#### Abstract

In view of the relevant teaching problems in the field of art and design, in order to study the teaching methods and contents of art design major from the perspective of the Internet economy, the evaluation indexes corresponding to the Internet are introduced into the partial least squares regression (PLS) path analysis model based on the relevant theoretical basis of the Internet. Through the method of model testing and relevant data analysis, the three-dimensional teaching method of art design is discussed, and the art design major is divided into five influencing factors, which are studied, respectively, according to the different influencing degrees. Finally, the model is verified by the experimental method, and the model is used to predict the three-dimensional teaching of art design from the perspective of Internet economy. The research shows that the overall proportion of economic strength remains between 70% and 90%, while the corresponding level of network design is relatively low. This study shows that the impact of economic strength research and related policies on the Internet economy is higher than the corresponding level of network design. Three-dimensional teaching occupies a dominant position in art design major. The proportion of network design and design frontier is relatively small, indicating that three-dimensional and information-based teaching can have a great impact on the art and design major from the perspective of the Internet. Different factors have different influences on art and design majors in Internet economy. The order of influence degree is innovation ability > design expression > design thinking. Based on the realization of Internet theory, this paper studies the three-dimensional teaching method of art design specialty, so as to provide a theoretical basis for the application and research of Internet in other fields.

#### 1. Introduction

Internet economy has broad application prospects in different fields such as remote sensing data, ecological environment, social media, sharing economy and higher education: Halim Dareen and Samuel [1] proposed the Internet telemetry data center in view of the shortcomings of the Internet economy in the field of remote mapping. The data center can analyze the relevant data by using the algorithm of neural network model, so as to realize the application of the data in the field of Internet economy. The optimization model has the advantages of simplicity, high efficiency, and practicability. In order to further adjust and optimize the ecosystem, Jinil persis et al. [2] proposed a new optimization model based on the theory of Internet economy. The model adopts multidecision intelligent identification technology to find the optimal solution through intelligent analysis and evaluation of the obtained ecological environment data. To explore culture and social media in the context of the Internet vision, Maddox [3] proposed a social media operation model based on Internet economy. This mode adopts the computing method of Internet of Things cloud platform to achieve accurate push of social media. In this mode, users’ browsing data are firstly summarized and imported into the cloud platform for analysis and calculation. Then, it can be divided into different types for output, and relevant content can be pushed through the analysis of Internet big data, so that relevant content can be analyzed and shared finally.

With the development of Internet economy, more and more fields have been integrated into the Internet economy. As a main content of Internet economy, sharing economy has made a series of achievements in various fields, but it is worth explaining that sharing economy still has some problems under the effect of Internet. Akhmedova et al. [4] proposed a trust evaluation model based on the Internet economy to solve the problems existing in the sharing economy. The model converts problems existing in the sharing economy into signals of different sizes and determines the solution of corresponding problems by the strength of signals. In order to analyze the signals corresponding to the problem, related theories of sharing analysis are introduced on the basis of the original trust model, so as to obtain the corresponding trust optimization evaluation model under the effect of the Internet of Things. The coordinated development of higher education and Internet economy is global in a sense. Scientific understanding and accurate evaluation of the coordinated development of higher education and Internet economy is related to the macroscopic distribution of school education structure and the macroscopic guidance of industrial structure. In order to better evaluate the higher education under the Internet economy, Sun [5] proposed the evaluation model of the coordinated development of higher education based on the fuzzy neural network with the help of the Internet economy analysis platform. The model adopts the correlation calculation method of the fuzzy neural network to conduct quantitative analysis on the relevant influencing factors of higher education and obtains the influence degree under different indicators. It is defined as evaluation coefficient, and then the corresponding relationship between evaluation coefficient and Internet economy is studied. In this way, the evaluation system between Internet economy and higher education can be established. In order to study the application of Internet economy in the development of social group economy, Ridley Duff and Bull [6] provided a dichotomy model based on Internet economy theory. In order to maximize the role of social group economy in Internet economy, the model adopts resource allocation theory to divide social group economy twice. As a result, the solidarity economy will change to different degrees under the influence of the Internet economy.

There are a variety of teaching methods in the field of art design. The traditional teaching methods of art design are inconsistent with the reality and other related problems in talent training.

