Intelligent prediction algorithm of economic trend index based on rough set support vector machine

Abstract

In order to improve the ability of automatic estimation and prediction of economic trend index, an intelligent prediction model of economic trend index based on rough set support vector machine is proposed. The statistical analysis of intelligent prediction of economic trend index is carried out by using the equivalent approximate linear model, and the regression analysis model of intelligent prediction of economic trend index is established. Combining with the rough set support vector machine big data fusion technology, the feature extraction and information mining are carried out in the process of intelligent prediction of economic trend index, and the statistical time analysis series of economic trend index is constructed. The spatial distribution of economic trend index distribution series is reconstructed, and the economic trend is evaluated and predicted in the high dimensional economic trend index forecast series distribution space. The principal component characteristic analysis and fuzzy closeness analysis of economic trend index are carried out by using fuzzy relational degree scheduling method. Taking economic cost, economic development prospect and economic growth rate as constraint indexes, the method of multi-factor joint estimation is adopted. Realize economic trend index intelligent forecast. The simulation results show that the accuracy of fast estimation of economic trend index is high, the time cost is small, and the ability of intelligent prediction is stronger.

Keywords

Rough set support vector machine economic trend index intelligent prediction

1. Introduction

In the analysis and evaluation of economic trends, it is necessary to carry out intelligent prediction and prediction of economic trend indicators. In order to give full play to the compelling mechanism of resolving overcapacity, readjustment of industrial structure and transformation and upgrading, The Federation will further increase the scientific research power of enterprises, scientific research institutes, and colleges and universities, and closely revolve around the major technical issues of industry development and common technical problems of industry development, and the Federation will further increase the scientific research power of enterprises, scientific research institutes, and universities and colleges [1]. The new breakthroughs in the research and development of industry technology provide powerful technical support for the restructuring and upgrading of the industry. At present, the new material technology represented by polyurethane and isoprene rubber, the modern coal chemical technology represented by advanced coal gasification technology and the independent research and manufacture of large-scale equipment in the modern coal chemical industry, taking methyl alcohol to olefins and aromatics, Methanol deep processing technology represented by methanol protein and methanol gasoline, energy saving green tire technology represented by meridian, and new energy saving and emission reduction technologies represented by petrochemical industry to reduce energy consumption and green development [2]. They are playing a very important role in speeding up the adjustment of industrial structure, improving the quality of economic operation and promoting sustainable development for the whole industry. However, the capacity and technological achievements of the industry’s technological innovation are still far from meeting the urgent needs of the industry to resolve the contradiction between overcapacity and transformation and upgrade. The industry’s product structure has been significantly optimized, its technological innovation capability has been significantly improved, and energy conservation and emission reduction have been achieved. There is a fundamental improvement in safety and environmental protection, an overall improvement in economic benefits and sustainable development capacity, and a greater improvement in the competitiveness of the industry market and the level of international operation [3].

2. Economic trend index statistical series analysis and regression analysis model construction

2.1. Statistical sequence analysis of economic trend index

In order to design the intelligent prediction model of economic trend index, build the statistical sequence analysis model of Cheng economic trend index, combine big data sampling and information fusion technology, using the equivalent approximate linear model to carry on the statistical analysis model in the process of intelligent prediction of economic trend index, the initial data set X ={ x₁, x₂, ⋯ , x_n }, n is the series number of the test sample data set X of the economic trend index information. In the course of economic trend index information management, through the planning of economic statistical regional progress, operational reliability evaluation and economic trend analysis, supervision and maintenance, The whole life cycle economic trend index management of economic trend analysis [4]. The process constraint parameter of economic trend index information estimation is expressed as a P-dimensional vector in X data set, and X contains c categories. The fuzzy membership attribute of economic trend index information is represented, the classification attribute of economic trend index information is classified and recognized by fuzzy cluster analysis method [5], and combined with the economic trend index and economic growth attribute, the attribute of economic trend index and economic growth are classified and recognized by fuzzy cluster analysis. Carry on the feature classification recognition, adopt the block information feature detection and the data fusion matching method to carry on the economic trend index information adaptive grouping matching, based on the rough set comprehensive big data information processing technology, the statistical analysis of index time series ${x_{i}}_{i = 1}^{N}$ of economic trend index is obtained. The information fusion distribution matrix of intelligent prediction of economic trend index is obtained by using the method of information fusion reconstruction of economic trend index: $L = [\begin{matrix} x_{1}^{T} \\ x_{2}^{T} \\ ⋮ \\ x_{N}^{T} \end{matrix}] = [\begin{matrix} x_{1} & x_{1 + τ} & \dots & x_{1 + (m - 1) τ} \\ x_{2} & x_{2 + τ} & \dots & x_{2 + (m - 1) τ} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ x_{N - 1} & x_{N - 1 + τ} & \cdot \cdot \cdot & x_{N - 1 + (m - 1) τ} \end{matrix}]$ (1)

