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Abstract Recently， the impact of climate change on national stability has become increasingly significant. Therefore， many countries are exploring the relationship between climate change and national stability. An effective Fragile State Metric is crucial to study the relationship between them. To solve the issue， we formulate Fragile State Metric System （FSM） including three parts： indicator System Establishment， FSM model， and analysis of the indirect impact of climate change on national fragility.
First， based on Fragile State Index， we establish FSM including evaluation system with two levels of indicators， fragility index model with more rational indicator weight， and quantitative analysis of the indirect Impact of climate change. Moreover， by using Principal Component Analysis and K-Means Clustering Method to establish fragility rating criteria， we find 2.5 is a tipping point from vulnerable to fragile. Second， considering the applicability of FSM， we test the system in the smaller and larger range. As a result， the effect is not ideal. Therefore， FSM is modified to achieve a wider range of applicability by stratifying the indicator system.
Keywords： Fragile State Metric System （FSM）， Principal Component Analysis， K-Means Clustering Method
【中圖分类号】 F591 【文献标识码】 A【文章编号】 2236-1879（2017）24-0126-02
1. Background
Since the 20th century， the global climate is undergoing tremendous changes， and the effects of Climate Change are already being realized and vary from region to region. The effects affect the species distribution area， biological diversity and so on. However， the impact of climate change goes far beyond these， and will indirectly increase the vulnerability of nations by affecting other factors and indicators. Many of these effects will alter the way humans live， and may have the potential to cause the weakening and breakdown of social and governmental structures. Consequently， destabilized governments could result in fragile states.
Our objective is to develop an evaluation system to measure each country’s ability to provide the basic essentials to its people. It is consistent with government stability， which is affected by cohesive， economic， political and social drivers. We try to find these drivers and provide the evaluation of human intervention’s effect for countries based on them.
2. Notations
In this section， we will begin by defining a list of the nomenclature used in this report： 3. Fragile State Metric System （FSM）
3.1 Data Pre-processing。
Collecting sufficient data is the basis of developing a complete index system. On the website of Fund for Peace， we found 12 indicators of 178 countries. Then， we searched the indicator data to measure climate change.
Since the dimensions of the 12 indicators are different， the data can’t be directly compared. To normalize the data， we use K-Means Clustering Method to normalize the data. All data is converted to number between -1 and 1.Comparing these 12 indicators， the indexes can be classified as four types， such as cohesion-type index， economy-type index， policy-type index and society-type index. Consequently， we acquire standardized data of 12 indicators， represented by.
3.2 Indicator System Establishment。
Indicators are selected to measure state fragility according to Fragile State Index. We divide the 12 indicators to 4 types， such as cohesion-type index， economy-type index， policy-type index and society-type index：
Cohesion includes security， factionalized elites， and group grievance.
Economy includes economic decline， uneven economic development， and human flight and brain drain.
Policy includes state legitimacy， public services， and human rights and rule of law.
Society includes demographic pressure， refugees and IDPs， and external intervention.
3.3 FSM Model Building through PCA。
3.3.1 FSM Building。
Step Ⅰ： We apply Principal Component Analysis to the above 12 indicators on the use of SPSS [1]. Then， we choose the eigenvalue greater than 1 as the principal components. Thus， we acquire Component 1 and Component 2：
The eigenvalue of principal component 1 is 8.708， accounting for 72.567% of the total variance.
The principal component 2 has a characteristic value of 1.126， accounting for 9.383% of the total variance.
Component 1 and component 2 cumulatively explain the total variance of 81.985%.
Step Ⅱ：We get the composition matrix of those two principal components and the 12 indicators by SPSS. Then， we can calculate various weights for each indicator respectively for the principal component 1 and principal component 2， represented by w1i and w2i symbols.
Step Ⅲ：Through cumulative sum of the standardized data for various indicators and the corresponding weights， respectively， we get score for principal component 1 and principal component 2. Fi （i=1， 2） symbol represent score for each principal component. Since the 12 indicators data for each country are different， the F1 and F2 will vary from state to state. From Table 2， we can see that the two principal components explain the total variance differently. We determine the weight of the two principal components in the total score by the degree of interpretation. Afterwards， the model of the FSM can be obtained. When we apply indicator data to our formula above， we find coefficient of component is equal to 72.567/81.950， and component 2 is 9.383/81.950. Finally， we get our Fragile State Metric Model.
