Research on Financial Difficulties Prediction and Optimization Strategies of Small and Medium-sized Enterprises Based on Support Vector Machine

While some outstanding SMEs are growing and becoming leaders in various industries, some SMEs are standing still or in financial difficulties for various reasons [1]. Some prestigious small and medium-sized enterprises have even come to the closure of the situation, which makes other small and medium-sized enterprises are facing the development of the problem of anxiety [2-3]. The study of the causes and financial characteristics of financial distress in SMEs can effectively prevent the formation and outbreak of financial distress, help operators to manage the enterprise, stabilize the value chain between the enterprise and stakeholders, and safeguard the interests of enterprise investors [4-6].

First, it is to enhance the ability of enterprise management to prevent risks. Management is a strategy maker, if it can use appropriate methods to predict the financial crisis and take timely control measures, not only can effectively avoid the enterprise in financial difficulties, but also enable the enterprise to amend and improve the long-term strategy, and promote the healthy development of the enterprise [7-8]. Secondly, it is to stabilize the value chain between the enterprise and the stakeholders, and to avoid the deterioration of the value chain to appear chain reaction. The daily operation of an enterprise will inevitably form a dependent relationship with many business associates, involving the exchange of funds and the formation of a value chain [9-10]. If an enterprise is in financial difficulties, it will inevitably affect the business affiliates, resulting in a “domino effect”, so that the upstream and downstream enterprises are affected. Therefore, enterprises should not only control the occurrence of financial crisis, but also fully judge the financial status of related enterprises before conducting business, so as to minimize losses [11-12]. Finally, it is to guide investors to make better investment, and the business condition of the enterprise directly affects the interests and losses of investors. For investors, with the help of financial distress prediction, they can understand the probability of financial crisis in advance, so as to reduce the loss by reducing the investment or investment portfolio, and for the potential shareholders, financial distress prediction is also conducive to their reasonable choice of investment objects [13-15].

Meanwhile, the demand for credit risk modeling comes from banks’ requirement to quantitatively assess the necessary risk capital to support their lending activities [16]. The Basel Capital Accord, introduced in 1988, was the first attempt to impose risk management and minimum capital requirements on financial institutions. Minimum capital requirements were implemented by allocating bank assets into four risk weights. Due to insufficient data granularity, banks began to transfer risk and ignore the potential risk profile of their debtors [17-19]. With the ongoing refinement of the Basel Accord, banks can choose and use one of two credit risk management techniques, a standardized approach or an internal ratings-based approach. Small and medium-sized enterprises (SMEs) are the backbone of the world’s sustained economic and social welfare growth [20]. One of the biggest challenges faced by SMEs over the last few decades has been financing. This has become more prevalent with the introduction of capital requirements, which have put pressure on the lending capacity of banks. The subsequent Basel Accord has added an additional burden on banks by raising minimum capital ratios and creating higher barriers to SME financing [21-22].

With the deepening of China’s reform and opening-up, SMEs have become an important force in promoting the sustained, stable and rapid growth of the market economy with their vigorous development. However, while developing rapidly, SMEs also face many financial problems, and may even fall into financial distress and eventually go bankrupt. Literature [23] proposes the need for in-depth understanding and clear distinction between the concept of enterprise financial distress, and improve the sound financial distress prediction index system, so as to realize the accurate prediction of enterprise financial distress, which commonly used algorithms for machine learning.

