# Quantitative Influence Analysis of the Development Scale of Market Economy on the Level of Music Innovation

Authors: Yang Li; Qiuyi Zhang; Tianzhuo Gong
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Music art is a form of conveying cultural information and humanistic emotions. From ancient times to the present, the form of music has undergone great changes. The change of music form is closely related to the change in dynasties, the development of the market economy, and the change in humanistic spirit. Today, the development of music has reached a relatively prosperous stage, which is closely related to the rapid development of the market economy. At the heart of the quantitative analysis is the study of associations between data. However, it will be a difficult task to analyze the relationship between the development scale of the market economy and the form of music innovation only by artificial means. This research mainly uses a convolutional neural network and long and short-term memory neural network technology to quantitatively analyze the relationship between the development scale of the market economy and the form of music innovation, which is mainly a quantitative analysis of classical music, pop music, and rap music. The research results show that convolutional neural networks and long short-term memory neural networks have sufficient capabilities to quantitatively analyze the relationship between the market development scale and the form of music innovation. Neural networks with LSTM layers have lower errors in predicting market economic correlates than neural network methods without LSTM layers. The error is reduced by 0.27%. For the prediction of innovative forms of music, the largest prediction error is only 2.93%, which is closely related to the variability of popular music. The linear correlation indices for the predictions of the three forms of musical innovation also all exceed 0.955.


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## Body

## 1. Introduction

Music is an art form that reflects national culture and the emotions of life. From ancient times to the present, the form of music has undergone many changes. However, the original intention of the music is to convey a cultural message and a way of life [1, 2]. Poetry, lyrics, and music are an ancient form of music, and ancient people endowed life emotions in this form of music art. In today’s era, music is often in the form of pop songs or rap to show the charm of music. Ancient music often expresses the difficulties of life and the customs of the motherland, which will also be accompanied by the production of some musical instruments [3]. The music of today’s era is often used to express one’s own life emotions, life pressure, and the customs of the motherland. In general, the size of a market’s development affects how people live and produce, which in turn affects how people influence music creation. Once people’s way of life and production changes, it will lead to changes in the form of music that people create because the form of music is an art form that reflects people’s voices and moods [4, 5]. After the rapid development of the market economy, people’s life and production methods will undergo major changes, which will affect their mood and culture, which will lead to changes in the form of music innovation. For example, the economic development of the Tang Dynasty was relatively high, which resulted in a wide range of development scales and forms of music art. In the 21st century, China’s economy has also developed rapidly, and the support of the economy has led to the rapid development of musical instruments [6]. This allows people to create more forms of music. For example, this has derived many forms of popular music, folk music, classical music, and so on. It can be seen from the above that the development scale of the market economy will affect the development of music innovation. For the quantitative analysis between the form of music innovation and the development scale of the market economy, it is difficult to solve only by artificial means. This is because the music data and the data of the market economy development scale are huge, and there is a cumbersome relationship between these data. This study intends to use big data technology to quantitatively analyze the relationship between music innovation and market development scale.Big data technology is a field that has developed rapidly in recent years, which also promotes the development of intelligent life and production [7, 8]. The core advantage of big data technology is the processing of cumbersome data. Regardless of the field, these research objects and developmental forms can be quantitatively analyzed. The form and the amount of data computation in each field are huge, which is difficult to handle only by manual or professional knowledge [9]. The development of big data technology also has an important relationship with the computing performance of computers. In recent years, the computing performance of computers and the development of hardware devices have also promoted the rapid development of big data technology [10, 11]. Today’s computer has enough performance to support the operation of data in most fields. In the current life and production, the relationship between data is basically related to space, time, and environment. Big data technology has provided algorithms that can deal with spatial, temporal, and environmental correlations. In the quantitative analysis of the market development scale and the form of music innovation, it is mainly related to time and space, and the algorithms mainly include CNN and LSTM [12, 13]. The development of the market is closely related to time data, and there is a large spatial correlation between the elements of market development scale and the mapping of elements of musical innovation forms. The biggest advantage of big data technology is the processing of huge-scale data [14], and the quantitative analysis between the market size and the form of music innovation requires the support of data. Therefore, big data technology has obvious advantages in studying the relationship between market development scale and music innovation.Quantitative analysis of innovative forms of music mainly includes classical music, pop music, and rap. There are large differences in the data of these musical forms. And with the rapid development of new media technology and Internet technology, the amount of music data is huge. The development of the market economy will also produce great changes with the development of time, which will generate a huge amount of data. The relationship between the data of the music innovation form and the data of the market economy development scale is complex, and it is a nonlinear relationship. The time correlation algorithm of big data technology can fully extract the relevant characteristics of the development scale of the market economy and the changes in the form of music innovation. The spatial correlation algorithm of big data technology can map the nonlinear relationship between music innovation form and market size.This study uses a convolutional neural network (CNN) and long short-term memory (LSTM) neural network in big data technology to quantitatively analyze the relationship between market development scale and music innovation forms, which mainly include classical music, pop music, and rap music. This research mainly consists of 5 sections, and the research contents are as follows: Section1 mainly introduces the research significance of music innovation and the research background of big data technology. The current state of development of innovative forms of music is presented in Section 2. Section 3 mainly shows the working principle of CNN and LSTM technology in big data technology and the scheme of quantitative analysis. Section 4 mainly analyzes the relationship between CNN and LSTM algorithms in a quantitative analysis of the market development scale and the form of music innovation. Section 5 summarizes the entire study.