3.3.2 FSM Scoring System。
We use MATLAB software to classify 78 countries according to the K-Means clustering method [2]. Then， we acquire the following state fragility assessment system.
3.4 Indirect Impact of Quantitative Analysis。
In Section 3.2， we have qualitatively described climate changes indirectly increase the vulnerability of nations by affecting those 12 indicators. In order to illustrate this indirect effect more clearly， we quantify the impact of climate change on the 12 indicators. Since the relationship between climate change indicators and the 12 indicators is often nonlinear， we want to perform the curve fitting to explore the relationship. To simplify the problem， we use some other indicators to act as the substitutes of those 12 indicators. The substitutes include GDP per capita， access to electricity， inflation and other more simplified indicators， which also reflect the four factor types.
4. Model Improvement
Since our FSM model is obtained by applying principal component analysis to the index system， the rationality of the index system is crucial to the adaptability of the model. Our model will not work well on smaller “states” （such as cities） or larger “states” （such as continents）， as the index system is not adaptable. Some indicators used in smaller states are clearly too broad and not specific. Meanwhile， the use of these indicators in larger states is far from enough to measure his situation.
In order to solve the above issues， we will solve the problem of adaptability by stratifying the indicator system. We amend the original 12 indicators of the system to establish a new system. We divide it into three tiers and take two more significant indicators for the smaller “state” for each type of factor； for the state， we take three indicators for each type of factor； for the larger “state”， four representative indicators for each type of factor [3].
References
[1] [1]Mishra， Puneet， et al. Detection and quantification of peanut traces in wheat flour by near infrared hyperspectral imaging spectroscopy using principal-component analysis. Journal of Near Infrared Spectroscopy 23.1（2015）：15-22.
[2] Wei-Xiang XU， Quanshou Zhang， An Algorithm of Meta-Synthesis Based on the Grey Theory and Fuzzy Mathematics [J].，Systems engineering theory and practice， 2001
[3] Chen J， Yang J， Zhao J， et al. Energy demand forecasting of the greenhouses using nonlinear models based on model optimized prediction method[J]. Neurocomputing， 2016， 174（PB）：1087-1100.
First， based on Fragile State Index， we establish FSM including evaluation system with two levels of indicators， fragility index model with more rational indicator weight， and quantitative analysis of the indirect Impact of climate change. Moreover， by using Principal Component Analysis and K-Means Clustering Method to establish fragility rating criteria， we find 2.5 is a tipping point from vulnerable to fragile. Second， considering the applicability of FSM， we test the system in the smaller and larger range. As a result， the effect is not ideal. Therefore， FSM is modified to achieve a wider range of applicability by stratifying the indicator system.
Keywords： Fragile State Metric System （FSM）， Principal Component Analysis， K-Means Clustering Method
【中圖分类号】 F591 【文献标识码】 A【文章编号】 2236-1879（2017）24-0126-02
1. Background
Since the 20th century， the global climate is undergoing tremendous changes， and the effects of Climate Change are already being realized and vary from region to region. The effects affect the species distribution area， biological diversity and so on. However， the impact of climate change goes far beyond these， and will indirectly increase the vulnerability of nations by affecting other factors and indicators. Many of these effects will alter the way humans live， and may have the potential to cause the weakening and breakdown of social and governmental structures. Consequently， destabilized governments could result in fragile states.
Our objective is to develop an evaluation system to measure each country’s ability to provide the basic essentials to its people. It is consistent with government stability， which is affected by cohesive， economic， political and social drivers. We try to find these drivers and provide the evaluation of human intervention’s effect for countries based on them.
2. Notations
In this section， we will begin by defining a list of the nomenclature used in this report： 3. Fragile State Metric System （FSM）
3.1 Data Pre-processing。
Collecting sufficient data is the basis of developing a complete index system. On the website of Fund for Peace， we found 12 indicators of 178 countries. Then， we searched the indicator data to measure climate change.