More researchers have focused on the optimization and innovation of corporate financial distress forecasting methods, and the main core methods used include, ANS-REA algorithm, Support Vector Machines, Logit Models, Artificial Neural Networks, and Genetic Algorithms. Literature [24] envisioned a new dynamic financial distress prediction method and obtained good results in practice, while it was found that the proposed Adaptive Neighbor SMOTE-Recursive Ensemble Approach (ANS-REA) algorithm outperforms other algorithms in coping with imbalanced dataset classification. Literature [25] constructed a dynamic assessment and prediction method of corporate financial distress based on entropy weighted (EBW), support vector machine (SVM) and vertical sliding time window (VSTW) algorithms of enterprises, and demonstrated it with practical cases, pointing out that the proposed method improves the managers’ corporate financial management to a certain extent. Literature [26] compared and analyzed the performance of Logit model, artificial neural network, support vector machine technology, partial least squares, and the hybrid model of support vector machine and partial least squares in the prediction of corporate financial distress, and found that the hybrid model has the optimal performance, and elucidated that the smaller the size of the enterprise in financial distress, the higher the leverage ratio of the enterprise in financial distress, the higher the chance of financial distress. Literature [27] analyzed financial distress prediction with reference to 12,000 small and medium-sized enterprises (SMEs) data and used logistic regression, artificial neural networks and random forest techniques to estimate binomial classifiers for financial distress prediction, and in the process of analyzing the risk period had to be adjusted in order to improve the accuracy of financial distress prediction. Literature [28] uses genetic algorithm to optimize the combination of base classifiers, and then the annual financial distress prediction of enterprises, compared with the three commonly used dynamic prediction methods, in the prediction accuracy is more advantageous. Literature [29] combines intellectual capital, financial ratios, and corporate governance variables with logistic regression modeling to establish a financial distress prediction framework, and verifies that the proposed model has the ability to reliably predict corporate financial distress in real case tests. Literature [30] discusses the prediction model of corporate financial distress based on the combination of sparse principal component analysis, corporate governance characteristics, market transaction data, and support vector machine, and concludes that the prediction efficiency and accuracy of the prediction model have been significantly improved. Literature [31] develops a corporate financial distress prediction model that covers traditional financial variables, important corporate governance variables, and in the performance evaluation, it is shown that the introduction of dynamic distress threshold theory has higher prediction accuracy than the traditional threshold model.

In this paper, the SME financial distress prediction problem is characterized as a classification problem, i.e., based on the financial history of SMEs, they are classified into normal and distressed categories correspondingly. Facing the output variable parameters, which is the key to improve the accuracy of financial distress prediction, the enterprise financial input variables are first normalized. The principal component analysis (PCA) is used to reasonably select the input variables of enterprise financial distress, the idea of dimensionality reduction is used to eliminate the redundant information of the variables, and the original input variables are normalized to eliminate the negative impacts due to the differences in the units of the input variables. The Gray Wolf Optimization (GWO) algorithm is introduced to optimize the penalty coefficients and kernel function parameters of the SVM model and determine the fitness function, calculate the fitness function value of each individual gray wolf in the new position, and use the resulting optimal parameters of the SVM model for the prediction of the financial distress of small and medium-sized enterprises. We analyze the performance of this paper’s SME financial distress prediction in terms of the performance of the optimization parameters, the fitness curve and the confusion matrix prediction results, etc., and verify the actual prediction accuracy of this paper’s model in the two cases of balanced and unbalanced data classification samples.

2

Financial distress prediction model for SMEs based on GWO-SVM

Financial distress prediction (FDP), also called financial crisis early warning, refers to the identification of the future financial status of an enterprise through its externally disclosed historical financial information and the use of certain prediction models [32]. Due to the superior generalization performance of Support Vector Machine (SVM), it is widely used in enterprise financial distress prediction models.

Small and medium-sized enterprises (SMEs) are at greater risk of financial crisis because of their small size, limited resources, and varying business conditions. Financial crisis will not only make the company face operational difficulties, but also cause a series of chain reactions, which will bring adverse effects to the overall economic environment. Accurately predicting the risk of financial crisis in SMEs plays a very important role in ensuring the healthy development of enterprises and maintaining market stability. Based on this, this paper focuses on the research of SME financial crisis risk prediction method based on SVM, and establishes a prediction model of SME financial difficulties.

2.1

Principles of forecasting financial distress in SMEs

When an enterprise is in financial distress, it has four manifestations: illiquidity, equity deficiency, debt delinquency and undercapitalization, and bankruptcy is mostly used as a sign of financial distress in China. Enterprise financial distress prediction is essentially a classification problem, according to the financial history of the enterprise, the enterprise financial will be divided into normal and distressed two categories. Let the input variable of enterprise financial distress obtained at the ith moment be {x_il, x_i2, ⋯, x_im}, and its corresponding financial state be y_i, y_i has the value of 1 or -1, where 1 stands for normal and -1 stands for distress, then the number model of enterprise financial distress prediction is: (1) ${\hat{y}}_{i} = f (x_{1}, x_{2}, \dots, x_{m})$

2.2

Treatment of financial input variables for SMEs

The use of univariate reflecting the financial situation of the enterprise’s information is limited, but all the information reflecting the financial situation of the enterprise input to the prediction model to learn, measurement is quite large, the information redundancy is serious, so the input variable selection in the prediction of financial distress is very critical, and the task is to select from a set of input variables in the number of n number of the optimal input variables for a group of m(m < n) to come. In this paper, principal component analysis (PCA) is used to extract the input variables of the financial prediction model, and then the selected input variables are input into the SVM for learning [33].

