Fuzzy clustering discrete equilibrium analysis on the promotion of government venture investment to enterprise innovation

Abstract

In order to effectively improve the accuracy of related analysis models in the application of government risk investment, a government risk investment prediction model based on fuzzy clustering discrete algorithm is put forward in this paper. First of all, government risk investment problem is analyzed. Based on Markowitz theory, the general government risk investment model is considered, and the market value constraint and the upper bound constraint are combined to improve the government risk investment model and obtain the mixed constraint government risk investment model. Secondly, the fuzzy clustering discrete algorithm is introduced in the analysis process of government venture investment model, and it is used to solve the mixed constraint analysis model of government venture investment. In addition, to further improve the performance of discrete algorithm based on fuzzy clustering in the model solving process, automatic contraction and expansion of factors is used to carry out adaptive learning of related parameters based fuzzy clustering discrete algorithm, and improve the convergence of the algorithm. Finally, the simulation experiments on some stock samples of investment sector show that the algorithm in this paper can obtain more ideal government venture investment schemes, so as to reduce investment risk and obtain greater investment returns.

Keywords

International perspective enterprise innovation fuzzy clustering discrete equilibrium analysis

1 Introduction

In the 1980s, the financial field developed rapidly and the process of innovation, freedom and integration continued to deepen. However, with the increase of the risks in the financial field, especially in the field of investment, the prediction and control of risks in the financial field has become increasingly concerned and become a research hotspot, and it is of great practical significance [19].

The core of financial risk control is how to quantitatively predict and analyze potential financial risks. In order to improve the performance of government risk investment analysis method, literature [3] proposed a value at risk (VaR) model, which has gradually become the main calculation model for risk control in the financial field. However, after a long period of theoretical and practical verification, it shows that VaR model has some drawbacks when it is applied in the financial risk control, and additivity is an important attribute of financial risk control. But VaR model does not have an additivity [4], and at the same time, VaR model can not make clear the loss caused by the events when there is a tail risk in the financial field. In view of this, literature [18] proposed an homogeneity measurement improved method for the defects of VaR model, which can determine the risk boundary on the financial risk control interval [1]. To solve this problem, some scholars put forward constraint value at risk (CVaR) model [13]. The improved model can effectively represent the average degree that the loss in financial risk exceeds the rated level, effectively prevent the financial risk of small probability events, and measure the degree of risks [14], so it is recognized as a relatively mature and effective financial risk presentation model [9].

Although model building has relative strengths, the parameter setting of the model is another important factor to test the model’s accuracy [6]. In particular, some key parameters in the model, such as expected revenue, have a great impact on the accuracy of the CVaR model [11] and high sensitivity. For this case, an effective method is to use robust optimization method for parameter setting, for example, aiming at the problem of uncertain investment returns, literature [5] uses box-like attributes for robust optimization of government venture investment, thus controlling the robust optimization process. Literature [10] analyzes and studies the government venture investment problem based on the uncertainty set, which is an uncertainty set of Elli based on the id form of fuzzy clustering discrete algorithm. Literature [11] shows that there are certain non-equilibrium and extreme cases in the return process of government venture investment, and there is a certain sharp peak tilt in the return process of both long and short-term investment. Recently, literature [8] indicates that the inharmoniousness in the portfolio investment process has a property of multiple distributions. The above research indicates that the risk prediction of government venture investment is a valuable research direction [21].

The problem existing in the above literature is that the uncertainty sets adopted here are symmetric [7], that is, the equilibrium return of asset investment is considered, which is different from the real situation [12]. In view of this, this paper proposes a fuzzy clustering discrete optimization model of CVaR government risk investment that takes asset non-equilibrium income into account, and at the same time, a fuzzy clustering discrete algorithm is introduced to optimize the CVaR government risk investment model, and through empirical analysis, the effectiveness of the proposed government risk investment analysis method is verified [17].

2 Government risk investment analysis model

2.1 Effective boundary of composite model

Investors need to think about the following steps in making government risk investment decisions [15]: (1) solve the effective government risk investment by using the selected stock securities, and obtain the corresponding portfolio weight; (2) analyze the expected rate of return and the variance of government risk investment, and obtain the weight calculated value of government risk investment; (3) analyze the points at the boundary of the government risk investment analysis model, and then obtain the calculated value of the government risk investment weight. Among them, what most critical is to calculate the effective value of government risk investment boundary in the following model (1) and obtain the management weight optimization of government risk investment as Equation 1 ${\begin{matrix} min f_{1} = x^{'} \sum x \\ max f_{2} = μ^{'} x \\ s . t . x \in S \end{matrix}$ (1)

Where ∑ is the covariance matrix of government risk investment problem; x is the weight vector of each model of government risk investment problem; S is the feasible research domain of government risk investment problem; and μ is the expected rate of return. The traditional calculation methods of government venture investment include constraint method, weight summation method and quadratic programming optimization method. In this paper, quadratic programming optimization method is selected as the calculation method for accurate boundary.