Jiang and Yang [7] proposed the new media interactive teaching concept and mode based on Internet economy in order to further solve the shortcomings and deficiencies in the field of art design. This concept is obtained by introducing the relevant theories of Internet economy into the art teaching model, which can more accurately describe and represent the problems existing in the field of art design. In the process of the development of art design, there often appear problems such as lack of professional personnel and weak theoretical foundation. Zhou [8] proposed that stylized teaching could be adopted in the classroom and practical activities of art design to further improve the application of Internet economy in the field of art design. This theory combines the contents of Internet economy and art design, which can well describe the art design under Internet economy. In view of the problems existing in the healthy development process of interdisciplinary art design, Atayero et al. [9] proposed an art-based model under the joint action of Internet economy and art and design profession. This model adopts the method of theoretical calculation to conduct quantitative analysis on the relevant factors of art design, which is introduced into the Internet economy, so as to find out the relevant models for optimizing art design.

In order to better study the development trend of the Internet economy, the development scale of the Internet in the past decade is summarized, as shown in Figure 1. The Internet shows rapid changes along with the timetable, because the development of high-tech industry promotes the development of the Internet to a certain extent.

The above studies mainly analyze the role of Internet economy in different fields, but there are relatively few studies on the art design under Internet economy. In order to study the application of Internet in art design major, based on the relevant theories of Internet economy, this paper adopts PLS path analysis model to conduct targeted analysis on the relevant content of art design. In addition, the three-dimensional teaching method is adopted to study and analyze the art design major from the perspective of the Internet economy. Finally, the optimization model is used to predict and analyze the relevant methods of art design major. This research can provide theoretical model and support for the application of Internet economy in other fields.

#### 2. Basic Theory

##### 2.1. Concepts Related to the Internet Economy

Internet economy is a general term for economic activities with Internet technology as the platform, network as the medium, and applied technological innovation as the core, and is the sum of economic activities generated based on the Internet [10–12]. Now, the Internet is very important to the economy, according to the Internet can control the direction of the economy. In addition to its significant impact on economic development, the Internet has fundamentally changed people’s way of life. The Internet can solve the employment problem of countless people and increase the number of jobs. The Internet has changed the imbalance of the world’s development. The birth of the Internet is an important milestone in the history of human development. The Internet will continue to have a profound impact on many aspects of human social life, as well as the economic development of the world. The overall distribution of Internet economy can be divided into three parts: network economy [13], e-commerce [14], and business model [15], which correspond to the three main components of the development of Internet economy. These three parts are realized by means of economic development, human resources, and economic structure, as shown in Figure 2.

It can be seen from the above research that the main influencing factors of Internet economy include the economic component of Internet, the policy orientation of Internet research, and the resource elements of Internet development. In order to more accurately explain the role of Internet economy in life, the main types of Internet economy [16–18] are summarized, as shown in Table 1. E-commerce accounts for the largest proportion in the Internet economy, with e-commerce companies such as Tmall and JD Finance as the main part. Real-time communication accounts for 25%, including our commonly used QQ and Wechat. Internet finance and online games accounted for 17 percent and 16 percent, respectively, with products such as Alipay and League of Legends. Search engine accounts for the smallest, mainly including Baidu, Google, and other functions of the search software.

Internet economy has different forms of expression in different aspects of life, corresponding to different industrial structures [19, 20]. The main engines of integrated development of Internet come from three industries: the primary industry dominated by agriculture and animal husbandry; secondary industries, mainly including gas and electricity; the tertiary industry dominated by public services. The secondary industries also include water, construction, and manufacturing, which are closely related to people’s lives. The corresponding tertiary industry includes market service, consumer service, and basic service, which are the supplement and foundation of public service (Figure 3).

##### 2.2. Evaluation Model of Internet Economy

In order to better analyze the manifestations of Internet economy in different aspects, based on the previous analysis and evaluation of Internet economy, this paper uses principal component analysis [21] to build an empirical econometric model to measure the competitiveness of Internet economy, so as to evaluate the competitiveness of Internet economy in all aspects. According to different evaluation methods, Internet economy mainly includes economic strength evaluation, network facilities evaluation, human resources evaluation, e-commerce evaluation, and corresponding application evaluation, as shown in Figure 4. The evaluation of economic strength can be divided into economic environment, economic level, support of relevant policies, and corresponding policy level according to different relevant policies. Research on network facilities is the basis of Internet economy and the main research index of Internet economy, and the corresponding network facilities level includes information level, network level, and industry level. It is also worth explaining the human resources in the field of Internet economy. Relevant studies show [22, 23] that the development of Internet economy is closely related to the corresponding talent cultivation, indicating that the quality of talents, scientific and technological quality, teaching quality, and the level of human resources development are the main driving force of Internet economy.