The time delay of embedded dimension m, block information feature detection in statistical series analysis of economic trend index is τ. The estimation model of economic trend index is statistically analyzed, and the statistical characteristic $L$ = $U$ * $S$ * $C$ is decomposed by singular value decomposition $L$ . The characteristic decomposition matrices $U$ and $C$ of the statistical series of economic trend index are orthogonal matrices, and the correlation knowledge base is used to process the fusion of the economic trend index series, and the characteristic decomposition matrices is: $C = (c_{1}, c_{2}, \dots, c_{n})$ (2)

Where, $S$ is the singular value of the economic trend index rough set information $L$ . For the management data of the economic trend index rough set, the parameter automatic collection model of the economic trend index information is constructed, and the characteristic quantity is satisfied: $S = diag (σ_{1}, σ_{2}, \dots, σ_{n}), σ_{1} \geq σ_{2} \geq \dots \geq σ_{n} \geq 0$ (3)

By means of principal component analysis (PCA), the rough set information of economic trend index is tested by full sample regression. The results show that the influencing factor of economic trend index is the subspace characteristic of N × m, and the subspace distribution matrix $X$ is: $X = [\begin{matrix} x_{1} \\ x_{2} \\ ⋮ \\ x_{3} \end{matrix}] = [\begin{matrix} a_{1}^{T} c_{1} & a_{1}^{T} c_{2} & \dots & a_{1}^{T} c_{m} \\ a_{2}^{T} c_{1} & a_{2}^{T} c_{2} & \dots & a_{2}^{T} c_{m} \\ ⋮ & ⋮ & ⋱ & ⋮ \\ a_{N}^{T} c_{1} & a_{N}^{T} c_{2} & \cdot \cdot \cdot & a_{N}^{T} c_{m} \end{matrix}]$ (4)

In the above formula, $J_{x}^{(N)}$ is obtained by the initial statistical sample information $J_{x_{i}}^{(N)}$ of the economic trend index. Based on the fuzzy clustering center fusion method, the statistical analysis model of the qualitative economic trend index is constructed, and the rough set database model of the economic trend index information is designed based on the relational knowledge base. The $J_{x}^{(1)}$ is calculated as follows: $δ x_{i + 1} \approx J_{x_{i}}^{(1)} δ x_{i}$ (5)

Where, δ $x$ _i = $x$ _j - $x$ _i, the rough set information of economic trend index is used as data carrier, $x$ _j is used to represent $x$ _i nearest neighbor, and the fuzzy proximity analysis method of regional quality of economic statistics is used to control the quality and benefit, and the $x$ _j ∈ $R$ ^m. j ∈ 1, 2, ⋯ , N is used to control the quality and benefit. The fusing characteristic quantity of economic trend index is constructed, which is expressed as the statistical characteristic value ${x_{i}}_{i = 1}^{N}$ and information distribution of economic trend index obtained by ${x_{i}}_{i = 1}^{N}$ , when δ $x$ _i+1 = $x$ _j+1 - $x$ _i+1 is obtained. The statistical sequence analysis model of economic trend index is as follows: $F_{U} = \sum_{j = 1}^{M} \underset{j \in N_{j}}{Min} (F_{jk})$ (6) $F_{V} = \sum_{j = 1}^{M} \underset{j \in N_{j}}{Max} (F_{jk})$ (7)

Through the above-mentioned algorithm design, the statistical sequence sampling and the rough set information base scheduling of the economic trend index information are realized [6].