2.2.1

Pre-processing of financial input variables for SMEs

Enterprise financial data in the collection process, may be due to some financial personnel’s own limitations, will produce some errors and noise data, so first of all the error and noise data deletion process, at the same time in order to avoid the larger input volume of the prediction of the results of the enterprise financial predicament to dominate, as well as the next input variable selection needs, the enterprise financial input variables for the normalization of the process, so that the range of processing Between, the normalization formula is specifically shown below: (2) $x^{'} = \frac{x - x_{\min}}{x_{\max} - x_{\min}}$

2.2.2

PCA’s financial input variable extraction for SMEs

PCA utilizes the idea of dimensionality reduction, a statistical method that reduces multiple indicators into several composite indicators with almost no loss of information, and is able to well eliminate redundant information between variables. The main ideas for the extraction of enterprise input variables are as follows: 1)

Let there be a total of m input variables for corporate financial distress, X = (X₁, X₂,⋯, X_m) and n samples for each variable: x_i(i = 1, 2,⋯, m). Then the principal components of these input variables are: (3) ${\begin{matrix} F_{1} = e_{1}^{T} X = e_{11} X_{1} + e_{21} X_{2} + \dots e_{m 1} X_{m} \\ F_{m} = e_{m}^{T} X = e_{1 m} X_{1} + e_{2 m} X_{2} + \dots e_{m m} X_{m} \end{matrix}$

How much information of the input variables is determined by the variance of the principal components, the first principal component F₁, and the principal components are uncorrelated and independent, and their correlation coefficients are zero. 2)

Calculate the correlation matrix of the original input variables, and let the sample data matrix be: (4) $M = {(α_{1}, α_{2}, \dots, α_{m})}^{T} = (β_{1}, β_{2}, \dots, β_{m})$

where α_i denotes the vector consisting of all the sample values of each input variable and β_i denotes the sample vector of each input vector X. The covariance matrix (S) and correlation matrix (R) are given by: (5) $S = S_{a b} = \frac{1}{n} \sum_{k = 1}^{n} [[M_{a k} - \frac{1}{n} \sum_{c = 1}^{n} M_{a c}) (M_{b k} - \frac{1}{n} \sum_{d = 1}^{n} M_{b d})]$ (6) $R = R_{a b} = S_{a b} / (\sqrt{a a} \sqrt{b b})$

3)

In order for the master PCA to treat each of the original corporate financial distress input variables equally and to eliminate the negative effects due to differences in the units of the input variables, it is necessary to standardize each of the original input variables to obtain: (7) $X^{*} = (X_{1}, X_{2}, \dots, X_{m})$

4)

The eigenvalues λ_i(i = 1, 2,⋯, m) are calculated according to R and sorted to accumulate the variance contribution of each principal component, taking the first p principal components (p < m) in order, up to the point where the cumulative contribution reaches a certain percentage, the number of new input variables is determined, and the new input variables are used as inputs to the SVM.

2.3

Financial distress prediction for SMEs based on GWO-SVM

2.3.1

Gray Wolf Optimization Algorithm

The wolf pack groups in the Gray Wolf Optimization (GWO) algorithm are divided into α, β, δ, ω4 classes, and different groups have different roles [34].

The GWO algorithm simulates the hunting behavior of wolves, which mainly includes 3 steps: encirclement, hunting and attack. 1)

Surrounding

In the hunting process, the gray wolf firstly surrounds the prey, and its mathematical model is: (8) $D = | C \cdot X_{p} (t) - X (t) |$ (9) $X_{2} = X_{β} - A_{2} \cdot (D_{β})$ (10) $X (t + 1) = X_{p} (t) - A \cdot D$

where A = 2a · r₁ − a, C = 2 · r₂; t is the current number of iterations; X_ρ is the location of the prey (global optimal solution vector); X is the current location of the wolves (potential solution vector); D is the distance between the wolves and the prey. the GWO algorithm decreases a linearly from 2 to 0 during the iteration process, and r₁, r₂ is a random vector between [0, 1]. 2)

Hunting.