In order to better analyze the evaluation indicators of Internet economy, the empirical econometric model is used to carry out relevant research. In general, if you have *m* samples, each sample has *n* indices *x*_{1}, *x*_{2}, … *x*_{n}, they are integrated into Z comprehensive variables through principal component analysis:where *a*_{i} is the model parameter. The variation relationship among parameters in formula (1) is as follows: . The number needs to satisfy three conditions: (1) *y*_{i} and *y*_{j} are independent; (2) find the corresponding correlation coefficient matrix; (3) work out the corresponding feature vectors.

The specific calculation steps are as follows:(1)Standardized processing of original indicator data:(2)The correlation coefficient matrix can be presented as(3)*Z* non-negative eigenvalues of the feature equation *c*(*i*) are calculated by using the correlation coefficient matrix, and the corresponding eigenvectors of *c*(*i*) are shown as follows:(4)Major components of the Internet economy are selected, and define the proportion of the variance of the first principal component to the total variance as *η*:

It is generally believed that when *η* ≥ 0.85, it is considered that the current principal component basically retains the information of the original factor, so that the number of factors is reduced and a good screening effect is achieved. In order to make a detailed analysis of the variation trend of relevant industries in different Internet economies, the proportion chart of different economic indicators is drawn, as shown in Figure 5: relevant indicators include economic environment, economic level, economic policy, relevant policy level, corresponding information level, network level, and relevant industry level. Among them, the proportion of economic strength remains between 70% and 90%, while the corresponding level of network design is relatively low, about 40% to 60% as a whole. This study shows that economic strength and related policies have a greater impact on Internet economy than the corresponding level of network design.

#### 3. PLS Path Analysis Model

In order to quantitatively analyze the proportion of Internet economy in related fields, partial least squares regression method is adopted to analyze the teaching methods of art design under Internet economy [24–26]. Partial least squares regression is a new multivariate statistical data analysis method, which mainly studies the regression modeling of multiple dependent variables to multiple independent variables. The partial least squares method is a combination of the advantages of principal component analysis, canonical correlation analysis, and multiple linear regression analysis [27, 28]. The path of the PLS model is shown in Figure 6. The relevant data collected by Internet economy are imported into the corresponding network society for corresponding data processing, and then the related content of data economy is fed back and studied through information economy. Then, the research content of information economy is checked through digital life, corresponding technical level and human resources. Finally, the calculation results of Internet economy in the PLS model are derived through relevant industrial structure.

##### 3.1. Basic Theory of PLS Path Model

The main reasons for adopting the PLS analysis method in this paper are as follows: first, compared with other models, the assumptions of the PLS analysis method need not be so strict, and the requirements of sample data also obey the multivariate normal distribution. Second, PLS analysis can be used regardless of the size of the sample data. Third, the PSL analysis method can enlarge the original sample data by hundreds of times and then quickly converge, so that the same characteristics of the original sample data can be obtained in the new sample data. Fourthly, the PLS analysis method can not only measure the reflection indicator model but also measure the constituent indicator model. Before using the PLS path model to analyze the impact path for parameter estimation, model parameters need to be estimated and analyzed [29]. Before using the PLS path model to analyze the influence path and estimate parameters, it is necessary to assume that the information exchange between explicit variables is completed through latent variables, and the information transmission between latent variables is due to the adjacent relationship. PLS path model parameter estimation process is generally divided into two steps. First, the latent variables are estimated iteratively based on internal and external relations. Then, using the principal components of independent variables and dependent variables, PLS regression was performed. The PLS path model parameter estimation process is generally divided into following steps:(1)Explicit variable centralization: assume that in *k* observation samples, each sample has *n* groups of measurable standardized explicit variables *ξ*. All latent variables and explicit variables are linear.(2)External estimation: calculate the external estimation value of each potential variable, and calculate the potential variable *γ*_{i}. The corresponding formula is as follows: where is the external weight; is the scalar weight. In formula (6), the latent variable *γ*_{i} is iterated *t* times to obtain its external estimate vector , whose variance is 1.(3)Internal approximation: using relevant formulas to calculate the internal estimates of potential variables and calculate the internal weights, where *r* is the matrix corresponding to the model. Corresponding internal estimates where is the internal weight of the scalar; is the internal weight of the latent variable, is the vector of intrinsic estimates; is the corresponding estimate vector.(4)Weight estimation: the weight estimation equation of the measurement model corresponding to the reflection type is where is the weight estimation. The weight estimation equation of the measurement model corresponding to the constitutive type is where is the parameter corresponding to the estimation function.(5)The end condition is taken as the basis for judgment: after the end of each iteration, it is necessary to judge whether the iteration is over. The corresponding end condition of iteration is where and are iterations.(6)Calculate the value of latent variable, and the equation is as follows: where *T* indicates the end of the iteration, and is the latent variable.(7)Finally, load and path coefficients of variables are calculated, respectively.

