# Multivariate Statistical Analysis of Quality Improvement Effect of Innovation and Entrepreneurship Education Based on Random Matrix Theory

Authors: Xiaohang Wu; Zhihua Qin
Journal: Mathematical Problems in Engineering
 (2022)

---

## Abstract

The reform can better improve students’ innovation and entrepreneurial skills and comprehensively improve the innovation and entrepreneurial competitiveness of college students, which is conducive to their survival and development in the market. Therefore, this paper analyzes the data generated in the educational process from the perspective of educational data mining and studies students’ entrepreneurial interests and motivations so as to improve the quality of students’ entrepreneurial guidance. The knowledge map, an important visualization tool in personalized learning systems, is used as a research object to analyze students’ online evaluation data. We develop a prototype system for improving teaching quality—a knowledge map generation and knowledge point recommendation path analysis system. We hope to further explore new ways and methods to promote the reform of innovation and entrepreneurship education in colleges and universities, giving full play to the proper role and value of innovation and entrepreneurship education.


---

## Body

## 1. Introduction

Theoretically speaking, “dual innovation” covers the core competitiveness of college students, the technological innovation of college students, and the breakthrough power of college students’ business model. As a college counselor, if you can start from these aspects, you will have a complete and clear understanding of the “dual innovation” of college students. The analysis of these aspects will enable us to observe the core strengths and weaknesses of college students in the field of “dual innovation” [1,2]. In the current environment where full competition highlights the dynamics of the market, if students can survive in the market through “dual innovation,” it will bring them great rewards in terms of wealth and life growth experience [3]. However, some students do not take full advantage of innovation and entrepreneurship training to improve their overall skills because they believe it will not help them to seek employment [4].Through the innovation and entrepreneurship education reform, the significance of innovation and entrepreneurship education is really highlighted, and the smooth employment of college students is promoted. For example, under the call of innovation and entrepreneurship education reform, modern colleges and universities are more actively exploring effective ways for students to exercise their practical ability, such as creating school-enterprise cooperation and teaching mode of university competition system, and so on, increasing the link for students to go deeper into enterprises for practical exercise, allowing professional and technical masters of enterprises to guide students’ practical ability and really improve students’ working ability comprehensively [5–8]. The competition system enhances students’ competitive consciousness, cultivates good competition and cooperation spirit, and has more advantages than disadvantages for the overall training and development of students [9]. Such an educational reform is conducive to the development of students’ innovative and entrepreneurial skills, enabling them to have a stronger competitive edge in a highly competitive workplace [10].In response to the current problems in entrepreneurship education data mining, such as the difficulty of comprehensively considering all the answer process records of students in the examination and overreliance on manual analysis and processing of data, this paper proposes a knowledge graph construction model based on text classification and cluster analysis, naming it KGG (knowledge graph generation) model, which is based on analyzing the online answer data of students collected by the intelligent assessment system. The model is based on the analysis of the online answer data collected by the intelligent assessment system, using text classification techniques to automatically classify assessment ventures into knowledge points and studying the association properties between assessment ventures and the knowledge points to which they belong [11]. The Delphi method was used to analyze the weights of the factors that determine the degree of mastery of students’ influence on entrepreneurship [12]. Factors that influence this are the number of correct and incorrect answers, the length of the answer choice path, and the number of correct choices as a proportion of the length of the answer choice path [13]. Students' mastery on the assessment venture was translated into students' learning characteristics on the knowledge points [14]. Student classes with similar learning characteristics are obtained through a clustering algorithm, and the answer characteristics of students in each class are extracted to correlate students and generate a student knowledge map. The model solves the problem of overreliance on manual processing of data in traditional educational analysis by classifying students according to different characteristics and helping teachers to develop corresponding personalized instructional programmes for different categories of students [15].


## 2. Analysis of the Dimensions Related to Innovation and Entrepreneurship among University Students

### 2.1. Risk Dimensions for University Students

The scientific and effective education of university students in “dual innovation” has been slowly developed from the practice of university students in “city creation” [16]. The risk analysis of university students' “dual innovation” is the starting point of university students' innovation and entrepreneurship education [17]. As a college counselor, it is important to understand the competitiveness of college students’ entrepreneurship and innovation and to improve the management effectiveness of college students, which will significantly reduce the risks faced by college students in the process of participating in the competition and can avoid losses. The full application of the “double innovation” competitiveness combined with their own capital market and social value is to improve the market evaluation of college students [8].