After encircling the prey, the wolves hunt the prey, assuming α, β, δ is the global optimal solution, the global second solution, and the third solution, respectively, and the other gray wolf populations ω are relocated according to α, β, δ, whose relocation equations are as in Eq. (11)-Eq. (13): (11) $D_{s} = | C_{1} \cdot X_{s} - X |$ (12) $D_{β} = | C_{2} \cdot X_{β} - X |$ (13) $D_{δ} = | C_{3} \cdot X_{δ} - X |$

where X_a, X_β, X_δ is the position of α, β, δ, C₁, C₂, C₃ is a random vector, and X is the position of the current solution. According to Eq. (3), Eq. (4) and Eq. (5) the approximate distance between the current solution and α, β, δ can be calculated. After that, the position of the current solution X and the position of the updated solution X(t + 1) Eq. (14)-Eq. (16): (14) $X_{1} = X_{α} - A_{1} \cdot (D_{α})$ (15) $X_{3} = X_{δ} - A_{3} \cdot (D_{δ})$ (16) $X (t + 1) = \frac{X_{1} + X_{2} + X_{3}}{3}$

where t is the current iteration number; X_α, X_β, X_δ is the position of α, β, δ; and A₁, A₂, A₃ is a random vector. 3)

Attack

The final stage of wolf hunting is attacking to achieve prey capture, i.e., obtaining the optimal solution. It is mainly realized by decreasing the value of a. When |A| ≤ 1, the next position of the wolf pack will be closer to the prey (X^*, Y^*), so as to realize the centralized attack on the prey; when |A| > 1, the wolf pack will be far away from the prey dispersed, the GWO algorithm loses the optimal solution position.

2.3.2

Support Vector Machines

If the training vector ${\vec{x}}_{i} \in R^{d}, i = 1, 2, \dots, n; y_{i} \in {- 1, 1}$ , the SVM model with slack variables is equation (10) [35]: (17) $\begin{matrix} \min_{w, b, ξ_{i}} (\frac{1}{2} | | \vec{w} | |^{2} + C \sum_{i = 1}^{n} ξ_{i}^{2}) \\ s . t . y_{i} (< \vec{w}, {\vec{x}}_{i} > + b) \geq 1 - ξ_{i} \\ ξ_{i} \geq 0, i = 1, 2, \dots, n \end{matrix}$

where b is the hyperplane deviation; C is the penalty coefficient; n is the number of samples; ξ_i is the slack variable; $\vec{w}$ is the normal vector of hyperplane $[\vec{w}, {\vec{x}}_{i}] + b = 0$ ; $\frac{1}{2} | | \vec{w} | |$ is the distance from ${\vec{x}}_{i}$ to the distance from hyperplane $[\vec{w}, {\vec{x}}_{i}] + b = 0$ . By theoretical derivation, the optimal classification function of SVM model is equation (18): (18) $f (x) = sgn {\sum_{i = 1}^{n} a_{i}^{*} y_{i} K ({\vec{x}}_{i} \cdot \vec{x}) + b^{*}}$

Of these, $K ({\vec{x}}_{i} \cdot \vec{x}) = \exp {- | | \vec{x} - {\vec{x}}_{i} | |^{2} / 2 g^{2}}$ .

2.3.3

Financial distress prediction based on GWO-SVM

1)

Fitness function

Since the SVM model penalty coefficient C is mainly used to control the approximation error and complexity of the model, the larger the value of the model approximation or the higher the degree of fit, but the generalization ability will be reduced; the kernel function parameter g affects the classification accuracy of the SVM model. Therefore, for the SVM classification performance is vulnerable to the influence of the penalty coefficient C and the kernel function parameter g, the GWO algorithm is used to optimize the selection of the SVM parameters, and the classification accuracy T is selected as the fitness function as equation (19) [36]: (19) $T = \frac{right}{Total} \times 100 %$

Where, Total is the total number of samples; right is the number of correctly categorized samples. 2)

Algorithm flow

The process of financial distress prediction algorithm based on GWO-SVM can be described as;

Step1: Read the enterprise financial distress evaluation index data, generate SVM training set and test set, and normalize the data, the normalization formula is equation (20): (20) $x^{'} = a + \frac{x - x_{\min}}{x_{\max} - x_{\min}} \times (b - a)$

Where, x′ is the data after normalization; x, x_max, x_min is the original data, maximum and minimum values in the original data respectively; a, b is the minimum and maximum values after normalization. In this paper, we take a = −1, b = 1.