2.2. Regression analysis model of intelligent forecast of economic trend index

The regression analysis model of intelligent prediction of economic trend index is established, and the feature extraction and information mining in the process of intelligent prediction of economic trend index are carried out with the combination of rough set support vector machine big data fusion technology [7]. Select the number of principal components of intelligent prediction of economic trend index, calculate the factor coefficient affecting economic trend index, and adopt the sparse statistical analysis method of sample information. The statistical distribution covariance matrix C of the intelligent prediction model of economic trend index is obtained as: $C = \frac{1}{N} [X - \bar{X_{l}}] {[X - \bar{X_{l}}]}^{T}$ (8)

Where $\bar{x_{i}} = \frac{1}{N} \sum_{k = 1}^{N} x_{ik}$ (9) $X = [X_{1}, X_{2}, \dots, X_{m}]$ (10)

Assuming that the n-dimensional principal component characteristic component generated by the economic trend index information database S is expressed by x = (x₁, x₂, ⋯ , x_n), the statistical characteristic function of the actual economic trend index of optimization scheme n is expressed as follows: $F_{i} = \sum_{k = 1}^{M} \sum_{j \in N_{j}} x_{j k} F_{j k}$ (11)

Under the model of fuzzy cluster analysis, several (K) data subsets of economic trend index information query is obtained. A_k is the fusion feature cluster set of economic trend index information, and the correlation degree {F_i, F_U} of economic trend index intelligent prediction is obtained: $μ_{F_{i}} = a_{F_{i}} + b_{F_{i}} Δ + c_{F_{i}} Φ$ (12)

Where, $a_{F_{i}} = \frac{F_{U} F_{v}}{(F_{U} + F_{v}) F_{i}}$ , $b_{F_{i}} = \frac{(F_{V} - F_{i}) (F_{i} - F_{U})}{(F_{U} + F_{v}) F_{i}}$ , $c_{F_{i}} = \frac{F_{i}}{F_{U} + F_{v}}$ . The statistical time analysis series of economic trend index is constructed, the spatial distribution of economic trend index distribution series is reconstructed [8], and the joint statistical analysis formula of economic trend analysis quality and benefit of cost control coefficient S_i is obtained as follows: $B_{i} = \sum_{k = 1}^{M} \sum_{j \in N_{j}} x_{j k} B_{j k}$ (13)

By using the method of multi-objective constrained evolution analysis, the mathematical model of closeness degree is expressed as follows: $\begin{matrix} max & Θ_{Q_{i}} = \frac{a_{Q_{i}}}{a_{Q_{i}} + c_{Q_{i}}} \\ max & Θ_{E_{i}} = \frac{a_{E_{i}}}{a_{E_{i}} + c_{E_{i}}} \\ max & Θ_{C_{i}} = \frac{a_{C_{i}}}{a_{C_{i}} + c_{C_{i}}} \\ S . t . & Q_{i} \geq Q_{th} \\ E_{i} \geq E_{th} \\ C_{i} \leq C_{th} \\ Q_{jk} \geq 0, E_{jk} \geq 0, C_{jk} \geq 0 \\ \sum_{j = 1}^{Nj} x_{jk} = 1, \forall i, 1 \leq k \leq M, 1 \leq j \leq N_{j} \end{matrix}$ (14)

According to the above analysis, the rough set support vector machine big data fusion technology is combined to carry out the intelligent prediction of economic trend index in the process of intelligent prediction [9].

3. Optimization of intelligent prediction model for economic trend indexes

3.1. Feature extraction and information mining in the process of intelligent prediction of economic trend index

On the basis of statistical analysis of the intelligent prediction process of economic trend index by using the equivalent approximate linear model, the intelligent prediction model of economic trend index is designed. An intelligent prediction model of economic trend index based on rough set support vector machine is proposed [10]. The regression analysis model of intelligent prediction of economic trend index is established, and the probability of using index factor series of economic trend is obtained. ${\begin{cases} {\dot{m}}_{i} (t) = - m_{i} + \frac{α^{r e p}}{1 + p_{j}^{n} (t - σ)} \\ {\dot{p}}_{i} = - β^{r e p} (p_{i} - m_{i} (t - τ)) \end{cases}$ (15)

