1. Introduction

Mixed teaching mode (MTM) refers to combining the advantages of traditional learning methods with those of digital or online learning, complementing each other's strengths to achieve better teaching outcomes. MTM can fully unleash the autonomy of both teachers and students, which can better reflect the initiative, enthusiasm, and creativity of students as the main body of the learning process ^[1]. With the gradual advancement of education reform, MTM has been applied in many universities ^[2]. Digital media technology, which integrates text, image, sound and animation, increases the range of information received by different senses, and is one of the key technologies that have received much attention at present. Animation design (AD) mainly combines manga and animation with story plot forms, using related expression techniques such as 2D and 3D animation, animation special effects, etc., to form a unique visual art creation mode. In the context of the continuous development of information technology, AD has become a hot research direction with strong development potential and broad application prospects in the digital media technology specialty. AD is an emerging design, which is divided into character modeling design and scene design ^[3]. AD mainly uses kinematics principles to make static characters and scenes move continuously in 2D and 3D. Applying MTM to AD education can effectively improve the quality of design and promote it towards innovation ^[4]. Teaching resources (TRs) are various conditions that can be utilized to effectively carry out teaching, including materials such as textbooks, cases, movies, pictures, courseware, and teacher resources, teaching aids, infrastructure, etc. However, in the mobile network environment, AD under mixed teaching still faces some difficulties. This includes a wide variety of TRs, lack of classification, etc., which seriously hinders the further improvement of students' learning effects. Data mining (DM) uses relevant technologies to analyze data and can search for hidden information to achieve classification, which can be used in the integration of TR ^[5]. The artificial bee colony (ABC) is an optimization method proposed to mimic the behavior of bees, which is a specific application of swarm intelligence. The main feature is that there is no need to understand the special information of the problem. Only a comparison of the advantages and disadvantages of the problem is needed. The global optimal value is finally highlighted in the population through the local optimization behavior of each artificial bee individual, with a fast convergence speed. The Apriori algorithm is a frequent itemset method for mining association rules. The core idea is to mine frequent itemsets through two stages: candidate set generation and downward closure detection of plot. Therefore, the research integrates AD TR by improving ABC and Apriori to improve the learning effect under MTM.

2. Related works

MTM can effectively improve the teaching efficiency of teachers ^[6]. This method has a good application effect in the teaching of different courses and promotes the development of education. Affected by the epidemic, MTM has promoted the application of online teaching methods in China. Researchers have integrated online teaching mode into oral Chinese teaching and formed an MTM. Researchers have compiled relevant oral Chinese teaching courses and designed a flow chart of mixed teaching. In the final teaching effect demonstration, the mixed mode can improve the teaching effect of oral Chinese teaching ^[7]. Zhang et al. adopted MTM and constructed a teaching evaluation method to improve the evaluation effect of college English distance learning. By comprehensively calculating the weight information, the evaluation method in the experiment could effectively evaluate the effect of English distance learning ^[8]. Wu has studied the application effect of MTM in English teaching. In this study, researchers used MTM to integrate ideological and political courses with English courses. In the integrated teaching of different courses, MTM could promote integrated teaching. This played an enlightening role in the reform of the teaching evaluation system of English and other courses ^[9].

In MTM, a large number of TRs need to be analyzed, summarized and classified. DM technology can effectively process TR information. Therefore, scholars have integrated DM with English teaching. The research object selected in the study is the teaching content of writing. The research uses an association rule algorithm to analyze students' grades. This method can provide high reference value for teaching evaluation in MTM and can provide reference opinions for teachers' teaching methods ^[10]. DM can rely on meta-heuristic algorithm to process data information. ABC can perform feature extraction, analysis, and prediction on data. For each preprocessing step in DM, ABC can perform effective feature selection ^[11]. Wisse and others believed that the ABC model could provide students with problem-solving methods. The model could be used not only in students' basic learning tasks, but also in students' learning guidance. According to students' feedback, ABC model had an accurate and stable practical application effect ^[12]. Zhang et al. introduced a method to improve ABC. The introduction of this method could help ABC optimize parameters at different stages, thus enhancing the convergence and learning efficiency of ABC. The model proposed in the final experiment could obtain better problem-solving strategies and better test results ^[13]. In DM, Apriori can mine association rules contained between data information ^[14]. Kalhotra et al. used Apriori to conduct in-depth information mining for online payment. By analyzing online transaction information in website data, researchers could identify abnormal data and judge whether there were criminal facts. This could effectively curb the occurrence and deterioration of criminal incidents ^[15]. Kammun et al. proved that the combination of Apriori method and K-means could predict the correlation between components in industry. When a fault occurred, the combined method could accurately determine the sequence of the fault occurrence and propose the optimal solution in a reasonable time. This method had strong robustness and could be used in DM in industry ^[16]. Mohamed et al. integrated Apriori with other methods to build a hybrid algorithm. Finally, in the validation of data sets, this method could improve the efficiency and accuracy of DM model under optimal support ^[17].