### 2.2. Innovation Dimension for University Students

From a technological innovation perspective, university students may have weak application technology innovation ability and innovative execution ability of new application products [18]. If a university student wants to continue and develop in a fiercely competitive market, he or she must break the inherent management stubbornness in the university students themselves. Accelerating the pace of new technological innovation and rationalizing the process of applying new technologies to actual production into production capacity and service efficiency are two qualities that university students with the competitiveness of “dual innovation” must possess [19].


## 2.1. Risk Dimensions for University Students

The scientific and effective education of university students in “dual innovation” has been slowly developed from the practice of university students in “city creation” [16]. The risk analysis of university students' “dual innovation” is the starting point of university students' innovation and entrepreneurship education [17]. As a college counselor, it is important to understand the competitiveness of college students’ entrepreneurship and innovation and to improve the management effectiveness of college students, which will significantly reduce the risks faced by college students in the process of participating in the competition and can avoid losses. The full application of the “double innovation” competitiveness combined with their own capital market and social value is to improve the market evaluation of college students [8].


## 2.2. Innovation Dimension for University Students

From a technological innovation perspective, university students may have weak application technology innovation ability and innovative execution ability of new application products [18]. If a university student wants to continue and develop in a fiercely competitive market, he or she must break the inherent management stubbornness in the university students themselves. Accelerating the pace of new technological innovation and rationalizing the process of applying new technologies to actual production into production capacity and service efficiency are two qualities that university students with the competitiveness of “dual innovation” must possess [19].


## 3. Knowledge Graph Construction Model Ideas

The model in this paper is based on textual classification and methods such as Delphi method and cluster analysis to textually analyze the mapping relationship between the measured entrepreneurship and the knowledge points and to extract the students’ individual mastery values on each entrepreneurship by combining the data from the students’ answer process on each entrepreneurship into students’ learning characteristics on each knowledge point [20]. The clustering algorithm was used to classify students into categories with common characteristics based on their different learning characteristics on each knowledge point. The feasibility of the clustering algorithm is verified, and the learning characteristics of each group of students are analyzed to generate a student knowledge map with the same characteristics by combining the learning characteristics of each group of students. The general flowchart of the model is shown in Figure 1.Figure 1
General flow diagram of the model.


### 3.1. Knowledge Graph Construction Model Building Steps

This section will explain how to use the algorithm in data mining to analyze the entrepreneurship and detail data in the evaluation process step by step to build a knowledge map to reduce the cost of human and material resources, mainly including four steps: evaluation and entrepreneurship text classification, student feature extraction, cluster analysis, and knowledge map construction. It is described in detail below.The evaluation entrepreneurship and knowledge points are automatically associated through text classification. A knowledge graph is essentially a knowledge base called a semantic network, i.e., a knowledge base with a directed graph structure. In layman’s terms, a knowledge graph is a data structure composed of entities, relationships, and attributes. It is the database 2.0. Due to the large number of evaluation entrepreneurship, the problem of manual classification by experts is solved, and this method has high cost and low efficiency, and the classification effect is determined by the accuracy of model classification. The evaluation entrepreneurship text classification in this section includes the extraction of entrepreneurship knowledge point mapping relationship based on TF-IDF and VSM, word segmentation and stop word filtering, text feature extraction, model classification, result evaluation, and classification result output. The text classification process is shown in Figure2, and the entrepreneurial text classification process in this paper is shown in Figure 3.Figure 2
Text classification process.Figure 3
Startup text classification process.


### 3.2. Entrepreneurship-Knowledge Mapping Extraction

The KGG model first classifies the assessment ventures involved in the analysis into knowledge points using the text classification algorithm in text analysis. If an assessment venture belongs to multiple knowledge points, it is impossible to determine the learning characteristics of students on the multiple knowledge points corresponding to the venture, so each assessment venture is considered to belong to one knowledge point, and the data from the students' answer process are mined for deep analysis to obtain the learning characteristics of each student on each knowledge point. The learning characteristics of each student on each knowledge point are different [21]. The textual analysis was achieved by combining the entrepreneurship answers of the single-choice questions and the text of the entrepreneurship questions together. To facilitate the analysis, the connections between entrepreneurship and knowledge points are represented in the form of an entrepreneurship-knowledge point matrix QK, which is represented as follows：(1)QK=qk11qk12⋯qk1nqk21qk22⋯qk2n⋮⋮⋱⋮qkm1qkm2⋯qkmn.


