Cluster Analysis Algorithm-Oriented Identification of Key Issues and Construction of Practical Paths for Modernization of Vocational Education Governance

Vocational education governance refers to the process in which the main body of vocational education governance plays the function of scientific governance and enhances the effectiveness of vocational education according to the objectives of vocational education training, following the laws of vocational education development and relying on vocational education resources [1-2]. Under the new historical orientation, promoting the modernization of vocational education governance is a political requirement for realizing the visionary goal of socialist modernization, and it is also the subject of accelerating the construction of modern vocational education system and promoting the high-quality development of vocational education [3-5].

As a natural choice to achieve the goal of high-quality development of vocational education, modernizing the governance of vocational education is an important grasp to promote the modernization of the education governance system and governance capacity in an all-round way. Vocational education governance modernization is a continuous dynamic development process in which all fields and levels of vocational education governance activities make corresponding changes and transcendence in order to promote the modernization and development of the state, society and human beings, with clear generative logic and rich scientific connotation [6-9]. Accompanied by the deep integration of the new round of information technology and real industry, such as big data, artificial intelligence and the Internet of Things, the real industry has a surge in the demand for talents with applied technology, and at the same time, it also puts forward higher requirements for the modernization of the governance of vocational education [10-14]. As an important content of the modernization of vocational education governance, building a modernized governance system for vocational education at the undergraduate level is a key initiative to cultivate high-level technical talents, which is conducive to matching the demand for innovative technical and skilled talents in the industry and promoting the high-quality development of vocational education [15-19]. In view of this, based on the background of skill-based society, clarifying the scientific connotation and value implication of the modernization of undergraduate vocational education governance, exploring the reality of the dilemma of the modernization of vocational education governance in undergraduate level institutions and exploring the specific practice path are of great practical significance for the comprehensive promotion of the high-quality development of vocational education [20-22].

This paper collects the relevant elements in related studies related to the identification of key issues in the modernization of vocational education governance, and streamlines the relevant factors into key identification elements by using principal component analysis. After constructing a standardized sample matrix, the correlation coefficients between the key factors are calculated, and the eigenvalues of each element are obtained by solving the characteristic equation to get the contribution rate of each element to the identification of the key issues of modernization of vocational education governance, so as to obtain the main indexes of the key issue identification. Then the CUBN clustering algorithm is used to identify the noise points in the sample data, and the nearest neighbor distance method is used to perform categorization processing on the data. Finally, the principal component analysis method and clustering algorithm can be used to construct a practical platform for identifying key issues in the modernization of vocational education governance. The study first analyzes the effectiveness of the CUBN clustering algorithm to lay the foundation for the reliability of the identification results of the practice platform. Then the vocational colleges and universities in Province H are selected as the case study objects, and the key problems of vocational education governance modernization are identified and analyzed by clustering analysis. According to the clustering results, we intervene in the existing problems and analyze the improvement effect of the key problems of modernization of vocational education governance.

2

Method

2.1

Methodology for Identifying Key Issues and Establishing Indicators

From the relevant research data, it is found that [23], the key factors for identifying the key issues of modernization of vocational education governance mainly include disciplinary teams, financial supply, talent training, scientific research, disciplinary construction, management system and cultural heritage. Because the identification factors of key issues of modernization of vocational education governance are very many, and the relationship between them is more complex, which leads to the complex relationship between various indicators when designing key issue identification indicators. Therefore, this paper mainly uses the principal component analysis method in the process of designing the key problem identification indicators for modernizing vocational education governance. The method of streamlining multi-indicators and multi-variables into a few main indicators is called principal component analysis (PCA) [24], which is also known as feature extraction, and its basic idea is to achieve the purpose of variance optimization by transforming the multi-dimensional data set represented by the effective feature components with fewer dimensions, while maintaining the main information of the original data.