From the above research, DM can effectively and timely process information. Among them, Apriori and ABC can perform feature extraction and association rule mining, which have a good effect in practical applications. Therefore, this experiment selects these two methods to improve the MTM method in the AD of the digital media technology specialty.

3. Digital media professional AD under MTM

3.1 AD learning based on MTM

It is necessary to clearly understand the application characteristics of MTM to study the application of MTM in digital media technology professional AD. The main content of MTM is the combination of online and offline approaches. In this context, online teaching is not the auxiliary of AD teaching, but the necessary content of the whole teaching activity ^[18]. The offline teaching is also not the teaching of AD courses in the traditional way, but based on the early learning results obtained online to further develop more scientific and in-depth teaching activities. Online and offline mixed teaching does not include theories, strategies, methods, teaching organization forms and other related contents. Because it regards teaching as a comprehensive overall process. In addition, there is no unified teaching model for hybrid teaching. However, there are common goals. These goals are to integrate the advantages of online and offline teaching, improve students' learning initiative and cognitive participation, and minimize the differences in primary school students' learning results. MTM will reconstruct traditional classroom teaching. Because it extends and expands the time and space of traditional teaching. Therefore, ``teaching'' and ``learning'' can take place at different times and places, which is also its core value. Combining the advantages and specific meanings of MTM, its basic feature framework in Fig. 1 can be obtained.

MTM implements the whole teaching process in AD from three aspects. The first is to clarify the course learning objectives that match the online and offline mixed teaching. In the teaching preparation stage, teachers need to decompose the knowledge points of all courses according to the teaching syllabus of the specialty. Then students need to study the video materials of online AD before class to master the learning points. At the same time, teachers explain and expand the important knowledge involved in this part in the offline course and actively guide students to find problems in inquiry. Secondly, teachers need to conduct online or offline guidance in stages through group discussion and group mutual evaluation for interaction and in-depth discussion of learning results by virtue of the advantages of online teaching. During the implementation of MTM, it is necessary to gradually increase the difficulty of learning knowledge and update the knowledge system according to the current frontier dynamics of the discipline. At the same time, it needs to use a variety of computer design software in digital media technology to continuously improve the teaching effect. Finally, multi-platform and multi-form teaching forms are applied to create a more effective and interesting teaching community for AD. It can provide an attractive high-quality learning environment for the in-depth study of students majoring in digital media technology, which can promote the scientific and efficient teaching process. Fig. 2 shows the action path and relationship of MTM in AD.

Fig. 1. Framework of basic characteristics of mixed teaching mode.

Fig. 2. The action path and relationship of mixed teaching mode in animation design.

3.2 AD resource feature selection based on ABC

According to online and offline teaching, that is, the mixed teaching method, the teaching mode of AD in digital media technology specialty is established. The feature selection of AD resources is studied and re-used by ABC to provide a basis for further integration and recommendation of resources. ABC is a swarm intelligent optimization algorithm developed on the basis of simulating bees' foraging behavior. It has the advantages of simple operation, easy implementation, fast convergence speed, and few control parameters. ABC is widely used in function optimization, DM and other optimization problems ^[19]. ABC is divided into employed bees and non-employed bees. The non-employed bees include scouting bees and following bees. Employed bees and following bees are responsible for exploiting honey sources, and investigating bees are responsible for randomly searching for new honey sources, mainly reflecting the advantages and disadvantages of honey sources through fitness values. Fitness refers to the relative ability of an individual with a known genotype to transfer their genes to their offspring gene pool under certain environmental conditions. It is a measure of an individual's survival and reproductive opportunities. These together realize the process of constantly seeking the optimal solution ^[20]. Fig. 3 shows the basic flow of ABC.