The change relationship among weight, potential variable, and path coefficient calculated by using the above steps is shown in Figure 7. The weight coefficient shows a linear change with a slow increase in the number of iterations. When the number of iterations is 450, the coefficient rises rapidly, after which the curve still shows a linear change. The slope of the corresponding curve is higher than the linear change of the first stage, indicating that the increase of the number of iterations increases the growth rate of the weight coefficient. The potential variables show a typical two-step change: when the number of iterations is 450, it shows a linear increase, and when the number of iterations is 450, it shows a linear decrease. On the whole, the curve still shows increasing change. The corresponding curve was obtained by summarizing the relevant data of path coefficients. The curve showed a linear increase before the number of iterations was 450. When the number of iterations is 450, the curve rises rapidly. As the number of iterations continues to increase, the curve keeps an approximate constant trend. The research shows that the turning point of curve change is when the number of iterations is 450.

##### 3.2. Model Test

In order to verify the above models, reliability and validity tests were conducted.(1)The so-called reliability test is to test the reliability or stability of index data in the measurement model, and judge whether the sample data are reliable from the test results. CR (compositereliability) and CA (Cronbach’s Alpha) are two indexes of reliability test. The reliability test uses the sample data to make repeated measurements and observe whether the structure is consistent each time. The higher the test value, the more reliable the results. The corresponding formula is as follows: where *k* represents the number of explicit variables in this latent variable, and *λ*_{i} represents the factor load of the *i*-th explicit variable in this latent variable. Generally, it is considered that if CR > 0.7, the model has high reliability. *N* represents the number of cross-sectional sample cities, *S*_{i} represents the variance of the *i*-th sample city data, and *S*_{t} represents the total variance of sample data. The main purpose of CA is to verify whether the sample is reliable at all times. Generally, it is considered that when CA > 0.7, the model has high reliability. When 0.5 < CA < 0.7, the reliability of the model is general and belongs to the acceptable range. When 0.4 < CA < 0.5, the model reliability is in the acceptable range. When CA < 0.4, the reliability of the model is poor and unacceptable.(2)The validity test is to check the correlation degree of each obvious variable under the latent variable. The factor load value *λ* and AVE (average variance extracted) value in the result are the main indicators of validity test. *λ*_{i} is the factor load value of the *i*-th explicit variable in the latent variable. The judgment criterion is that when the factor load *λ*_{i} > 0.5, the relationship between the latent variable and its explicit variables meets linear equivalence, which is acceptable. If *λ*_{i} < 0.5, there is no linear equivalence relation between the latent variable and its explicit variables, which is unacceptable. For the AVE value, it is generally considered that AVE > 0.5:

The model testing method was adopted to calculate relevant indicators under the PLS path model, and relevant parameters of different indicators were obtained as shown in Table 2.

For more detailed analysis of the influence of the Internet economy, the Internet is divided into 15 secondary indexes and 7 first-level indicators, the first-level indicators include the following: the Internet economy, the development of network society, information economy, the numerical value of life, level of information technology, and the corresponding human resources investment and industrial structure adjustment and optimization. The corresponding inspection indicators are summarized and analyzed, as shown in Figure 8.

In Figure 8, the variation range of factor load value *λ* is 0.6–0.95, the corresponding variation range of CR is 0.70–0.96, the corresponding variation range of CA is 0.6–0.85, and the variation range of AVE is 0.7–0.94. The study shows that AVE and CR vary widely and the corresponding variation value is also high, indicating that the influence degree of these two parameters is obvious.