Since the dimensions of the 12 indicators are different， the data can’t be directly compared. To normalize the data， we use K-Means Clustering Method to normalize the data. All data is converted to number between -1 and 1.Comparing these 12 indicators， the indexes can be classified as four types， such as cohesion-type index， economy-type index， policy-type index and society-type index. Consequently， we acquire standardized data of 12 indicators， represented by.
3.2 Indicator System Establishment。
Indicators are selected to measure state fragility according to Fragile State Index. We divide the 12 indicators to 4 types， such as cohesion-type index， economy-type index， policy-type index and society-type index：
Cohesion includes security， factionalized elites， and group grievance.
Economy includes economic decline， uneven economic development， and human flight and brain drain.
Policy includes state legitimacy， public services， and human rights and rule of law.
Society includes demographic pressure， refugees and IDPs， and external intervention.
3.3 FSM Model Building through PCA。
3.3.1 FSM Building。
Step Ⅰ： We apply Principal Component Analysis to the above 12 indicators on the use of SPSS [1]. Then， we choose the eigenvalue greater than 1 as the principal components. Thus， we acquire Component 1 and Component 2：
The eigenvalue of principal component 1 is 8.708， accounting for 72.567% of the total variance.
The principal component 2 has a characteristic value of 1.126， accounting for 9.383% of the total variance.
Component 1 and component 2 cumulatively explain the total variance of 81.985%.
Step Ⅱ：We get the composition matrix of those two principal components and the 12 indicators by SPSS. Then， we can calculate various weights for each indicator respectively for the principal component 1 and principal component 2， represented by w1i and w2i symbols.
Step Ⅲ：Through cumulative sum of the standardized data for various indicators and the corresponding weights， respectively， we get score for principal component 1 and principal component 2. Fi （i=1， 2） symbol represent score for each principal component. Since the 12 indicators data for each country are different， the F1 and F2 will vary from state to state. From Table 2， we can see that the two principal components explain the total variance differently. We determine the weight of the two principal components in the total score by the degree of interpretation. Afterwards， the model of the FSM can be obtained. When we apply indicator data to our formula above， we find coefficient of component is equal to 72.567/81.950， and component 2 is 9.383/81.950. Finally， we get our Fragile State Metric Model.
3.3.2 FSM Scoring System。
We use MATLAB software to classify 78 countries according to the K-Means clustering method [2]. Then， we acquire the following state fragility assessment system.
3.4 Indirect Impact of Quantitative Analysis。
In Section 3.2， we have qualitatively described climate changes indirectly increase the vulnerability of nations by affecting those 12 indicators. In order to illustrate this indirect effect more clearly， we quantify the impact of climate change on the 12 indicators. Since the relationship between climate change indicators and the 12 indicators is often nonlinear， we want to perform the curve fitting to explore the relationship. To simplify the problem， we use some other indicators to act as the substitutes of those 12 indicators. The substitutes include GDP per capita， access to electricity， inflation and other more simplified indicators， which also reflect the four factor types.
4. Model Improvement
Since our FSM model is obtained by applying principal component analysis to the index system， the rationality of the index system is crucial to the adaptability of the model. Our model will not work well on smaller “states” （such as cities） or larger “states” （such as continents）， as the index system is not adaptable. Some indicators used in smaller states are clearly too broad and not specific. Meanwhile， the use of these indicators in larger states is far from enough to measure his situation.
In order to solve the above issues， we will solve the problem of adaptability by stratifying the indicator system. We amend the original 12 indicators of the system to establish a new system. We divide it into three tiers and take two more significant indicators for the smaller “state” for each type of factor； for the state， we take three indicators for each type of factor； for the larger “state”， four representative indicators for each type of factor [3].
References
[1] [1]Mishra， Puneet， et al. Detection and quantification of peanut traces in wheat flour by near infrared hyperspectral imaging spectroscopy using principal-component analysis. Journal of Near Infrared Spectroscopy 23.1（2015）：15-22.
[2] Wei-Xiang XU， Quanshou Zhang， An Algorithm of Meta-Synthesis Based on the Grey Theory and Fuzzy Mathematics [J].，Systems engineering theory and practice， 2001
[3] Chen J， Yang J， Zhao J， et al. Energy demand forecasting of the greenhouses using nonlinear models based on model optimized prediction method[J]. Neurocomputing， 2016， 174（PB）：1087-1100.