Where, i = lacl, tetR, cl ; j = cl, lacl, tetR. The high-dimensional economic trend index forecast series distribution space carries on the economic trend appraisal and the forecast, uses the fuzzy correlation degree dispatching method to carry on the principal component characteristic analysis of the economic trend index [11], n refers to the fuzzy closeness degree of project budget cost in economic statistics region, which is the Hill coefficient of the piecewise regression test of economic trend index forecast. The cross-equilibrium control method is used to analyze the sample series of economic trend index and self-adaptive evaluation, and the regression analysis model is obtained: ${\begin{cases} {\dot{m}}_{i} (t) = - m_{i} - α^{r e p} \frac{p_{j}^{n} (t - σ)}{1 + p_{j}^{n} (t - σ)} + α^{r e p} \\ {\dot{p}}_{i} = - β^{r e p} (p_{i} - m_{i} (t - τ)) \end{cases}$ (16)

The distribution characteristics of index information of economic trend is expressed are as follows:

$\begin{matrix} A = diag {1, 1, 1}, C = diag {β, β, β}, \\ D = diag {β, β, β} \end{matrix}$ (17) $W = [\begin{matrix} 0 & 0 & - α \\ - α & 0 & 0 \\ 0 & - α & 0 \end{matrix}], u = [\begin{matrix} α & α & α \end{matrix}]^{T}$ (18)

Combining the fuzzy association degree mining method to obtain the multi-factor sample variance statistical analysis result R2 of the economic trend index information, which can be expressed as: $R_{2} = \frac{μ_{w}}{2 π Kh} [1.7 ln \frac{R_{eh}}{r_{f}} + 12 Z_{f} + 25 Z_{f}^{2}]$ (19)

In the form, Z_f is the characteristic state cascade data saturation in the process of intelligent prediction of economic trend index [12], which can be obtained from the following formula: $Z_{f} = 0.1 \sqrt{\frac{μ_{R}}{1.5 (1 - S_{or} - S_{wi}) - Z_{f}}}$ (20)

By using rough set integration method, the edge attribute value of D = (d_γ) _γ∈Γ is defined as the characteristic distribution of economic trend index information, and the following results are obtained: $f = \frac{100 Z_{f}^{2}}{μ_{R}}$ (21) $f = \frac{1}{1.5 (1 - S_{or} - S_{wi}) - Z_{f}}$ (22)

According to the above-mentioned analysis, the economic trend is evaluated and predicted in the distribution space of high-dimensional economic trend index prediction series, and the principal component characteristic analysis and fuzzy proximity analysis of economic trend index are carried out by using fuzzy correlation degree scheduling method. Improve the ability to estimate and forecast economic trends [13].

3.2. Multi-factor combined estimation of economic trend indicators.

According to the model statistical analysis results of the economic trend index information mentioned above, the combined fault model of the economic trend index is constructed, and the subsection regression test constraint parameter R₃ is obtained to express the economic trend index prediction as follows: $R_{3} = \frac{μ_{o}}{2 π Kh} ln \frac{r_{w}}{r_{w}^{'}}$ (23)

The feature vectors of rough set information are represented by y^(k), $s_{j}^{(k)}$ and $y_{j}^{(k)}$ are the fitting depth of intelligent prediction of economic trend index, which can be expressed as follows: $\begin{matrix} R = \frac{μ_{w}}{2 π Kh} [\frac{1}{m} ln \frac{R_{eh}}{2 (i + 1) r_{w}} + 1.7 ln \frac{R_{eh}}{r_{f}} \\ + 12 Z_{f} + 25 Z_{f}^{2} + \frac{μ_{o}}{μ_{w}} ln \frac{r_{w}}{r_{w}^{'}}] \end{matrix}$ (24)

The relationship between indicators of economic trends and indicators of economic growth can be expressed as follows: $Q_{H} = \frac{Δ p}{R} = \frac{Δ p}{\frac{μ_{w}}{2 π Kh} R_{p}}$ (25)

Where: $\begin{matrix} R_{p} = \frac{1}{m} ln \frac{R_{eh}}{2 (i + 1) r_{w}} + 1.7 ln \frac{R_{eh}}{r_{f}} + \\ 12 Z_{f} + 25 Z_{f}^{2} + \frac{μ_{o}}{μ_{w}} ln \frac{r_{w}}{r_{w}^{'}} \end{matrix}$ (26)

Under the constraint of joint parameter [14], the quadratic fitting value of intelligent prediction of economic trend index satisfies: $ξ = 2 ρ_{max} λ_{max} (Q_{i}) N δ^{2} KT$ (27)

Convergence conditions satisfy: $\begin{matrix} J^{*} (x (t_{+ 1})) - J^{*} (x (t_{k})) \leq \\ - \sum_{i = 1}^{N} \int_{t_{k}}^{t_{k + 1}} L_{i} (x_{i}^{*} (s; t_{k + 1}), u_{i}^{*} (s; t_{k + 1})) ds + ξ δ^{2} \end{matrix}$ (28)

Where: $ρ_{max} \geq ∥ x (s; t_{k + 1}) - x_{i}^{c} ∥$ (29)

Taking the economic cost, the prospect of economic development and the economic growth rate as constraint indexes, this paper adopts the method of multi-factor joint estimation to realize the intelligent prediction of economic trend index [16 –19].