The following is constructed by identifying the main components of key issue identification in the modernization of vocational education governance as the constituent elements of key issue identification using principal component analysis. 1)

The design of the sample matrix (assuming that there is n subject to be evaluated and m evaluation indicators) is a single sample: (1) $x_{i} = (x_{i 1}, x_{i 2}, x_{i 3}, \dots, x_{i m}) = (,,, \dots,)$

The entire sample space is constructed as: (2) $X = [\begin{matrix} X_{i n} & \dots & X_{i m} \\ ⋮ & ⋱ & ⋮ \\ x_{n 1} & \dots & x_{n m} \end{matrix}]$ 2)

By standardizing the sample matrix and eliminating the effects among its indicators, it is obtained: (3) $X = [\begin{matrix} a_{i 1} & \dots & a_{i m} \\ ⋮ & ⋱ & ⋮ \\ a_{n 1} & \dots & a_{n m} \end{matrix}]$

$a_{i j} = (x_{i j} - \bar{x_{j}}) / \sqrt{\frac{{(x_{i j} - {\bar{x}}_{j})}^{2}}{n}} (i = 1, 2, 3 \dots, n; j = 1, 2, 3 \dots, m)$ of them. (4) ${\bar{x}}_{j} = \frac{1}{n} \sum_{j = 1}^{n} x_{i j} (j = 1, 2, 3 \dots, m)$ 3)

Analyzing the correlation of the indicator system. The statistical method of studying the degree of closeness between evaluation indicators is called correlation analysis. Because after the characterization of the evaluation indicators, there is usually a reuse of the information of the evaluation object, which is determined by the correlation between the quantitative indicators, but this situation will reduce the scientificity and rationality of the evaluation. In order to avoid this situation, it is necessary to analyze the correlation of the evaluation indicators, that is, by reaching the correlation coefficient analysis of each indicator, calculate their correlation coefficients, and according to the principle of correlation to subtract the evaluation indicators with larger correlation coefficients, with the aim of eliminating the impact of the duplication of the information reflected in them on the results, and to ensure the reasonableness and effectiveness of the evaluation indicator system. The correlation coefficient matrix for this sample matrix has been derived below: (5) $R = [\begin{matrix} r_{11} & \dots & r_{1 m} \\ ⋮ & ⋱ & ⋮ \\ r_{m 1} & \dots & r_{m m} \end{matrix}]$

Where r_ij is the correlation coefficient between the original variables x_i and x_j, which is modeled in the following matrix: (6) $r_{i j} = \frac{\sum_{k = 1}^{n} (a_{k i - \bar{a_{1}}}) (a_{k i - \bar{y_{1}}})}{\sqrt{\sum_{k = 1}^{n} {(a_{k i - \bar{a_{i}}})}^{2} \sum_{k = 1}^{n} {(a_{k i - \bar{a_{j}}})}^{2}}} (i = 1, 2, 3 \dots, n; j = 1, 2, 3 \dots, m)$

$\bar{a_{1}} = (\sum_{k = 1}^{n} a_{k i}) / n$ of them. (7) $r_{i j} = \frac{\sum_{k = 1}^{n} (a_{k i - \bar{a_{1}}}) (a_{k i - \bar{a_{1}}})}{\sqrt{\sum_{k = 1}^{n} {(a_{k i - \bar{a_{i}}})}^{2} \sum_{k = 1}^{n} {(a_{k i - \bar{a_{1}}})}^{2}}} (i = 1, 2, 3 \dots, n; j = 1, 2, 3 \dots, m)]$

where ${\bar{a}}_{i} = (\sum_{k = 1}^{n} a_{k i}) / n$ .

R is a real symmetric matrix (i.e., $r_{i j} r_{j i}) =$ ), it is sufficient to compute the upper or lower triangles. 4)

Find the eigenvalues and eigenvectors of the correlation coefficient matrix. Its eigenvalues λ_i(i = 1, 2, 3⋯, m)(i = ) can be found by solving the eigenequation $| λ K - R |$ and arranging them in order of magnitude, i.e., λ₁ ≥ λ₂ ≥ ⋯ ≥ λ_m ≥ 0. Then its corresponding eigenvalues λ_i eigenvectors e_i = (i = 1, 2, 3⋯, m) = (i = ) are found separately, assuming $| e_{i} | = 1$ here, i.e., $\sum_{j = 1}^{m} e_{j i}^{2} = 1$ , where e_ij denotes the jth component of the vector.