Fig. 3. Schematic diagram of artificial bee colony algorithm.

In honey source harvesting, formula (1) is the renewal method.

(1)

$ U_{ij} =r\cdot \left(S_{ij} -S_{kj} \right)+S_{ij} . $

In formula (1), $r$ is a random number between $[- 1$, $1]$. $k\in (1$, $2$, ..., $M)$. $j\in (1$, $2$, ..., $N)$, where $k\ne j$. $U_{kj} $ refer to the updated honey source location, $S_{ij} $ refers to the currently marked honey source location, and $S_{kj} $ refers to the randomly selected honey source location in the region. formula (2) is the fitness value when mining honey source.

(2)

$ f(\theta )=\frac{1}{1+f_{i} } . $

In formula (2), $f(\theta )$ represents fitness value, and the most ideal value is 1. $f_{i} $ represents the average absolute error of the network corresponding to the $i$-th honey source. According to the honey source information marked by the employed bees, the following bees adopted the roulette method to select the honey source. formula (3) is the calculation of probability.

(3)

$ P_{i} =\frac{f(\theta _{i} )}{\sum _{i=1}^{L}f(\theta _{i} ) } . $

In formula (3), $\theta _{i} $ is the $i$-th honey source. $f(\theta _{i} )$ is the fitness value of the honey source $\theta _{i} $. $i\in (1$, $2$, ..., $T)$. $T$ refers to the number of honey sources. $P$ is the probability of being selected. The bee colony can select the best honey source by comparing the fitness value of honey source, which is the best solution. However, ABC is easy to fall into local minimum in complex problems. The search accuracy is low frequently. Moreover, the optimization mechanism destroys the diversity of the population, resulting in a lower convergence rate in the later stage. Therefore, the study introduces the global optimal solution and adaptive inertia factors $\omega _{1} $ and $\omega _{2} $ to improve ABC, namely, improved artificial bee colony (IABC), to accelerate the later convergence speed and improve the prediction accuracy. formula (4) is IABC.

(4)

$ V_{ij}^{new} =\omega _{1} r_{1} (S_{ij} -S_{kj} )+\omega _{2} r_{2} (y_{jbest} -S_{kj} )+\omega _{1} S_{ij} . $

formula (5) is the calculation of $\omega _{1} $.

(5)

$ \omega _{1} =\omega _{\min } -(\omega _{\min } -\omega _{\max } )\left(\frac{n}{n_{\max } } \right)^{2} . $

formula (6) is the calculation of $\omega _{2} $.

(6)

$ \omega _{2} =\omega _{\max } +(\omega _{\min } -\omega _{\max } )\left(\frac{n}{n_{\max } } \right)^{2} . $

In formula (6), $n$ and $n_{\max } $ represent the current iteration and the maximum iteration. $\omega _{\max } $ and $\omega _{\min } $ represent the maximum and minimum values of inertia factors. $\omega _{1} $ is the speed at which the new honey source approaches the original honey source or the field honey source. $\omega _{2} $ is the speed at which the new honey source approaches the optimal honey source of the population. From formulas (7) and (8), when $n=0$, $\omega _{1} $ and $\omega _{2} $ take the minimum and maximum values, respectively. When $n=n_{\max } $, $\omega _{1} $ and $\omega _{2} $ take the maximum and minimum values, respectively. At first, $\omega _{2} $ is relatively large. The optimization speed is fast. The convergence speed is relatively fast. As the iteration continues, $\omega _{1} $ gradually increases, the search scope of random honey source expands. The diversity of race is also improved. It effectively improves the convergence accuracy and the optimization ability. The IABC first initializes the bee colony. The employed bee will search for new honey sources in the neighborhood. By comparing the advantages and disadvantages of the new and old honey sources, it will mark the honey sources with large fitness value and discard the old honey sources. Then the following bees determined the location of the new honey source by calculating the fitness. When the number of honey source updates reaches the limit, the following bees or employed bees will be transformed into scouting bees to continue to search for new honey sources. When the last iteration number reaches the maximum iteration number, the algorithm terminates. Fig. 4 shows the IABC.