4. Simulation empirical analysis

In order to verify the application performance of the method in the intelligent prediction of the economic trend index, the experiment analysis is carried out, the experiment is carried out by using the Matlab to design the model, the five economic statistics areas are the test objects, and the sample sequence size of the rough set information base of the economic trend index is 2000, The prior data distribution of the training set is 120 and the economic trend index is shown in Table 1.

Table 1
Economic trend indicators economic statistical regional prior data distribution

Regional code for economic statistics	Economic growth level (100%)	Economic growth rate (100%)	Cost control/$10,000
A	[0.45 1.00]	[0.63 1.75]	[23.0 52.0]
B	[0.63 1.00]	[0.56 1.74]	[53.0 75.0]
C	[0.57 1.00]	[0.57 1.64]	[42.0 44.0]
D	[0.67 1.00]	[0.64 1.56]	[44.0 65.0]
E	[0.68 1.00]	[0.57 1.64]	[54.0 66.0]

According to the prior distribution set of economic trend index in Table 1, the optimal solution set of economic trend index is estimated. The estimated results are shown in Table 2.

Table 2

Estimation results of optimal solution set of economic trend index

Economic trend analysis group	Economic growth level (100%)	Economic growth rate (100%)	Cost control/$10,000
EC11	0.876	0.565	676.5
EC 12	0.676	0.654	654.0
EC 13	0.978	1.675	544.5
EC 21	0.657	0.555	344.0
EC 22	0.786	1.765	566.0
EC 23	0.765	0.676	552.0
EC 31	0.797	0.767	565.0
EC 32	0.876	0.666	655.0
EC 33	0.675	1.246	576.0
EC 34	0.665	1.544	565.0
EC 35	0.867	1.575	557.0
EC 41	0.786	0.954	554.5
EC 42	0.655	1.565	663.0
EC 43	0.676	0.676	676.5
EC 51	0.978	1.553	544.0
EC 52	0.978	0.977	565.5
EC 53	0.765	1.078	667.0
EC 54	0.968	0.766	779.0

The analysis of the above results shows that the intelligent prediction of economic trends can be realized effectively by using this model, and the precision of test estimation can be achieved. The comparison results are shown in Fig. 1, and the results of analysis in Fig. 1 are shown in Fig. 1. In this model, the precision of intelligent prediction of economic trend index is smaller, the precision is higher, and the ability of anti-interference is stronger.

Fig. 1

Comparison of precision of intelligent prediction of economic trend index.

The economic growth rate is tested and compared as shown in Fig. 2. The analysis shows that this method can improve the economic growth rate by intelligently prediction the index of economic trend.

Fig. 2

Economic growth rate test.

5. Conclusion

In this paper, an intelligent prediction model of economic trend index based on rough set support vector machine is proposed. The statistical analysis of intelligent prediction of economic trend index is carried out by using the equivalent approximate linear model, and the regression analysis model of intelligent prediction of economic trend index is established. Combining with the rough set support vector machine big data fusion technology, the feature extraction and information mining are carried out in the process of intelligent prediction of economic trend index, and the statistical time analysis series of economic trend index is constructed. The spatial distribution of economic trend index distribution series is reconstructed, and the economic trend is evaluated and predicted in the high dimensional economic trend index forecast series distribution space. The principal component characteristic analysis and fuzzy closeness analysis of economic trend index are carried out by using fuzzy relational degree scheduling method. This trend can be used to secure individual privacy [15] Taking economic cost, economic development prospect and economic growth rate as constraint indexes, the method of multi-factor joint estimation is adopted. Realize economic trend index intelligent forecast. The simulation results show that the accuracy of fast estimation of economic trend index is high, the time cost is small, and the ability of intelligent prediction is stronger. This method has good application value in economic trend index budget.

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