2.2 Quadratic programming optimization method

In general, the above algorithms adopt simple multiple quadratic programmings to optimize the management weight of government risk investment. What obtained by this method is not the accurate boundary of government risk investment problem, but only the rough calculation result of effective boundary. Through research and analysis, Markowitz designed a key line calculation method, which uses the weighting method to analyze the government risk investment model (1), and retain the weight parameters in the model, so it changed the calculation method taking parameters as prior variables in the classical algorithms, so this processing method is called the quadratic programming method.

Compared with traditional algorithms such as constraint method and weight summation method, quadratic programming algorithm can realize the accurate solution of effective boundaries rather than rough solution. Meanwhile, the greatest advantage of quadratic programming algorithm is that it can reveal the effective combination of the hyperbolic front and back links of the government venture investment and accelerate the calculation process.

2.3 Model design

This paper studies two key indicators: government risk investment constraint and government risk investment quantity. The number of shares quantity groups is n = [5, 10, 50, 100, 200, 300, 400]. Then, different constraints are used for setting, and the effective boundaries of the government venture investment problem are solved by the fuzzy clustering discrete algorithm and quadratic programming algorithm, respectively. Later, the efficient evaluation index of the fuzzy clustering discrete algorithm is obtained by this comparison method, and the specific process is shown in the algorithm block diagram in Fig. 1.

Fig. 1

Algorithm efficiency evaluation process.

Fig. 2

Venn diagram of confidence coefficient and support degree.

Group 1: Select standard model for government venture investment issues, as Equation 2: ${\begin{matrix} min f_{1} = x^{'} \sum x \\ max f_{2} = μ^{'} x \\ s . t . 1^{'} x = 1; x ⩾ 0 \end{matrix}$ (2)

Group 2: Apply the upper bound constraint to the standard government venture investment selection problem in formula (2), and obtain the improved composite model shown in formula (4). In formula (2), u is the upper bound of the standard government venture investment model; 1 is the vector whose element is 1 and 0 is the vector whose element is 0 as Equation 3: ${\begin{matrix} min f_{1} = x^{'} \sum x \\ max f_{2} = μ^{'} x \\ s . t . 1^{'} x = 1; 0 ⩽ x ⩾ u \end{matrix}$ (3)

The stocks whose number is 5 and 10 are studied in this research, and the upper bound of these two groups is set as 0.4, while the upper bound of the remaining groups [100, 200, 300, 400] is set as 0.1.

Group 3: The standard government risk investment model shown in formula (1) is improved by using market value constraint, as shown in formula (5), where parameter m is the market value in the selected research objects, and it is a numerical vector as Equation 4: ${\begin{matrix} min f_{1} = x^{'} \sum x \\ max f_{2} = μ^{'} x \\ s . t . 1^{'} x = 1; m^{'} x ⩾ m \end{matrix}$ (4)

In this paper, market value vector m of the research object is selected as the mean market value of the stock it represents in the stock market.

3 Continuous attribute discretization method based on fuzzy clustering

The decision rules extracted based on rough set theory are not necessarily adaptive, that is, the knowledge learned from examples is not necessarily correct. This problem is mainly caused by two reasons: on the one hand, the sample data may contain incompatible information, that is, same condition attributes may produce different decision results; On the other hand, the sample data may contain noise, and the resulting rules may be wrong. To address both of these issues, several measurements of evaluation rules will be discussed below.

Deterministic rules can be extracted from coordinated knowledge system, while uncertain rules will be extracted from uncoordinated knowledge system. To describe the uncoordinated knowledge system, the roughness measure is defined as Equation 5: $ρ_{B} (X) = 1 - \frac{| \underline{B} X |}{| \bar{B} X |}$ (5)

If and only if B is certain according to the equivalence relation, when ρ_B (X) >0ρ_B (X) >0, XX is rough. Rough type reflects the incompleteness degree of knowledge.

For the sample set X, its rough membership function is defined as Equation 6: $μ_{X} (x) = \frac{| X \cap [x]_{R} |}{| [x]_{R} |}$ (6)

The rough membership function describes the degree that a collection of objects belongs to a basic category.