#### 3.2.1. Participle and Deactivator Filtering

Since computers are unable to directly classify unstructured texts and entrepreneurship texts are unstructured, direct manipulation of the assessment entrepreneurship text to automatically classify it into knowledge points cannot be achieved using a computer [22]. Therefore, it is necessary to preprocess the assessment entrepreneurship so that the computer can understand and process it. In order to improve retrieval and save storage space, deactivation filtering is carried out to filter the words that are in the deactivation list after the word separation of the assessment venture, so that the text can be classified efficiently and accurately.After the splitting and deactivation filtering steps, the measured entrepreneurship text is denoted byQ=Q1,Q2,…,Qj,…,Qm, where Qj denotes the jth entrepreneurship and m denotes the number of entrepreneurships. The following analysis will be conducted using the preprocessed entrepreneurship text Q.The term frequency-inverse document frequency (TF-IDF) index, an important weighting function in information mining, is used to evaluate the importance of a word in an article [23, 24].  In this paper, we choose the TF-IDF method to extract text features and transform the measured entrepreneurship Q into a vector space model (VSM) [25], which represents words as vectors and uses the operations between vectors to analyze the relationship between words.The measured ventureQ is analyzed by TF-IDF to obtain text features Ch=Ch1,Ch2,…,Chj,…,Chm, where Chj denotes the text features of the jth venture. The formula for calculating the weight of the feature term Chji is as follows:(2)Chji=TFj,i×IDFi,where TFj,i denotes the word frequency of the ith text feature item in the jth venture text, IDFi denotes the number of occurrences of feature item i in the whole text dataset, and TF-IDF is suitable for classification if a word has a high frequency TF in one measured venture and a low frequency in other measured ventures.


### 3.3. Cluster Analysis

Based on the level of mastery of each student on each venture, combined with text classification to classify the venture into knowledge points, use equation (3) to obtain the feature matrix SK.(3)SK=sk11sk12⋯sk1nsk21sk22⋯sk2n⋮⋮⋱⋮skh1skh2⋯skhn,where sktx denotes the mastery of student st, sktx ∈ {0,1}, and ℎ denotes the number of knowledge points. sktx value is determined by the average of the mastery of student st on the same entrepreneurship as knowledge point kx.(4)sktx=sqta+sqtb+⋯+sqtov.The criteria for students’ learning characteristics on a knowledge point take three forms: high, medium, and low criteria. Ifsktx ∈ [0.7,1], the student has a good mastery of the knowledge point, which is a high standard; if sktx ∈ [0.3,0.7), the student has an average mastery of the knowledge point kx, which is a medium standard; if sktx ∈ [0,0.3), the student has a poor mastery of the knowledge point kx, which is a low standard. The learning characteristic criteria are illustrated in Figure 4.Figure 4
Learning characteristic criteria.The students are clustered using the DBSCAN clustering algorithm to obtain the clustered student class-knowledge point learning characteristics matrix CK.(5)CK=ck11ck12⋯ck1nck21ck22⋯ck2n⋮⋮⋱⋮cky1cky2⋯ckyn,where ckzx∈0,1 and ckzx indicates the mastery level of student class Cz on knowledge point kx, i.e., the cluster centre of the mastery level of student class 55 on knowledge point kx. As the learning characteristics of the students were obtained by analyzing the factors affecting their mastery during the examination, the Delphi method was used to unify the opinions of the experts, the weights of the influencing factors were determined, and the clustering effect was verified by the average score of each class of students on each knowledge point, thus verifying the rationality of applying the Delphi method to this paper [25].