#### 4. Teaching Methods of Internet in Art Design Majors

##### 4.1. Major of Art Design

With the continuous development of technology, the Internet has become an indispensable part of people’s daily life. In order to meet the needs of the society, art design majors need to carry out reforms. The reform of practical teaching in basic painting courses needs to be based on the application of network platform, design frontier dynamics, information teaching means, three-dimensional teaching and teaching plan, and other elements to make students develop the habit of collecting all kinds of knowledge through the network [30]. In order to better analyze the influence of different elements on art design majors from the perspective of Internet economy, the element analysis charts of different art design majors are summarized. It can be seen from Figure 9 that three-dimensional teaching occupies a dominant position in art design majors, accounting for about 40% of the overall proportion. Corresponding information teaching can also affect the development of art design major, accounting for about 28%. The proportion of network design and design front is relatively small, about 16% and 8%, respectively. Corresponding teaching programs accounted for the smallest proportion, only 6%. It shows that adopting three-dimensional and information-based teaching can have a great influence on the art design major from the perspective of Internet. At the same time, it also shows that the description and analysis of art design can be better carried out from these two perspectives.

##### 4.2. Improvement and Analysis of Teaching Methods

Based on the above analysis, the teaching framework of art design from the perspective of the Internet economy is obtained, as shown in Figure 10. The teaching framework of art design can be divided into four parts: art design, service design, innovative design, and transformation design, and different contents need to be carried out on the basis of the Internet. According to different design schemes, the obtained art design modes are also different, which can be expressed as follows. When there is no change, there will be visual expression of drinking. Moderate change will lead to the emergence of existing models and corresponding systems. Major Internet changes will make new models and systems replace the original models. Radical changes will make future models dominant in the field and profession of art design. Therefore, according to the different influence, the syllabus of art design can be divided into three parts: design direction, design field, and design background.

On the basis of the above research, aiming at the related problems of art design major from the perspective of Internet economy, the PLS model was adopted to carry out targeted research on three-dimensional teaching of art design. The summary of relevant research results is shown in Figure 11. Three-dimensional teaching of art design major can be divided into five aspects: research ability, innovation ability, design realization, design expression, and design thinking. The PLS model is used to carry out relevant calculation and inspection on the influence of different aspects of art design to obtain the corresponding calculation results. In order to express the relevant results vividly, the form of score and proportion is used to explain. 1–5 in the figure, respectively, represent the corresponding score. Among the different influencing factors, the overall score is 2, and the score of research ability is 5, which indicates that research ability has the lowest influence on art design major. The proportion of innovation ability, design expression, and design thinking are the same. It shows that innovation ability, design expression, and design thinking have great influence on art design major.

The above analysis shows that innovation ability, design expression, and design thinking are the influential factors of three-dimensional teaching in art design major under the background of Internet economy. In order to better analyze and predict the influence of these three factors, the PLS model is used to calculate and predict the three factors, and the results are shown in Figure 12.

It can be seen from the prediction chart of the influence degree of different factors on art design specialty that the changes of different factors are generally manifested as the change rule of quadratic function. It indicates that the relevant data of different factors conform to the change of quadratic function. As time goes on, the curve slowly rises to its maximum value and then slowly decreases, and eventually remains constant. The difference is that the maximum value and symmetry axis of the three factors are different, indicating that different factors have different impacts on the art design major in the Internet economy. The order of influence degree is innovation ability > design expression > design thinking.

#### 5. Conclusion

(1)With the increase of iteration times, the weight coefficient shows a trend of slow increase first, then rapid change, and finally linear increase. The potential variables show a typical two-stage change. The research shows that when the number of iterations is 450, it is the turning point of the curve change, so finding the optimal number of iterations of the path analysis model can further improve the accuracy of the model.(2)The three-dimensional teaching of art design can be divided into five aspects: research ability, innovation ability, design realization, design expression, and design thinking. Among them, research ability has the lowest influence on art design major, while innovation ability, design expression, and design thinking have the greatest influence on art specialty.(3)Through the calculation and analysis of different influencing factors by using the path analysis model, it is concluded that the corresponding influencing degree is innovation ability > design expression > design thinking, indicating that innovation ability has the greatest influence on artistic design.#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The author declares that there are no conflicts of interest.