When mining classification rules with rough set theory, a large number of classification rules are often generated, including rules generated due to the influence of noise. To eliminate this influence, the confidence coefficient and support degree of these rules are defined. Assume X_i ∈ U/C, X_j ∈ U/D, and a certain rule is Des (X_i, C) → Des (X_j, D), where X_i ∩ X_j ≠ 0, then the confidence coefficient, support degree and support number of the rules are respectively defined as Equations 7–9: $μ_{C_{c}} (X_{i}, X_{j}) = | X_{i} \cap X_{j} | / | X_{j} |$ (7) $μ_{Sc} (X_{i}, X_{j}) = | X_{i} \cap X_{j} | / | U |$ (8) $support (α) = | [α] |$ (9)

Confidence coefficient represents the percentage that the instances in the condition attributes meet this decision rule. Support degree describes the percentage that the instances satisfying the rule in all sample instances, and support number represents the number of samples satisfying rule α. Then we can set thresholds for confidence coefficient, support degree and support number, and remove the rules generated by individual noise samples or with a low credibility.

Inductive machine learning based on rough set theory processes discrete data, while most of the data in practical industrial applications have continuous attributes, such as temperature, pressure, current, power, etc. In order to realize rough set processing of continuous data, it is necessary to study the discretization method of continuous data and discretize continuous attributes into a finite number of semantic symbols. Fayyad proposed the binarization method of continuous attributes based on information gain, and then extended this method to two intervals dividing continuous attributes into multiple intervals instead of a single threshold. Slowinski adopted experts’ domain knowledge to discretize continuous attributes in the medical field into “low”, “medium”, “high” and “very high”. Hu studied the discrete method of lifting attributes along the concept tree. Miao Duoqian put forward a discretization method based on rough set theory [15]. Robert systematically analyzed various strategies of disretization [20].

The simplest discretization method is that users divide continuous attribute range into several non-overlapping intervals according to their prior knowledge, and this method requires users to have a full understanding of the data characteristics. The discretization method of lifting along the concept tree requires that the concept tree of attributes established before discretization limits the application of this method. The algorithm proposed by Miao has a very clear division of data space. When the new data comes from the space which is not covered by the sample data, it is difficult to give accurate category prediction. Fuzzy clustering is a method which is widely used in machine learning and data mining, and it aggregates objects into a limited number of categories according to their level of similarity. Compared with other algorithms, this method does not require users to have a lot of prior knowledge, nor does it need to establish the concept tree of the object. Because this algorithm not only provides the discrete values of each data but also returns the center of each fuzzy region and the subordinating degree of each attribute value belonging to the clustering center, the discrete values can also be calculated by fuzzy discrimination when the new data comes from outside the sample data space. Therefore, this paper uses Fuzzy c-mean (FCM) clustering algorithm to discretize continuous attributes.

FCM clustering algorithm was originally put forward by Bezkek. Considering a sample set X = {x₁, x₂, ⋯ , x_n}, where x_i = (x_i1,x_i2, ⋯ , x_ik) is a k-dimensional vector, the set is divided into c fuzzy subsets according to certain criteria, where c is the clustering number given by the user, and the clustering results are expressed by a clustering center vector and membership matrix: $μ = [u_{ij}]_{i = 1 \dots c, j = 1 \dots n} μ = [u_{ij}]_{i = 1 \dots c, j = 1 \dots n}$

Where u_ij denotes the membership degree that sample x_j belongs to category i, and μ_ij meets the following Equation 10: ${\begin{matrix} \sum_{i = 1}^{c} μ_{ij} = 1 j = 1, 2, \dots, n \\ 0 < \sum_{j = 1}^{n} μ_{i < j} < n i = 1, 2, \dots, c \end{matrix}$ (10)

The objective function of FCM algorithm is as follows Equation 11: $J (u_{ij}, u_{ij}) = \sum_{i = 1}^{c} \sum_{j = 1}^{n} u_{ij}^{m^{'}} ∥ x_{j} - v_{j} ∥^{2},$ (11)

Where m’ is the exponential weight affecting the fuzziness degree of membership matrix, Equations 12 and 13: $v_{i} = \frac{1}{\sum_{j = 1}^{n} (u_{ij})^{m^{'}}} \sum_{j = 1}^{n} (u_{ij})^{m^{'}} x_{j}, i = 1, 2, \dots, c$ (12) $u_{ij} = \frac{(1 / | | x_{j} - v_{i} | |^{2})^{1 / m^{'} - 1}}{\sum_{k = 1}^{c} (1 / | | x_{j} - v_{k} | |^{2})^{1 / m^{'} - 1}}$ (13)