Step2: Set the parameters of GWO algorithm: population size N, maximum number of iterations T; set the penalty coefficient C and the kernel function parameter g to take the range of values, and initialize the SVM parameters.

Step3: Randomly generate gray wolf packs, and the individual position of each gray wolf pack consists of penalty coefficient C and kernel function parameter g.

Step4: The SVM model learns the training set based on the initial penalty coefficient C and kernel function parameter g, and calculates the fitness function value of each gray wolf according to Equation (14);

Step5: Based on the fitness function value, the gray wolf pack is divided into 4 different classes of gray wolves α, β, δ and ω.

Step6: Update each individual in the gray wolf pack according to Equation (3) ~ Equation (5);

Step7: Calculate the fitness function value F_new of each gray wolf individual at the new location and compare it with the optimal fitness function value F_g of the previous selection generation; if F_new > F_g, the fitness function value F_new of the gray wolf individual replaces F_g and retains the location of the gray wolf individual; conversely, retain F_g.

Step8: If the current number of selected generations t > T, the algorithm terminates and outputs the global optimal position, that is, outputs the optimal values best_C and best_g of the SVM model; otherwise, return to Step5 to continue optimization.

Step9: apply the optimal parameters best_C and best_g of SVM model to predict the test set.

3

Performance Assessment of Financial Distress Prediction Models for SMEs

The experiments in this chapter were conducted under the environment of Windows 10 (64bit) operating system using Matlab R2016b simulation software with LIBSVM 3.24 software package installed. The modeling dataset used for the experiment consists of 46 data sets with 13 attribute financial indicators, including 23 SMEs in normal financial condition and 23 enterprises in financial distress, with a ratio of 1:1, 70% of the dataset is selected as the training set and the remaining 30% as the test set.

The Chinese securities market gives special treatment to listed companies in financial distress by defining their corresponding stocks as ST stocks, and the company is correspondingly defined as an ST company. In this paper, we will extend the references to the concept by using non-ST proxies for financially healthy SMEs and ST proxies for SMEs in financial distress.

3.1

Performance Comparison of Optimization Parameters

On the same dataset, the parameter seeking of SVM is carried out using grid search, GA, PSO, GWO, and the SME financial distress prediction model constructed in this paper, and the parameter seeking results of each optimization algorithm are shown in Table 1. From the table, it can be seen that the grid search method consumes the longest CPU time, and the classification accuracy is also lower than the algorithms of GA, PSO, GWO and the model in this paper, indicating that the SVM algorithm’s grid search method has poor parameter finding ability. The CPU time of this paper’s model is 48.44s, and the classification accuracy can reach 87.01%, which is the best parameter seeking performance among the five algorithms. Compared with the GWO algorithm, the CPU time consumed by the model algorithm of this paper is reduced by 6.85s and the classification accuracy is improved by 2.18%, which indicates that the model of this paper effectively improves the GWO algorithm.

Table 1.

Accuracy and Accuracy

Algorithm	Accuracy(%)	CPU time(s)
Grid Search	78.21	99.05
GA	82.55	70.03
PSO	84.76	58.42
GWO	84.74	55.29
Model of this article	87.01	48.44

3.2

Comparison of adaptation curves

The fitness curves of GA, PSO, GWO and the optimized SVM of the model of this paper are specifically shown in Fig. 1. It can be concluded from the figure that the GA algorithm starts to converge at 70 iterations, and the fitness value is 88.36%, which has the slowest convergence speed and the lowest convergence accuracy compared with the other optimization algorithms. The PSO algorithm converges faster relative to the GA algorithm, and starts to converge at 55 iterations, and the convergence accuracy reaches 91.85%, which improves the convergence accuracy by 3.49% compared to the GA algorithm. The GWO algorithm converges at converged at 65 iterations and the adaptation value reaches 93.47%, which improves both the convergence speed and convergence accuracy compared to GA algorithm, and slower compared to PSO algorithm, but the convergence accuracy is further improved by 1.62%. The accuracy of this paper’s model starts to improve when iterating to 30 times, and then gradually rises, and converges completely when iterating to 50 times, and the adaptability value reaches 96.34%, comparing with the GWO algorithm, this paper’s model not only converges faster, but also improves the convergence accuracy by 2.87%, and comparing with the GA algorithm and the PSO algorithm, the convergence speed is obviously improved, and the convergence accuracy improves quite a lot as well. Therefore, the model in this paper has a significant advantage in optimizing SVM parameter searching, and also achieves the improvement of GWO.