5)

Calculate the contribution rate of key indicators in the identification of key issues of modernization of vocational education governance as well as the cumulative contribution rate (i.e., the degree of contribution of key issue identification indicators to the original indicators).

Its contribution rate is: (8) $\frac{\sum_{k = 1}^{i} λ_{k}}{\sum_{k = e}^{m} λ_{k}} (i = 1, 2, 3 \dots, m)$

The cumulative contribution is: (9) $\frac{λ_{i}}{\sum_{k = i}^{m} λ_{k}} (i = 1, 2, 3 \dots, m)$

According to the principle of normal distribution, take the first, second, ..., k(k ≤ m) key problem identification indicators corresponding to the eigenvalues whose cumulative contribution rate reaches 85%-95%, i.e. λ₁, λ₂, ⋯, λ_k. 6)

Calculate the load of key problem identification indicators. The calculation method is as follows: (10) $w_{i j} = m (z_{i}, x_{j}) = \sqrt{λ_{i}} e_{i j} (i, j = 1, 2, 3 \dots, m)$

From this, the scores for each of the existing key problem identification indicators can be further calculated: (11) $Z = [\begin{matrix} z_{11} & \dots & z_{1 m} \\ ⋮ & ⋱ & ⋮ \\ z_{n 1} & \dots & z_{n m} \end{matrix}]$

Through the previous principal component analysis, on the basis of the components of the identification indicators of the key issues of vocational education governance modernization constructed in related studies, through the acquisition of data, the characteristic vectors and eigenvalues are analyzed, and the correlation effectiveness is analyzed, and the main indicators of the key issues of vocational education governance modernization identified by the students are obtained, which are respectively governance level, student development, education and teaching, integration of industry and education, policy guarantee, education management effect, graduate employment quality, teachers’ personal growth, 10 aspects of the integration effect of industry and education and the effect of system implementation.

2.2

Analysis of Critical Problem Identification Based on CUBN Clustering

CUBN is a comprehensive clustering method based on density, grid and distance. The data space is first divided into grid cells, then the classes in each cell are identified, and finally the connected classes are combined into the final clustering result. For ease of description, the classes in each cell are referred to as subclasses in the following. The CUBN method uses the following approach to identify subclasses in a grid cell. All “boundary points” (including true boundary points, noise points, and interior points) in a grid cell are first identified using a density-based criterion. The noise points in it are then eliminated and the true boundary points are categorized using a distance-based criterion, and finally all non-boundary points (interior points) are clustered into the subclasses to which they belong.

The CUBN algorithm first normalizes the input data to between 0 and 1. The input dataset is then assigned to k disjoint cells in d-dimensional space. In real-world problems, data points are usually distributed non-equilibrium in the data space, so the number of non-empty grid cells is often much smaller than the input parameter k, and the algorithm only needs to continue in the non-empty grid cells. In each non-empty grid cell, the subclasses therein are identified separately. In addition, this algorithm can be designed as a parallel computing algorithm, which will greatly improve the efficiency of algorithm execution.

2.2.1

Noise Point Cancellation Algorithm

Boundary points found by the boundary point recognition algorithm are categorized into three types which are true boundary points, noise points and interior points. Noise points are misidentified as boundary points due to their low density. There may be less dense regions within the class, which is why these internal points are also misidentified as boundary points. The difference between noise points and boundary and interior points is that noise points must be isolated, i.e., there are no interior or boundary points adjacent to them. It is based on this feature that the present algorithm removes the noise points from the set of boundary points.

2.2.2

Boundary point categorization algorithm

This algorithm applies the Nearest Neighbour Distance method [25] to group boundary points, i.e. boundary points that are close to each other are grouped together. The critical distance e is taken as p + r. If some boundary points do not have neighbouring boundary points, then the point is internal and it is removed from the set of boundary points.