## 3.1. Knowledge Graph Construction Model Building Steps

This section will explain how to use the algorithm in data mining to analyze the entrepreneurship and detail data in the evaluation process step by step to build a knowledge map to reduce the cost of human and material resources, mainly including four steps: evaluation and entrepreneurship text classification, student feature extraction, cluster analysis, and knowledge map construction. It is described in detail below.The evaluation entrepreneurship and knowledge points are automatically associated through text classification. A knowledge graph is essentially a knowledge base called a semantic network, i.e., a knowledge base with a directed graph structure. In layman’s terms, a knowledge graph is a data structure composed of entities, relationships, and attributes. It is the database 2.0. Due to the large number of evaluation entrepreneurship, the problem of manual classification by experts is solved, and this method has high cost and low efficiency, and the classification effect is determined by the accuracy of model classification. The evaluation entrepreneurship text classification in this section includes the extraction of entrepreneurship knowledge point mapping relationship based on TF-IDF and VSM, word segmentation and stop word filtering, text feature extraction, model classification, result evaluation, and classification result output. The text classification process is shown in Figure2, and the entrepreneurial text classification process in this paper is shown in Figure 3.Figure 2
Text classification process.Figure 3
Startup text classification process.


## 3.2. Entrepreneurship-Knowledge Mapping Extraction

The KGG model first classifies the assessment ventures involved in the analysis into knowledge points using the text classification algorithm in text analysis. If an assessment venture belongs to multiple knowledge points, it is impossible to determine the learning characteristics of students on the multiple knowledge points corresponding to the venture, so each assessment venture is considered to belong to one knowledge point, and the data from the students' answer process are mined for deep analysis to obtain the learning characteristics of each student on each knowledge point. The learning characteristics of each student on each knowledge point are different [21]. The textual analysis was achieved by combining the entrepreneurship answers of the single-choice questions and the text of the entrepreneurship questions together. To facilitate the analysis, the connections between entrepreneurship and knowledge points are represented in the form of an entrepreneurship-knowledge point matrix QK, which is represented as follows：(1)QK=qk11qk12⋯qk1nqk21qk22⋯qk2n⋮⋮⋱⋮qkm1qkm2⋯qkmn.


### 3.2.1. Participle and Deactivator Filtering

Since computers are unable to directly classify unstructured texts and entrepreneurship texts are unstructured, direct manipulation of the assessment entrepreneurship text to automatically classify it into knowledge points cannot be achieved using a computer [22]. Therefore, it is necessary to preprocess the assessment entrepreneurship so that the computer can understand and process it. In order to improve retrieval and save storage space, deactivation filtering is carried out to filter the words that are in the deactivation list after the word separation of the assessment venture, so that the text can be classified efficiently and accurately.After the splitting and deactivation filtering steps, the measured entrepreneurship text is denoted byQ=Q1,Q2,…,Qj,…,Qm, where Qj denotes the jth entrepreneurship and m denotes the number of entrepreneurships. The following analysis will be conducted using the preprocessed entrepreneurship text Q.The term frequency-inverse document frequency (TF-IDF) index, an important weighting function in information mining, is used to evaluate the importance of a word in an article [23, 24].  In this paper, we choose the TF-IDF method to extract text features and transform the measured entrepreneurship Q into a vector space model (VSM) [25], which represents words as vectors and uses the operations between vectors to analyze the relationship between words.The measured ventureQ is analyzed by TF-IDF to obtain text features Ch=Ch1,Ch2,…,Chj,…,Chm, where Chj denotes the text features of the jth venture. The formula for calculating the weight of the feature term Chji is as follows:(2)Chji=TFj,i×IDFi,where TFj,i denotes the word frequency of the ith text feature item in the jth venture text, IDFi denotes the number of occurrences of feature item i in the whole text dataset, and TF-IDF is suitable for classification if a word has a high frequency TF in one measured venture and a low frequency in other measured ventures.