3.3

Comparison of forecast results

In order to validate the effectiveness of the GWO-SVM-based SME financial distress prediction model proposed in this paper, it was compared with other algorithms based on PSO-SVM, GA-SVM, and Grid Search SVM on the same modeling dataset. The results of the confusion matrix produced by this paper’s model and the other compared algorithms are shown in Table 2. From the table, it can be observed that the classification accuracy of this paper’s model can reach up to 93.48%, where only one ST company is classified as normal company and three normal companies are classified as ST companies. Compared with the algorithms proposed in this paper, PSO-SVM, GA-SVM and GridSearch SVM are worse in terms of classification accuracy, which are only 80.43%, 82.61% and 78.26% respectively. Experiments show that the SME financial distress prediction model based on GWO-SVM in this paper is better than the other models in discriminating whether SMEs are in financial distress.

Table 2.

Confusion matrix table

Methods	Predicted/Actual	non-ST	ST	Accuracy (%)
Model of this article	non-ST	21	1	93.48%
	ST	2	22
	Total	23	23
PSO-SVM	non-ST	17	3	80.43%
	ST	6	20
	Total	23	23
GA-SVM	non-ST	17	2	82.61%
	ST	6	21
	Total	23	23
Grid Search SVM	non-ST	18	5	78.26%
	ST	5	18
	Total	23	23

4

Empirical Evidence on the Application of Financial Distress Prediction Models for Small and Medium-sized Enterprises

In this chapter, an empirical study of the GWO-SVM-based SME financial distress prediction model proposed in this paper is carried out. Firstly, the same number of financially distressed SMEs and financially healthy SMEs are selected as the sample set for training and testing using the pairwise principle (reciprocity principle) to realize this paper’s model for balanced data classification samples. Furthermore, based on the unbalanced classification problem in reality, i.e., the general situation that financially distressed SMEs and healthy SMEs present asymmetry, the data sample ensemble is reconstructed proportionally to carry out the processing of unbalanced data classification samples. The effectiveness of the GWO-SVM-based SME financial distress prediction model proposed in this paper is explored with two types of samples, namely, financially distressed SMEs and non-distressed SMEs, presenting balanced and unbalanced categorization situations.

4.1

Balanced Data Categorization Sample Processing

The basic composition of the sample set of balanced data used in this section is specified in Table 3. GongY, SongY, and ZongY in the table correspond to the datasets of SMEs on the industrial, commercial, and general sectors, respectively, and 1-Year-ST, 2-Year-ST, and 3-Year-ST represent the one, two, and three years prior to being identified by the firm as being in financial distress treatment. A sample of healthy firms with the same number of samples as the sample of financially distressed firms was randomly selected to collectively form three balanced categorized datasets, i.e., 1-Year-Predict, 2-Year-Predict, and 3-Year-Predict in the table.

Table 3.

Basic composition of data sample set

Sample collection	Total number of samples	Number of enterprises in financial distress	Number of financial health enterprises
GongY	282	141	141
ShangY	76	38	38
ZongY	54	27	27
1-Year-ST	122	61	61
2-Year-ST	170	85	85
3-Year-ST	182	91	91
1-Year-Predict	166	83	83
2-Year-Predict	206	103	103
3-Year-Predict	278	139	139

Selecting SVM, ICA-SVM model as a comparison model, the prediction accuracy of SVM, ICA-SVM and this paper’s model on the balanced data classification sample dataset is specifically shown in Table 4. From the comprehensive analysis of the results in the table, it can be known that the best prediction accuracies of this paper’s model and ICA-SVM model on each data sample set are higher than that of the non-feature selection work SVM model. And the prediction accuracy of this paper’s model is higher than ICA-SVM model on all data sample sets, and the prediction accuracy is higher than 80% level on all data sample data sets. In terms of different segments, all models achieve the highest prediction accuracy on ShangY on the business segment, and the prediction accuracies of SVM, ICA-SVM and this paper’s model reach 80.27%, 83.11% and 83.52%, respectively. The classification performance of several prediction models on the unsegmented 1-Year-ST, 2-Year-ST, and 3-Year-ST datasets is slightly lower than that on GongY, ShangY, and ZongY. The performance of all models on the 1-Year-ST, 2-Year-ST, and 3-Year-ST datasets shows a tendency to decrease with the longer distance from being processed by ST. Similarly, on the 1-Year-Predict, 2-Year-Predict, and 3-Year-Predict datasets, all models show a trend of decreasing prediction accuracy with the length of time that SMEs are in financial distress.