Fig. 4. Schematic diagram of the proposed IABC.

3.3 AD resource mining analysis based on Apriori

The improved Apriori is used to achieve further mining and association analysis of resource data after the IABC is used to obtain the optimal feature subset of AD resources. It can provide high-quality and personalized relevant TR for students majoring in digital media technology in MTM. The research first establishes the mining model. The first step of the model is to read the original data source of AD, and then obtain the quantized transaction database through preprocessing and quantizing steps. Apriori is used to perform DM and association analysis operations to obtain frequent itemsets of all levels. At the same time, the generated association rules and effective information are accurately recorded. Fig. 5 shows the mining model.

Fig. 5. The structure of the established data mining model.

Apriori can analyze the association degree in the data, mine the strong association rules between the data, and match personalized AD resources for students. The operation process of Apriori mainly includes two steps. First, the transaction database is scanned to obtain frequent itemsets ^[21]. Secondly, the composite conditions of minimum support and confidence are set. The association rules of data are mined. The data itemset is obtained. The support in Apriori in formula (7) is the frequency of itemsets in transactions.

(7)

$ \sup port(x)=\frac{number(x\subseteq T)}{\left|D\right|} . $

In formula (7), $\sup port$ is the support degree in Apriori, $D$ is the established transaction database, and $T$ is the specific transaction determined. On the basis of the support calculation, the items that cannot meet the requirements are removed, that is, the frequent itemsets are merged. The new candidate itemset in formula (8) is obtained.

(8)

$ C_{k} =L_{(k-1)m} \cup L_{(k-1)n} . $

$L$ represents the known frequent itemset, $C_{k} $ is the obtained candidate itemset, and $n$ and $m$ are the set in formula (8). Then the union is obtained according to the principle of pairwise matching. A new candidate set is formed at this time. In formula (9), the new candidate set cannot exist independently and needs to be further processed under the action of traversal.

(9)

$ C_{j} =C_{k} (j) . $

In formula (9), $C_{j} $ is a subset, located in the new candidate set, and $j$ is the $j$ subset of $C_{j} $. The number of subsets is obtained from formula (10).

(10)

$ count:=\left\{\begin{aligned} & count+1,&&C_{j} \subset I_{i} ~(i=1,~2,~3,~...,~N),\\ & &&\hskip 2.5pc (j=0,~1,~2,~...),\\ & count,&&C_{j} \not\subset I_{i}. \end{aligned}\right. $

$i$ is the $i$-th itemset, $C_{j} $ is located in $C_{k} $, representing a subset, and $N$ is a sequence in formula (10). According to the classic Apriori, with the gradual increase of the size of the candidate set, more unnecessary candidate sets are produced. Therefore, the itemset redundancy is removed in the self-connection. The calculation method is improved through transaction Boolean matrix compression to further improve the time performance of Apriori. In formula (11), the vector corresponding to $I$ is set as ${\bar{B}_{a}}$.

(11)

$ {\bar{B}_{a} } =\left[\begin{array}{c} {t_{1a} } \\ {t_{2a} } \\ {...} \\ {t_{ma} } \end{array}\right],~~t_{ja} \left\{\begin{aligned}&0,&&I\notin T_{a},\\&1,&&I\in T_{a}.\end{aligned}\right. $

In formula (11), $m$ is the total number of transactions, and $T_{a} $ means the $a$ transaction. According to formula (11), the transaction Boolean matrix can be obtained in formula (12).

(12)

$ B=[{\bar{B}_{1}}~~ {\bar{B}_{2} }~~...~~ {\bar{B}_{n} }]=\left[\begin{array}{c} {t_{11}~~ t_{12} ~~ ... ~~ t_{1n} } \\ {t_{21} ~~ t_{22} ~~ ... ~~ t_{2n} } \\ {... ~~ ... ~~ ...} \\ {t_{m1} ~~ t_{m2} ~~ ... ~~ t_{mn} } \end{array}\right] . $

In formula (12), $B$ represents the transaction Boolean matrix, and $n$ represents the total items. formula (13) is the vector calculation of itemset $\{ I_{i} $, $I_{j} \} $.