## 3.2.1. Participle and Deactivator Filtering

Since computers are unable to directly classify unstructured texts and entrepreneurship texts are unstructured, direct manipulation of the assessment entrepreneurship text to automatically classify it into knowledge points cannot be achieved using a computer [22]. Therefore, it is necessary to preprocess the assessment entrepreneurship so that the computer can understand and process it. In order to improve retrieval and save storage space, deactivation filtering is carried out to filter the words that are in the deactivation list after the word separation of the assessment venture, so that the text can be classified efficiently and accurately.After the splitting and deactivation filtering steps, the measured entrepreneurship text is denoted byQ=Q1,Q2,…,Qj,…,Qm, where Qj denotes the jth entrepreneurship and m denotes the number of entrepreneurships. The following analysis will be conducted using the preprocessed entrepreneurship text Q.The term frequency-inverse document frequency (TF-IDF) index, an important weighting function in information mining, is used to evaluate the importance of a word in an article [23, 24].  In this paper, we choose the TF-IDF method to extract text features and transform the measured entrepreneurship Q into a vector space model (VSM) [25], which represents words as vectors and uses the operations between vectors to analyze the relationship between words.The measured ventureQ is analyzed by TF-IDF to obtain text features Ch=Ch1,Ch2,…,Chj,…,Chm, where Chj denotes the text features of the jth venture. The formula for calculating the weight of the feature term Chji is as follows:(2)Chji=TFj,i×IDFi,where TFj,i denotes the word frequency of the ith text feature item in the jth venture text, IDFi denotes the number of occurrences of feature item i in the whole text dataset, and TF-IDF is suitable for classification if a word has a high frequency TF in one measured venture and a low frequency in other measured ventures.


## 3.3. Cluster Analysis

Based on the level of mastery of each student on each venture, combined with text classification to classify the venture into knowledge points, use equation (3) to obtain the feature matrix SK.(3)SK=sk11sk12⋯sk1nsk21sk22⋯sk2n⋮⋮⋱⋮skh1skh2⋯skhn,where sktx denotes the mastery of student st, sktx ∈ {0,1}, and ℎ denotes the number of knowledge points. sktx value is determined by the average of the mastery of student st on the same entrepreneurship as knowledge point kx.(4)sktx=sqta+sqtb+⋯+sqtov.The criteria for students’ learning characteristics on a knowledge point take three forms: high, medium, and low criteria. Ifsktx ∈ [0.7,1], the student has a good mastery of the knowledge point, which is a high standard; if sktx ∈ [0.3,0.7), the student has an average mastery of the knowledge point kx, which is a medium standard; if sktx ∈ [0,0.3), the student has a poor mastery of the knowledge point kx, which is a low standard. The learning characteristic criteria are illustrated in Figure 4.Figure 4
Learning characteristic criteria.The students are clustered using the DBSCAN clustering algorithm to obtain the clustered student class-knowledge point learning characteristics matrix CK.(5)CK=ck11ck12⋯ck1nck21ck22⋯ck2n⋮⋮⋱⋮cky1cky2⋯ckyn,where ckzx∈0,1 and ckzx indicates the mastery level of student class Cz on knowledge point kx, i.e., the cluster centre of the mastery level of student class 55 on knowledge point kx. As the learning characteristics of the students were obtained by analyzing the factors affecting their mastery during the examination, the Delphi method was used to unify the opinions of the experts, the weights of the influencing factors were determined, and the clustering effect was verified by the average score of each class of students on each knowledge point, thus verifying the rationality of applying the Delphi method to this paper [25].