Table 4.

Accuracy of prediction on balanced classification data sets

Sample collection	SVM(%)	ICA-SVM(%)	Model of this article(%)
GongY	77.81	82.12	83.15
ShangY	80.27	83.11	83.52
ZongY	73.74	77.98	80.4
1-Year-ST	78.01	80.56	80.58
2-Year-ST	77.98	79.5	81.29
3-Year-ST	74.48	77.03	82.3
1-Year-Predict	78.28	80.65	82.8
2-Year-Predict	76.26	80.12	82.59
3-Year-Predict	72.41	78.5	80.95

4.2

Sample processing for unbalanced data classification

In the real financial distress prediction classification problem, the financial distress enterprise and the healthy enterprise present asymmetry, i.e., it belongs to the unbalanced classification problem. In this paper, we reconstruct the original several data sample sets proportionally to the training samples as half of the original sample set, and the test sample set includes the remaining samples of distressed enterprises and the samples selected from the remaining samples of healthy enterprises with the same number of samples of distressed enterprises. This maintains the original proportional composition of the training sample in terms of the number of distressed firms and healthy firms. The basics of the new data sample set are shown in Table 5.

Table 5.

Basic composition

Sample collection	Total number of samples	Number of enterprises in financial distress	Number of financial health enterprises
N-GongY	282	152	130
N-ShangY	76	39	37
N-ZongY	54	22	32
N-1-Year-ST	122	71	51
N-2-Year-ST	170	66	104
N-3-Year-ST	182	85	97
N-1-Year-Predict	166	72	94
N-2-Year-Predict	206	99	107
N-3-Year-Predict	278	108	170

The prediction accuracy of all the models under the unbalanced data classification sample ensemble is shown in Table 6. From the results in the table, it can be illustrated that the prediction results of all three models are lower than when the number of financially distressed SMEs and healthy SMEs are balanced. Although the prediction accuracies of all models are reduced, the prediction accuracies of this paper’s models are still higher than those of SVM and ICA-SVM models on different datasets. In contrast to the SVM and ICA-SVM models where the prediction accuracy is lower than 70%, the prediction accuracy of this paper’s model is always higher than 70% on any dataset. In addition, the prediction accuracy laws of each model under the balanced data classification sample ensemble are also no longer applicable to the unbalanced data classification sample ensemble.

Table 6.

Accuracy of prediction on imbalanced classification data sets

Sample collection	SVM(%)	ICA-SVM(%)	Model of this article(%)
N-GongY	68.84	71.35	72.18
N-ShangY	75.65	76.53	78.17
N-ZongY	68.83	72.3	73.09
N-1-Year-ST	70.67	74.43	75.47
N-2-Year-ST	70.97	71.53	73.16
N-3-Year-ST	63.27	69.23	70.49
N-1-Year-Predict	71.27	74.88	77.17
N-2-Year-Predict	70.18	71.84	75.01
N-3-Year-Predict	69.98	71.47	72.24

Overall, under the balanced and unbalanced data samples, the GWO-SVM-based SME financial distress prediction model proposed in this paper achieves relatively satisfactory results and can be used as an effective method and approach for SME financial distress prediction.

5

Strategies for Solving Financial Difficulties of Small and Medium-sized Enterprises

In the above paper, this paper proposes a GWO-SVM-based financial distress prediction model for SMEs to improve the accuracy of SMEs’ financial distress prediction. After successfully predicting the financial difficulties of SMEs, how to solve the financial difficulties has therefore become an important content that SMEs must think deeply about in their development. This chapter will put forward the corresponding financial predicament solution strategy, in order to bring useful exploration for the enhancement of SMEs’ financial management level. 1)

Scientific financing arrangements

Small and medium-sized enterprises should face up to the objective reality of financing difficulties, scientific financing arrangements, and actively explore different financing channels to realize the diversification of financing risks and the overall cost of financing can be controlled. For example, in addition to external financing means, it is also necessary to make good use of internal financing means, so as to realize more diversified financing channels.