2.2.3

Computational complexity

To discuss the computational complexity of the algorithm, assume that the total number of nodes in the input sample set S is n, the total number of boundary points is m, and the total number of internal nodes is n − m. The algorithm first scans the input sample set S once and assigns the input samples to k grid cells with a computational n. It then identifies subclasses within each cell. Assuming that the total number of nodes within grid cell i is n_i and the total number of boundary points is m_i, the total number of internal nodes is n_i − m_i.

In the boundary point identification algorithm, for any node x, the distance between 2 and other nodes in the cell is calculated and compared with r, which is called a single calculation. For each boundary point, the distance between x + B and the other nodes in the cell is calculated once with all the remaining nodes and the computation amount is m_i × n_i. For each internal point, the computation amount is at least 1 and at most n_i. Corrosion operations are performed in the positive and negative directions in each dimension of the d-dimensional space, so the best computational complexity of the boundary point identification algorithm is $2 \times d \times (m_{i} \times n_{i} + (n_{i} - m_{i}))$ and the worst computational complexity is $2 \times d \times (m_{i} \times n_{i} + (n_{i} - m_{i}) \times n_{i}$ .

The computational complexity of the noise point elimination algorithm is $(n_{i} - m_{i}) \times m_{i}$ . The computational complexity of the boundary point categorisation algorithm is independent of n_i and is only related to m_i, which is m_i × m_i. The computational complexity of the interior point categorisation algorithm is $(n_{i} - m_{i})$ × m_i. So the worst computational complexity for identifying subclasses within each cell is $2 \times d \times (n_{i} \times n_{i}) + 2 \times m_{i} \times n_{i} - m_{i} \times m_{i}$ .

The subclass merging algorithm scans each subclass once and has a computational complexity of n.

In summary, the computational complexity of algorithm CUBN is: (12) $2 \times n + \sum_{i = 1}^{k} 2 \times d \times n_{i}^{2} + 2 \times m_{i} \times n_{i} - m_{i} \times m_{i}$

where m_i << n_i, $n = \sum_{i = 1}^{k} n_{i}$ , $m = \sum_{i = 1}^{k} m_{i}$ .

The computational complexity of the algorithm CUBN is approximate linear time complexity, the algorithm is executed efficiently and is suitable for clustering problems with large-scale datasets.

2.3

Practical Paths for Identifying Key Issues in Modernising Vocational Education Governance

This paper constructs a practice platform for the identification of key issues in the modernisation of vocational education governance based on the principal component analysis model and cluster analysis model, and the specific practice path is shown in Figure 1. The practice platform takes an integration and systemic perspective, and is constructed with the analysis engine as the center point and the identification of key issues related to modernizing vocational education governance as the main element. The practice platform includes core components such as data management, data mapping, analysis engine, analysis algorithms, visual presentation, and content modeling. The data management component is used to pre-process the collected data. The raw data collected by the system is often heterogeneous, with different formats (e.g., structured, semi-structured, unstructured documents, videos, images, relational databases, object repositories) and levels of granularity, and may involve many irrelevant attributes. Therefore, the data management component needs to pre-process the collected data into an appropriate format that can be used as input for a particular learning analytics method, which includes data cleansing, data integration, data transformation, data normalisation, etc. The analysis algorithm component is the algorithmic basis for the analysis engine to perform analysis tasks. In order to enhance the reusability of the analysis algorithms, the analysis algorithm component is independent of the analysis engine and is used to store various analysis method operations and their application specifications. It is worth mentioning that the Analysis Algorithm Component reorganises the above methods to form analysis modules corresponding to the objectives, such as monitoring, evaluation, identification, etc., and each analysis module is responsible for managing the list of analysis methods associated with it. The analysis engine acts as a pivot between the different components, using these generated key issue identification metrics, obtaining the data to be analysed from the data manager and labelling it with data in the data mapper, as well as calling cluster analysis methods from the analysis algorithms component to carry out the data analysis, with the results of the analysis ultimately being presented visually or fed back into the target selection menu as interactive data, for example, to make vocational intervention recommendations for modernising educational governance.