## 4. Experiments and Analysis of Results

For objective judgement and accurate processing of the experimental data, only single-choice questions were available in the entrepreneurship used in the experiment. Prior to processing in the analysis phase, the ventures were processed and the answers were included with the question stems as a complete venture text. Each venture was accompanied by a knowledge point label indicating the knowledge point to which the venture belonged.As the text needs to be preprocessed before the text is classified, the preprocessing steps include word separation and deactivation filtering. In order to save storage space and improve search efficiency, the deactivation word list of HIT, the most used tool, is chosen in this paper [26].By extracting text features Ch, each text feature has 3107 dimensions. As experts in this paper gave 1916 subordinate relationships between the assessment startups and knowledge points related to the knowledge points studied in this paper, the 1916 assessment startups with knowledge point labels were used as training samples. 100 startups participating in the assessment were used as the sample to be classified. K-NN obtained the training classification model by learning the subordination relationship between assessed startups and knowledge pointsn ℎtrain. The corresponding distribution of entrepreneurship and knowledge points in the training sample is shown in Figure 5.Figure 5
Corresponding distribution of training sample.In order to evaluate the classification effect of the sample Chest, the experts also labeled the sample Chtest with knowledge points and obtained the classification effect of the K-NN model by comparison. In this experiment, the F1 value of the K-NN model was 0.96. Finally, the distribution of the 100 entrepreneurship and knowledge points of the participants is shown in Figure6, and the distribution of entrepreneurship and knowledge points obtained after classification by the K-NN model is shown in Figure 7. K-NN model classification report is shown in Table 1.Figure 6
Distribution of entrepreneurship and knowledge points corresponding to participation in the assessment.Figure 7
Distribution of entrepreneurship and knowledge points after classification by the K-NN model.Table 1
K-NN model classification report.
Knowledge point labelAccuracyRecallF1 valueSupportK10.9310.9613K211111K30.810.894K411112K510.930.9615K610.710.837K711114K80.9510.9718K91116Average/sum0.960.960.96100Matrix QK obtained the relationship between entrepreneurship and knowledge points, and matrix SQ obtained the mastery level of each student on each entrepreneurship [27–29]. Using Equation (6) is used to obtain a matrix of learning characteristics for each student on each knowledge point SK, with the horizontal coordinates denoting the student, and the vertical coordinates denoting the knowledge point. A matrix of student-knowledge point learning characteristics SK is represented as follows:(6)SK=0.80.510.740.730.670.390.910.650.420.710.480.570.180.940.840.680.790.690.770.770.910.570.830.780.390.91⋮⋮⋮⋮⋮⋮⋮⋮⋮0.330.730.660.900.660.670.780.690.650.80.7210.970.700.690.960.560.9110.790.760.720.780.890.760.590.20.880.830.850.820.730.860.740.820.42.The DBSCAN algorithm is a typical clustering algorithm based on density. Using the DBSCAN algorithm was used to cluster students by learning characteristics and determine the clustering effect based on the contour coefficient.Figure8 shows the learning criteria based on students' mastery of each knowledge point, with the horizontal coordinates indicating the knowledge points and the vertical coordinates indicating the student classes. The DBSCAN clustering algorithm was used to group students into 5 classes. The learning characteristics of students in categories 1, 3, 7, and 8 are greater than or equal to 0.3 and less than 0.7. The learning characteristic criterion is medium. By analyzing the students in class 1, the mean value of the path length of answer choices during the answer process was 3.42 for questions of low standard, 2.57 for questions of medium standard, 2.51 for questions of high standard, and 2.65 for all entrepreneurship.Figure 8
Clustering results based on student feature extraction.The mean value of the answer choice path length was 2.18. For high standard questions the mean value of the answer choice path length was 1.95. For all entrepreneurship the mean value of the answer choice path length for student class 2 was greater than 0.7 for all knowledge points and the learning characteristics were stable, the mean value of the answer choice path length for all entrepreneurship for student class 2 was 1.21.The learning characteristics of student category 5 were less than 0.3 for all knowledge points except for point 3, which had a low standard of learning characteristics, and a medium standard of learning characteristics for point 3, which had a low fluctuating curve of learning characteristics and a stable level of mastery. The mean answer choice path length for all ventures was 3.25.The mean answer choice path length for entrepreneurship for each learning characteristic criterion for each category of students is shown in Figure9.Figure 9
Average path length for entrepreneurial answer selection for each learning feature criterion.By analyzing the average length of the entrepreneurial answer choice paths for each mastery standard for each category of students, we can obtain a stable master for student class 2, student class 4, and student class 5. The more hesitant the students, the higher the standard and the lower the mean of the path length of answer choices for students in student category 1 and student category 3.The average score for each category of students on each knowledge point was calculated to obtain a trajectory graph of the average score curve for each category of students on each knowledge point, as shown in Figure10.Figure 10
Trajectory of the average score curve.As seen in Figure10, the average score curve for each category of students on each knowledge point follows a similar trend to the clustering results curve based on student feature extraction, with different total scores on each knowledge point due to the different number of ventures on each knowledge point.


## 5. Conclusions

In practice, some universities will deliberately imitate and replicate the educational methods of other institutions so that innovative entrepreneurship education can certainly be used to learn from them. However, teachers still need to consider realistic factors in the specific implementation of entrepreneurship education methods. Each university should choose the innovation and entrepreneurship education method rationally and reasonably optimize with its own actual situation; secondly, innovation and entrepreneurship education can also be combined with the characteristics of the school to show the advantages of innovation and entrepreneurship education characteristics. As the number of adventures on each knowledge point is different, the total score of each knowledge point is also different. In the new era, each university in China should actively create an innovation and entrepreneurship education system with its own characteristics, so that innovation and entrepreneurship education can become a profound culture of the university while realizing the function of educating people.



---

*Source: 3789315-2022-07-22.xml*