FCM algorithm gives an iterative algorithm to approximately obtain the optimal value of the objective function. The algorithm is described as follows:

Set clustering number c, exponential weight m′ and stop threshold ɛ; Initialize membership matrix μ⁰;

Calculate fuzzy clustering center by u^(L) and formula (15): ${v_{i}^{(L)} | i = 1, 2, \dots c}$ ;

Calculate new membership matrix u^(L+1) by ${v_{i}^{(L)} | i = 1, 2, \dots c}$ and formula (16);

Calculation= $max_{ij} max_{ij}$ $| u_{ij}^{(L + 1)} - u_{ij}^{L} | | u_{ij}^{(L + 1)} - u_{ij}^{L} |$ . If Δ > ɛ, let L = L + 1 and return to the second step; If Δ ⩽ ɛ, stop the iteration.

On the basis of this algorithm, the data of each dimension in the data table of continuous attributes can be discretized successively, and thus they can be transformed into data that can be processed by the classical inductive learning algorithm.

4 Experimental analyses

4.1 Simulation environment

In order to verify the effectiveness of the improved fuzzy clustering discrete algorithm in the analysis process of government risk investment, the selected hardware platform is: CPU: i5-6500K, internal storage: RAM 6 G ddr4-2400K, operating platform of simulation system: Win7 flagship version. The selected comparison algorithms are genetic algorithm and standard fuzzy clustering discrete algorithm. The following two data sets are selected for the experimental data set:

Simulation data 1: Part of the stocks in the investment sector are selected as the experimental object, and the time interval is the stock yield of 50 months (January 2012-December 2016). The market value result of the stocks selects the market value of the stocks on November 20, 2016. The selected stock data is used to select stock samples, and the sample integrity parameter is 95%. Then 460 groups of stock samples can be selected according to this condition. Then 7 groups of experimental data samples with a stock number of 6, 12, 54, 108, 215, 330 and 400 are selected from the above stock samples. The stock group with a stock number of 6, 12 and 54 contains six groups, respectively; the stock group with a stock number of 108 contains five groups; the stock group with a stock number of 215 contains three groups; the stock group with a stock number of 330,400 contains two groups, respectively.

Simulation data 2: Among the selected part stock groups of the investment sector, 10 most typical and representative stocks are selected, and their relevant information is shown in Table 1.

Table 1
Stock data

No. Stock symbol Stock name Earnings per share (Yuan)

1 002041 Shandong Denghai Seeds 24.6

2 600598 Great Northern Wilderness 25.2

3 002447 Yiqiao Co., Ltd 16.8

4 000735 Luoniushan Co., Ltd 24.2

5 002321 HUAYING AGRICULTURAL 22.02

6 600108 Yasheng Group 15.1

7 000998 Yuan Longping High-Tech Agriculture 22.4

8 000592 Pingtan Development 16.0

9 600257 DAHU AQUACULTURE CO., LTD. 21.8

10 600965 Fucheng Co., Ltd 18.0

No.	Stock symbol	Stock name	Earnings per share (Yuan)
1	002041	Shandong Denghai Seeds	24.6
2	600598	Great Northern Wilderness	25.2
3	002447	Yiqiao Co., Ltd	16.8
4	000735	Luoniushan Co., Ltd	24.2
5	002321	HUAYING AGRICULTURAL	22.02
6	600108	Yasheng Group	15.1
7	000998	Yuan Longping High-Tech Agriculture	22.4
8	000592	Pingtan Development	16.0
9	600257	DAHU AQUACULTURE CO., LTD.	21.8
10	600965	Fucheng Co., Ltd	18.0

4.2 Result analysis

According to Table 2, compared with the two algorithms in literature [2] and literature [20], the algorithm in this paper can obtain more uniform results of stock government risk investment. However, the results obtained by the two algorithms in literature [2] and literature [20] have very poor equilibrium. At the same time, for the three returns: F_β (x, α), F_β (x, α) and CVaR_β (x), the returns and risks of the government risk investment obtained by the algorithm in this paper are relatively lowest, that is, the CVaR value solved by the algorithm in this paper has the minimum numerical result.