3

Results and discussion

3.1

Analysis of clustering algorithm effectiveness evaluation

In the practical path of identifying key issues of modernisation of vocational education governance constructed in this paper, the clustering analysis algorithm is the main component of the data analysis module, so it is necessary to assess and analyse the effectiveness of the CUBN clustering algorithm first, and to explore its feasibility in the path of identifying key issues of modernisation of vocational education treatment. The results of the effectiveness analysis of the clustering algorithm are shown in Figure 2, with (a)-(c) representing the data samples, the CUBN clustering results, and the DBSCAN clustering results, respectively. The number of data sample points used in the clustering algorithm effectiveness evaluation experiment n=80,000, and the data samples contain six classes with different densities and noisy data. When the experimental parameters are p=0.03, k=100, and t=6, as seen from the results of running the CUBN clustering algorithm in Fig. 2(b), the algorithm not only successfully identifies the six classes (represented by different colours), but also filters out the noise points and interference points. For comparison, the experimental results of the DBSCAN algorithm on the same dataset show that the two ellipses with interconnected interference points between them are grouped into one class when MinPts=5 and Eps=0.4.After dividing the data space into a grid, the DBSCAN clustering method only examines the number of data points contained in the grid cells, and if it is greater than a predetermined parameter, the cell is considered to be dense, and the classes are the connected dense cells. Through the comparative study of the CUBN method and the DBSCAN method, it is concluded that although the CUBN algorithm employs the grid clustering method like the DBSCAN method, the correctness of the clustering results is significantly better than that of the DBSCAN method.The CUBN method combines the advantages of the density-based and grid clustering methods, and not only is the algorithm executed efficiently, but also identifies the clusters of arbitrary shapes, filtering noisy data. The algorithm can accurately determine the boundaries of various categories in the data space. And it can filter out noise points. The boundary point categorisation algorithm will categorise the points within the same boundary layer into one boundary class, and the subsequent internal point categorisation algorithm will be performed on this boundary layer, which will not cause misclassification of internal points. Therefore, the existence of the boundary layer does not affect the clustering result.The CUBN algorithm merges the subclasses that are close to each other in each cell into the final clustering result through the subclass merging algorithm. The merged subclasses can form any shape or size, i.e., the CUBN algorithm can identify classes of any shape and size in the data space. It can be seen that the CUBN clustering algorithm has strong feasibility and effectiveness in the practical platform for identifying key issues in the modernization of vocational education governance.

3.2

Basic analysis of the modernisation of governance in vocational education

3.2.1

Overview of study cases

Among the higher vocational colleges and universities in Province H, divided by the type of organiser, there are 5 public schools among the 19 higher vocational colleges and universities in Province H, which are JM College, RJ College, WY College, ZF College and TY College, accounting for 26.32% of the higher vocational colleges and universities in Province H. There are 2 mixed ownership institutions, namely HZ College and WZ College. There are 12 private schools, and private higher vocational colleges and universities account for 63.16% of the total number of higher vocational colleges and universities in H province. Among them, there is 1 high-level higher vocational institution with Chinese characteristics (JM College), 1 national demonstrative higher vocational institution (HZ College), 1 national backbone higher vocational institution (JM College), and 3 provincial high-quality schools (HZ College, JM College, WY College). In order to improve the quality and level of higher vocational colleges and universities in Province H, in January 2022, the Department of Education of Province H issued a project to establish high-level vocational colleges and professional construction projects. At the same time, it is proposed that higher vocational colleges and universities should take the initiative to buttress the layout of the province’s leading industries and strategic emerging industries, and should actively improve the conditions for running schools. They should constantly deepen the integration of industry and education and cooperation between schools and enterprises, innovate the talent cultivation mode, strengthen the characteristics of the type of vocational education, and promote the effective articulation of the education chain and talent chain with the industrial chain and innovation chain. Based on this, this study takes 19 vocational colleges and universities in Province H as the case study objects, uses the proposed practice platform to identify the key problems in the modernisation of vocational education governance in different institutions, conducts cluster analysis based on the scores of each identification index obtained from the analysis, and intervenes and rectifies the modernisation of vocational education governance in various institutions according to different cluster characteristics.