(13)

$ {\bar{B}_{i}} \cdot {\bar{B}_{j} } =\left[\begin{array}{c} {t_{1i} \cdot t_{1j} } \\ {t_{2i} \cdot t_{2j} } \\ {... ~ ...} \\ {t_{mi} \cdot t_{mj} } \end{array}\right] . $

In formula (13), ${\bar{B}_{i}} \cdot {\bar{B}_{j} }$ represents the vector of itemset $\{ I_{i} $, $I_{j} \} $. Therefore, three compression rules of Boolean matrix are obtained. In rule 1, the number of transactions of item ${\bar{B}_{i} }$ must be greater than or equal to the minimum supported number in formula (14).

(14)

$ \sigma ({\bar{B}_{i} })\ge \left|T\right|\cdot \min \_ \sup . $

In rule 2, transactions with length less than $k$ can be deleted in mining of $F_{k} $ in formula (15).

(15)

$ \left|T_{id} \right|\ge k . $

The final rule is that only the items consistent with the previous $k-2$ items are necessary to realize their own connection in the mining of $F_{k} $.

4. Application effect of MTM in AD

The research applies MTM to digital media technology professional AD and uses improved ABC and Apriori to mine AD resources to provide students with better learning experience. First, the performance of IABC is verified. The simulation platform is Matlab R2017b. The Windows 10 operating system and Intel Core i5 2.9GHz 6-core CPU are deployed. The proposed IABC is compared with ABC and gbest-guided artificial bee colony (GABC), which are tested in the classical standard test functions Rastigin, Griewink, Sphere, and Rosenbrook. Fig. 6 is the fitness iteration curve. According to Fig. 6(a), the convergence of ABC and GABC in the Sphere test function is very similar, with convergence occurring at 500 iterations and fitness values around 10${}^{-15}$. In Fig. 6(b), the Griewank function results obtained by ABC and GABC converge at 125 and 100 iterations, with fitness values of 10${}^{-9}$ and 10${}^{-10}$, respectively, while IABC converge at 75 iterations, with fitness values of 10${}^{-12}$. From Fig. 6(c), in the Rosenbrock function, ABC and GABC converge in 10000 and 11000 iterations, respectively, and the fitness values are in the range of 0.1-1. According to Fig. 6(d), in the Rastigin function, ABC and GABC converge after 125 iterations, and the proposed IABC approximates to the optimal solution in about 67 iterations. The proposed IABC has better search accuracy and convergence speed.

Fig. 6. The fitness iteration curve change results of IABC, ABC, and GABC.

Fig. 7. Change of optimal value of three methods in Rastigin, Griewank, Sphere, and Rosenbrock functions.

The change of the optimal value of IABC, ABC, and GABC in Rastigin, Griewink, Sphere, and Rosenbrock functions is shown in Fig. 7. From Fig. 7(a), the optimal values of ABC, and GABC in the test function Sphere converge at 450 and 400 iterations, with the optimal values of $10 ^{-8}$ and $10 ^{-10}$, respectively. The IABC converges at 300 iterations, with the optimal values of 10${}^{-12}$. According to Figs. 7(b) and 7(c), the optimal value convergence of IABC, ABC, and GABC in Griewank function is $10^{-10}$, $10^{-5}$, and $10^{-8}$, respectively. Meanwhile, the optimal value convergence of IABC, ABC, and GABC in Rosenbrook function is about 210, 375, and 390 iterations, respectively. From Fig. 7(d), the optimal values of IABC, ABC, and GABC in Rastigin function converge to $10^{-11}$, $10^{-6}$, and $10^{-9}$, respectively. The proposed IABC still has faster convergence speed and can overcome the defect of local optimization.

Several experiments are carried out with three standard test functions, Rastigin, Griewink, and Sphere. The test dimensions, mean values, and variances of each function are recorded. The results of IABC, ABC and GABC are shown in Table 1. The mean and variance of IABC are both 0 in Rastigin and Griewank functions, and $3.47\times10^{-194}$ and $3.47\times10^{-194}$ in Sphere functions. They are obviously ahead of ABC and GABC, with better local and global search ability and convergence accuracy.