2)

Pay attention to investment risk analysis

In terms of financial investment, it is recommended that small and medium-sized enterprises to do a good job of investment risk analysis, investment risk analysis focuses on the profitability of the investment project as much as possible to make a precise prediction, avoid some features of the investment project to blindly follow the trend, but to do a good job of feasibility analysis. Enterprise managers in the investment analysis need to fully consider the time cost of capital, long-term investment, long-term benefit, investment income discount rate, etc., through the comprehensive and accurate analysis of these indicators to decide whether to invest, if the long-term investment income is difficult to make up for the cost of the investment project does not have the feasibility of the investment project, and vice versa can be invested.

3)

Strengthen internal control

Small and medium-sized financial difficulties need to be solved by utilizing the means that you do not control, through a good internal control mechanism, better for the various factors that lead to financial difficulties of enterprises to effectively deal with, reduce the possibility of financial difficulties. Improvement of the internal control mechanism, the focus is to be in the internal control environment, information communication feedback, risk control measures to continuously adjust and optimize the internal control mechanism to achieve the perfection of the internal control mechanism, so as to be able to do for the enterprise financial risk management and control of good.

4)

Strengthen cash flow management

In view of the financial difficulties of the cash flow crisis, it is recommended that small and medium-sized enterprises attach great importance to the development of cash flow management, set up a correct cash flow management concept, improve the cash flow management system, improve the cash inflow management, outflow management standardization, to ensure cash flow stability. Enterprise cash flow management should emphasize the reasonable cash flow in the enterprise operation, not only to meet the needs of normal operation, but also to have a certain degree of flexibility, can better cope with the fluctuation of the operation. Cash flow management should try to achieve the amount of income for expenditure, reasonable budget, for the annual total cash flow indicators for scientific budget, in the budget indicators to carry out cash flow management.

Due to the small and medium-sized enterprises itself is not enough financial strength, competitive strength is not strong, coupled with the intensification of market competition, small and medium-sized enterprises into financial difficulties are common, in this case, small and medium-sized enterprises must be in the financial difficulties to solve the problem of investing more energy, a comprehensive and good fund-raising, investment, cash flow management, internal control, and other important work, so as to better solve the financial difficulties for the better development of enterprises to provide a good financial security. Good financial security.

6

Conclusion

Combining the Gray Wolf optimization algorithm with the support vector machine model, this paper proposes a GWO-SVM-based financial distress prediction model for small and medium-sized enterprises (SMEs) to optimize the prediction accuracy of financial distress for SMEs. First, the performance evaluation test is carried out on this paper’s model. Comparing the parameter optimization performance of this paper’s model with that of grid search, GA, PSO, and GWO models, the CPU time and classification accuracy of this paper’s model are 48.44s and 87.01%, respectively, which show the optimal parameter optimization performance. On the fitness curve of the optimized SVM, the GWO algorithm converges at 65 iterations, and the fitness value reaches 93.47%, which is the best among the compared models. However, the model in this paper not only converges faster than the GWO algorithm, but also improves the convergence accuracy by 2.87%, which has a significant advantage. In the same modeling dataset for model prediction validity testing, the classification accuracy of this paper’s model can reach up to 93.48%, which is higher than that of PSO-SVM, GA-SVM and GridSearch SVM. For the two types of samples of financial distress SMEs and non-distressed SMEs presenting balanced and unbalanced classification, the classification accuracy of this model can reach up to 93.48%, which is higher than that of PSO-SVM, GA-SVM and GridSearch SVM. Model for empirical comparison of applications. In the balanced and unbalanced classification cases, this paper’s model always has the highest prediction accuracy for multiple different datasets, and the prediction accuracy level is always maintained above 80% in the balanced classification case and above 70% in the unbalanced classification case. Obviously, the GWO-SVM-based SME financial distress prediction model proposed in this paper has good prediction performance, can be widely applied to complex prediction environments, and is an effective method and approach for SME financial distress prediction.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Research on Financial Difficulties Prediction and Optimization Strategies of Small and Medium-sized Enterprises Based on Support Vector Machine

Mingyue Duan

Published Online: Sep 29, 2025

Received: Jan 01, 2025

Accepted: Apr 16, 2025

DOI: https://doi.org/10.2478/amns-2025-1097

KeywordsPrincipal component analysis, Gray wolf optimization algorithm, Support vector machine, Financial distress prediction

© 2025 Mingyue Duan, published by Sciendo.

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Principal component analysis, Gray wolf optimization algorithm, Support vector machine, Financial distress prediction