3.2.2

Results of the identification of key issues in vocational education governance

1)

Descriptive statistical analysis

This study used the Key Issues Identification and Analysis Platform to identify and analyze descriptive statistics on the key issues of modernizing the governance of vocational education in the above institutions. These statistical indicators cover various aspects such as the maximum value, minimum value, mean, standard deviation, and variance of the variables under study. The descriptive statistical analysis of the scores of the identification indicators of the key issues of modernisation of governance of vocational education in different institutions was carried out using SPSS software, and the results of the analysis are shown in Table 1. The results of the identification of key issues for modernising the governance of vocational education in the 19 vocational colleges found a wide range of identification scores for governance level issues, ranging from a minimum of 0.39 to a maximum of 4.85, with an overall average identification score of 2.42. This data demonstrates the differences in the level of governance of modernization of vocational education governance in different institutions. The results of the analysis of the identification of the key issues related to teaching and learning in modernizing vocational education governance in institutions ranged from 0.52 to 4.67, showing some variation. The average score for identifying this critical issue was only 2.47, indicating overall poor and stable performance. This data reflects the poor focus on education and teaching in the process of modernizing educational governance in all vocational institutions. The results of descriptive statistics can be found that the results of identifying the key issues of vocational education governance modernisation in vocational colleges and universities in Province H are poor, and there are big problems in education governance that need to be improved.

2)

Cluster analysis results

Subsequently, the CUBN clustering algorithm will be applied for grouping and the first task is to determine the t-value, i.e. to decide the number of categories into which to divide. Using the elbow rule, the t-value is incremented gradually from 1 to 10, and the optimal number of clusters is determined by observing the curve of change in the clustering effect, i.e., by determining the t-value at which the effect of the model starts to decrease significantly. The elbow rule relies on the complexity of the shape of the clusters to determine the number of clusters, for data sets with significant distinguishing features, when a specific threshold is reached, the degree of aberration will show a substantial improvement, and the subsequent downward trend will gradually level off. The results of the analysis on the optimal number of clusters are shown in Fig. 3, from which it can be seen that when the value of t for the CUBN clustering algorithm is taken as 5, a significant change in the trend is observed. Based on this observation, it was determined that the optimal value of t should be taken as 5, which means that the 19 vocational colleges and universities are most appropriately classified into four categories with respect to the key issues of modernisation of vocational education governance.

Table 1.

Descriptive statistical analysis results

Index	N	Minimum value	Maximum value	Mean value	Standard deviation
Management level	19	0.39	4.85	2.42	0.67
Student development	19	0.16	4.45	3.19	0.4
Education teaching	19	0.52	4.67	2.47	0.17
Production fusion	19	0.87	4.44	2.94	0.99
Policy security	19	0.92	4.05	3.49	0.61
Education management effect	19	0.71	4.69	2.25	0.79
Employment quality of graduates	19	0.01	4.28	3.28	0.48
Personal growth of teachers	19	0.46	4.85	2.15	0.61
Effect of production and education	19	0.11	4.29	2.73	0.41
Policy execution effect	19	0.8	4.46	3.09	0.14

The CUBN clustering algorithm in the practice platform was used to successfully identify five different groups in the 19 vocational colleges and universities participating in this key issue identification of vocational education governance modernization. The validity of the clustering results was further confirmed by using the ANOVA table obtained from the CUBN clustering analysis.The results of the ANOVA analysis are shown in Table 2.The Sig values (0.000) of the 10 key issue identification indicators are all lower than 0.01, which fully indicates that these indicators have a significant influence on the clustering results, thus verifying the accuracy of this clustering analysis.