Subsequently, the improved Apriori is verified. Association rule analysis is performed under the same confidence and minimum support and compared with the classical Apriori. The results are shown in Table 2. With the same confidence and support, the number of K-frequent itemsets obtained by the improved Apriori and Apriori are the same. It shows that the improved Apriori can accurately mine frequent itemsets, which verifies the effectiveness of the method.

To further verify the effectiveness of the improved Apriori, compare its running time with FP-growth and Aprioris, as shown in Fig. 8. Fig. 8(a) shows the execution time of the three algorithms with different minimum support. Fig. 8(b) is a comparison of the time required for the three methods to generate frequent itemsets when the minimum support and confidence are consistent. From Fig. 8(a), with the increase of minimum support, the running time of the three methods shows a downward trend. The Apriori has a running time range of 3.5 s to 15 s, and the FP-growth algorithm is between 3s and 4s. The improved Apriori has a minimum value of 2s and a maximum value of 3s. The required time is more stable and the running time is shorter. According to Fig. 8(b), the running time of the improved Apriori in frequent 1-itemsets and K-itemsets is about 2.5 s, which is at most 15s ahead of the FP-growth algorithm and has higher running efficiency.

Finally, the IABC and the improved Apriori are combined and applied to the mining of ADTR. First of all, 10 well-known universities in China cooperate to establish a professional AD resource library of digital media technology under MTM, including audio, graphics, images, animation, video, and other AD resources. The combined algorithm, FP-growth, and classic K-means are applied to the processing of the AD resource database in Fig. 9. The horizontal axis is the number of randomly divided AD resource samples, a total of 100. The vertical axis represents the accuracy rate. The accuracy of K-means is relatively stable, most of which is below 85%, and the maximum is 90%. Compared with K-means, FP-growth is slightly better. The accuracy rate is more than 6 times in the range of 90%$\mathrm{\sim}$95%, but most of them are in the range of 85%$\mathrm{\sim}$90%. Most of the combined methods are in the range of 90% to 95%, and the maximum is 97%. Compared with K-means and FP-growth, they are improved by about 10%, and their performance is better, which shows that they can effectively integrate AD resources.

Fig. 10 shows the student scoring results of the combination of IABC and improved Apriori in the mixed teaching of the AD in the digital media technology specialty. The horizontal axis is TR. The vertical axis is student score. In Fig. 10, before the application of the algorithm, students' scores are concentrated at about 70 points and rarely above 80 points. In combination with the application of the algorithm, the majority of students score more than 70 points, nearly half of them are between 80 points and 90 points. A considerable part exceeds 90 points. The proposed method can provide students with better learning experience. The teaching effect has been improved to a certain extent, which verifies the superior practical application effect of the method.

Fig. 8. Comparison of running time of FP-growth, Apriori, and improved Apriori algorithm.

Fig. 9. Classification accuracy results of animation design resources by three methods.

Fig. 10. Students' scores before and after the application of the algorithm.

5. Conclusion

MTM in the Internet environment provides a new direction for education reform. Digital media technology is no exception. The research explores the path of AD teaching according to the online and offline features of MTM. The improved ABC and Apriori are used to mine the deep information of TR, thus providing students with more accurate learning resources. The simulation results showed that the IABC converged with 300 iterations in the test function Sphere. The optimal value was $10^{-12}$. In Griewank and Rastigin functions, the optimal value of IABC converged at $10^{-10}$, and $10^{-11}$, respectively, with better convergence speed and accuracy. When the minimum support was different, Apriori's running time range was $3.5$ s${\sim} 15$ s and FP-growth was $3$ s$\sim4$ s. The improved Apriori's minimum value was 2 s, and the maximum value was 3s. At the same time, the running time of the improved Apriori in frequent 1-itemset and K-itemsets was about 2.5 s, which was up to 15s ahead of FP-growth. After the combination of IABC and improved Apriori, compared with K-means and FP-growth, the combined method increased by about 10%. In the student scoring, nearly half of the combined method was in the range of 80 to 90 points, which verified the effectiveness of the method in AD teaching. However, the study does not consider the influence of time factor when preprocessing TR data. Therefore, it is necessary to optimize the operation structure of the method to improve efficiency.