnitude of the causal link value is represented by a transition entropy value.
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