Table 2.

ANOVA analysis of cluster analysis

Index	Clustering		Error		F	Sig.
Index	Mean square	Freedom	Mean square	Freedom	F	Sig.
Management level	4.281	4	0.025	14	1.653	0.000
Student development	4.124	4	0.039	14	2.867	0.000
Education teaching	4.266	4	0.045	14	2.991	0.000
Production fusion	3.556	4	0.03	14	1.251	0.000
Policy security	4.995	4	0.067	14	1.825	0.000
Education management effect	2.154	4	0.057	14	2.221	0.000
Employment quality of graduates	2.639	4	0.024	14	1.366	0.000
Personal growth of teachers	4.188	4	0.068	14	2.397	0.000
Effect of production and education	2.685	4	0.049	14	2.535	0.000
Policy execution effect	2.776	4	0.031	14	2.169	0.000

The values of the 10 key issue identification indicators of the vocational institutions in these five categories were averaged in order to analyse the characteristics of the key issue of modernising the governance of vocational education for each group of institutions, and the results obtained from the cluster analysis are shown in Table 3. There are a total of 2 institutions in the first category, and their identification scores of key issues of modernisation of educational governance are relatively high, demonstrating the importance institutions attach to the governance of vocational education. There are a total of 4 vocational institutions in the second category, and they perform relatively well in identifying key issues related to modernizing vocational education governance. There are three and five institutions in the third and fourth categories, respectively, and they are slightly less successful in identifying the key issues of modernisation of vocational education governance than the institutions in the first two categories. Together, these phenomena indicate that the third and fourth categories of institutions need to be further improved and upgraded in the process of modernizing the governance of vocational education. Category 5 vocational institutions, of which there are five, have an average score of between 0.04 and 1.26 on each of the key issue identification indicators, with the worst performance in the area of personal growth of teachers (0.04). In summary, through the analysis of the data, five groups of vocational colleges and universities with different characteristics of vocational education governance modernisation and performance of key issues have been successfully summarised, which helps to understand their vocational education governance needs and characteristics more precisely, and provides useful references for the intervention and construction of vocational education governance modernisation.

Table 3.

The average of different clustering indices

Index	Cluster 1 (n=2)	Cluster 2 (n=4)	Cluster 3 (n=3)	Cluster 4 (n=5)	Cluster 5 (n=5)
Management level	4.83	3.13	2.8	0.59	0.75
Student development	4.87	3.54	2.04	4.97	0.53
Education teaching	4.29	3.69	2.63	0.91	0.83
Production fusion	4.72	3.34	2.13	4.14	0.37
Policy security	4.92	4.32	3.94	3.44	0.83
Education management effect	4.35	3.26	2.16	1.26	0.22
Employment quality of graduates	4.82	4.03	3.74	2.55	1.26
Personal growth of teachers	4.59	3.03	1.98	1.11	0.04
Effect of production and education	4.44	3.53	3.61	1.51	0.56
Policy execution effect	4.62	4.03	3.69	1.86	1.25

3.3

Analysis of the Practical Effectiveness of the Platform for Identifying Key Issues

This paper adopts the independent sample t-test method to test and analyse the improvement and construction effect of vocational education governance modernization in 19 vocational colleges and universities in Province H, and to explore the application practice effect of the key issue identification practice platform proposed in this paper. The results of the comparative analysis of the differences between the identification of key issues of the modernisation of vocational education governance and the improvement before and after the modernisation of vocational education governance in different clustered colleges and universities are shown in Table 4. A-J in the table represent governance level, student development, education and teaching, industry-teaching integration, policy guarantee, education management effect, graduate employment quality, teachers’ personal growth, the effect of industry-teaching integration, and the effect of system implementation, respectively. The results show that there is a significant difference between Cluster 3, Cluster 4 and Cluster 5 vocational colleges and universities in the 10 key issue identification indexes (P=0.048, 0.026, 0.014<0.05), which suggests that the application of the practice platform for identifying the key issues of modernisation of vocational education governance has a significant role in the improvement of education governance in vocational colleges and universities. In the analysis of differences between Cluster 1 and Cluster 2 institutions, there is no significant difference (P=0.062, 0.051>0.05) in the test of the 10 indicators of key issue identification, which may be due to the fact that the original modernisation of vocational education governance in Cluster 1 and Cluster 2 institutions is already more mature.