Table 2
Transaction fee influence

Cost ratio 0.00% 0.10% 0.18%

Guizhou Gas 0.0047 0 0

Daye Co., Ltd 0.2636 0.2524 0.2424

Canatal 0.1385 0.1297 0.1286

Lehui International 0.3217 0.3488 0.3522

HEBEI HENGSHUI LAOBAIGAN 0.2654 0.2484 0.2393

LIQUOR CO.,LTD.

iReader 0 0 0.0257

CVaR 0.03366 0.0263 0.03394

Cost ratio	0.00%	0.10%	0.18%
Guizhou Gas	0.0047	0	0
Daye Co., Ltd	0.2636	0.2524	0.2424
Canatal	0.1385	0.1297	0.1286
Lehui International	0.3217	0.3488	0.3522
HEBEI HENGSHUI LAOBAIGAN	0.2654	0.2484	0.2393
LIQUOR CO.,LTD.
iReader	0	0	0.0257
CVaR	0.03366	0.0263	0.03394

As shown in Table 2, in the transaction fee influence experiment, the three transaction fee ratios 0.00%, 0.10% and 0.18% are set here for experimental comparison. It can be seen that, when the transaction fee ratio is 0.18%, the more balanced the selection of stocks reflects the influence of transaction fee on the selection of stock government risk investment.

As shown in Table 3, in the influence experiment of investment upper limit, the three investment upper limits 0.15, 0.35 and 0.55 are set here for experimental comparison. According to the experimental results, the smaller the value of the investment upper limit is, the greater the value of the CVaR model of government risk investment will be, and the more obvious the change between different equity funds will be.

Table 3

Investment cap influence

Investment cap	0.15	0.35	0.55
Guizhou Gas	0.1175	0.0088	0
SJEC	0.1274	0.0054	0
Daye Co., Ltd	0.0873	0.2985	0.2539
Canatal	0.0724	0.0046	0.1322
Donghong Co., Ltd	0.0135	0.0043	0
Putailai	0.0326	0.0035	0
Lehui International	0.1257	0.2986	0.3449
Subote	0.0362	0.0043	0
Shanghai Tianyang	0.0647	0.0054	0
HEBEI HENGSHUI LAOBAIGAN	0.0871	0.0025	0.2439
LIQUOR CO.,LTD.
ACRYL	0.0024	0.0033	0
Hesheng Silicon Industry	0.0022	0.0035	0
Lidao New Material	0.0723	0.0873	0
Shanghai WuMao	0.0924	0.0036	0
iReader	0.0603	0.2613	0.0236
CVaR	0.0542	0.0345	0.0337

In order to verify the performance advantages of the algorithm in this paper, two algorithms in literature [2] and literature [20] are selected for comparison. The optimal value, mean value, variance index and calculation time of CVaR model are selected as evaluation indexes, and the results are shown in Table 4.

Table 4

Performance comparison

Algorithm	Optimum value	Mean value	Variance	Computing time/s
Literature [9]	0.03457	0.0358	0.0024	32.124
Literature [10]	0.03581	0.0365	0.0023	48.285
The proposed	0.03431	0.0336	0.0013	26.746
algorithm

Note: [9] refers [2, 10] refers [20].

According to Table 4, in terms of algorithm performance comparison, the optimal value of the CVaR model obtained in this paper is 0.03232; the mean value of the CVaR model is 0.0338; its variance index is 0.0012, and its calculation time is 26.741 s, so this algorithm is better than the two comparison algorithms in literature [2] and literature [20].

5 Conclusion

This paper put forward a fuzzy clustering discrete optimization model of risk constraint value government risk investment of non-equilibrium benefits, in order to transform the problem of solving CvaR model optimization with the minimum extremum into solving linear programming model. Furthermore, the fuzzy clustering discrete algorithm is introduced to optimize the CvaR model of government venture investment. Meanwhile, a way of self-adaptive variable step is designed for algorithm improvement, so as to optimize and improve performance. The empirical analysis results verified the effectiveness of the proposed government venture investment analysis method. The problem is that the algorithm research in this paper is not very deep, and there is still a room for improvement for its convergence speed and accuracy. Meanwhile, the design stage of the CvaR model didn’t fully consider the conditions of the real trading environment, which needs to be deepened and improved in the next study.

Footnotes

Acknowledgments

Youth Fund Project of Humanities and Social Science Research of Ministry of Education Titled “Research on Dynamic Influence Mechanisms of the Equity Participation of Government Venture Capital Guiding Funds on Venture Capital Firm’s Network Position, 2017-2020” (Grant No. 17YJC630023); Project of Social Sciences Circles’ Union of Yulin City Titled “Research on Influencing Factors of Private CapitalParticipating in Venture Capital Investment of Small and Medium-sizedEnterprises” (Grant No. YLSKGH2017-20), 2017-2018; Research Startup Projectof Advanced Talents of Yulin University Titled “Research on the Influences of Government Venture Capital Guiding Funds on Later Financing of Venture Enterprises” (Grant No. 17GK02); China Postdoctoral Science Foundation funded project (Grant No.2018M633560).

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