Table 4.

Education governance improvement difference analysis

Cluster	Stage	A	B	C	D	E	F	G	H	I	J	P
1	Before	4.83	4.87	4.29	4.72	4.92	4.35	4.82	4.59	4.44	4.62	0.062
1	After	4.91	4.91	4.98	4.94	5.00	4.99	4.98	4.94	5.00	4.92	0.062
2	Before	3.13	3.54	3.69	3.34	4.32	3.26	4.03	3.03	3.53	4.03	0.051
2	After	4.4	4.2	4.17	4.44	4.58	4.26	4.18	4.14	4.37	4.03	0.051
3	Before	2.8	2.04	2.63	2.13	3.94	2.16	3.74	1.98	3.61	3.69	0.048
3	After	4.1	3.92	4.19	3.50	4.13	4.23	3.7	4.07	4.09	3.72	0.048
4	Before	0.59	4.97	0.91	4.14	3.44	1.26	2.55	1.11	1.51	1.86	0.026
4	After	3.74	4.98	3.49	4.26	3.78	3.57	3.86	3.72	3.6	3.45	0.026
5	Before	0.75	0.53	0.83	0.37	0.83	0.22	1.26	0.04	0.56	1.25	0.014
5	After	3.4	3.34	2.36	2.22	2.77	2.02	2.65	2.08	3.38	3.28	0.014

4

Conclusion

This paper uses principal component analysis to extract the eigenvalues of the elements related to the identification of key issues in the modernisation of the governance of vocational education, and determines the main indexes for the identification of key issues based on the contribution rate. It then combines principal component analysis and cluster analysis to design a practical path for the identification of key issues of vocational education governance modernisation, and assists in intervening in the improvement of education governance modernisation in vocational colleges and universities through the identification of key issues and the clustering results. The CUBN clustering algorithm was tested to not only successfully identify the sample data of six different classes (represented by different colours), but also filter out the noise points and interference points in the data.

The identification results of key issues of vocational education governance modernisation among 19 vocational colleges and universities in Province H are poor and need to be improved urgently.The CUBN clustering algorithm successfully identifies 5 different groups of 19 vocational colleges and universities participating in this identification of key issues of vocational education governance modernisation. Among them, there are 5 vocational colleges and universities in the fifth category, and in the scores of each key issue identification index, the average score is between 0.04 and 1.26, and there is a big problem in the modernisation of vocational education governance. After applying the practice platform, it was found that it has a significant role in promoting the construction and improvement of modern educational governance in vocational colleges.

The above analysis shows that the platform for identifying and analysing key issues in modernizing the governance of vocational education proposed in this paper can help reform the governance of vocational colleges and universities, and truly achieve the high-quality development of modernised education governance.

Sprache:: Englisch

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Fachgebiete der Zeitschrift:: Biologie, Biologie, andere, Mathematik, Angewandte Mathematik, Mathematik, Allgemeines, Physik, Physik, andere

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Cluster Analysis Algorithm-Oriented Identification of Key Issues and Construction of Practical Paths for Modernization of Vocational Education Governance

Fan Li

Online veröffentlicht: 24. März 2025

Eingereicht: 24. Nov. 2024

Akzeptiert: 25. Feb. 2025

DOI: https://doi.org/10.2478/amns-2025-0702

SchlüsselwörterPrincipal component analysis, Characteristic equation, CUBN clustering, Key issue identification, Vocational education governance

© 2025 Fan Li, published by Sciendo

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

Schlüsselwörter
Principal component analysis, Characteristic equation, CUBN clustering, Key issue identification, Vocational education governance