## 2. Related Work

The development of innovative forms of music is rapid, and it is closely related to many factors. The changes in the form of music innovation are also closely related to the development of the market economy. A lot of research has been done on musical forms and other aspects by many researchers. May et al. [15] mainly used new concepts to study the aspects of popular music and music literacy. It first used popular music as a text resource to explore the accuracy and feasibility of music literacy. Then, he considered how to combine popular music with music education to promote the development of music education. It can also promote the development of music literacy. Elbir et al. [16] mainly study the music recommendation system of the music monitoring platform, which can complete the classification of music forms and genres according to people’s preferences. It mainly uses deep learning neural network models to extract musical features based on acoustic properties. The research results show that this deep model can better perform the recommendation and classification of music genres and musical forms. Dobrota et al. [17] mainly studied the students’ preference for classical music through questionnaires. The findings show that younger students have a higher degree of preference for classical music. Extracurricular activities in music courses had less effect on preference for classical music. This research will better guide the development of music teaching and the teaching of classical music. Andrea et al. [18] utilized deep learning and convolutional neural network methods to identify the positional and symbolic features of music in online music. This recognition task is mainly to identify musical positions based on musical notes, key signatures, staves, and other related features. The research results show that the CNN method can accurately identify the location of music with a recognition rate of over 80%. Fricke et al. [19] mainly study the accuracy of manual measurement and computer grade evaluation methods in the music preference evaluation system. The results show that the musical features extracted by artificial means are in good agreement with those extracted by computer. He also used PCA and Procrustes methods for analysis, which showed that computer-extracted features can be used to assess people’s preferences and preferred styles of music. Kertz-Welzel [20] believed that classical music is crucial in music education. It represents the essence of music. This study analyzes the educational perspectives of classical music from a philosophical and social perspective. It also explores the educational model of classical music dominated by British and American education. He believes that classical music is regarded as an essential music culture in music education all over the world. Kai [21] designed a music feature recognition system utilizing IoT technology. The sensors of the IoT system will be placed in different positions to obtain music information to further complete the analysis and processing of music signals. He uses a dynamic time regularization algorithm to analyze the maximum similarity of musical features. The research results show that the music recognition system is relatively stable, and it can capture high-quality music signals. It can also better assist people in completing the extraction and recognition of musical style and emotional features. Other researchers have also conducted more research on the related characteristics and identification of music using different methods. The innovation of this research is mainly to use the deep learning method to analyze the relationship between the development of the market economy and the form of music innovation, which is no longer limited to a single music feature. It also conducts a quantitative analysis of innovative forms of music.


## 3. Application of Big Data Technology in Quantitative Analysis of Music Form

### 3.1. The Significance of CNN and LSTM for Quantitative Analysis

This study mainly uses CNN and LSTM algorithms to achieve a quantitative analysis of the relationship between the scale of the market economy and the form of music innovation. Whether it is the scale of the market economy or the form of music innovation, both are closely related to time and space. The LSTM algorithm can be used to extract the temporal features of the scale factor of the market economy, which can form a mapping with a certain relationship to the musical innovation form. CNNs can map the complex nonlinear relationship between the size of the market economy and the form of musical innovation. The nonlinear relationship between the two is difficult to resolve by manual means. At the same time, there is a large amount of data in the factors of market economy scale and music innovation forms, which requires computers to process these complex data. In conclusion, CNN and LSTM methods can solve the cumbersome relationship between the factors of market economy development scale and the level of music innovation. This also enables quantitative analysis of data, which is not just a macro analysis.


### 3.2. The Quantitative Analysis Scheme Design and CNN Algorithm

This study mainly selects three forms of music for quantitative analysis, namely classical, pop, and rap music. Pop music and rap music are the two most popular forms of music in the current economic model. Classical music is also a relatively traditional music mode, which is closely related to the development of the market economy. Figure1 shows the design of the quantitative analysis of market economic development factors and music innovation forms. In this study, the data related to the development of the market economy are processed in the form of time series and input into the LSTM layer, which is also the input data of CNN. The relevant data of the music innovation form is used as the label data and the output data of the CNN. First, this scheme takes the factor of market economy development scale as the input data of big data technology, which will be used to map the relationship between music innovation forms. The relevant data of the market factors are organized into the form of time series, which will be passed through the LSTM neural network method. The LSTM method will extract the time characteristics of the development scale of the market economy because the development scale of the market economy has a greater relationship with the changes in time. The data extracted by the LSTM neural network method will be used as the input data of the CNN method. At this time, it needs to use the data in the innovative form of music as the output data of CNN, which will form a one-to-one mapping relationship.Figure 1
Scheme design of quantitative analysis of market economy scale and music innovation form.The CNN method has been applied in many fields, and it has also been shown to have high performance for feature extraction and nonlinear relation mapping. The development scale of the market economy and the innovative form of music are both difficult to quantify research objects in the form of data. Both need to be digitized, which can then be quantitatively analyzed using CNNs. Therefore, the advantage of CNN is to deal with the nonlinear relationship between data. Figure2 shows the workflow of CNN. The work of CNN mainly relies on convolutional layers, pooling layers, and activation functions to complete. The convolutional layer is the core part of CNN, which will complete the feature extraction of the research object and reduce the amount of parameter computation. It can also be seen from Figure 2 that CNN can complete the nonlinear relationship mapping between the input data and the output data, which is also done through the feature extraction function of the convolution layer and the pooling layer. The pooling layer is mainly divided into a maximum pooling layer and an average pooling layer. The sampling method is divided into two methods: upsampling and downsampling. In this study, we sampled max-pooling layers and downsampling methods to extract relevant features.Figure 2
The workflow of the CNN method.In the operation and iteration process of CNN, the process of CNN is adjusted by many hyperparameters, such as the number of filters, step size, and other factors. However, there is a certain relationship between these hyperparameters. Equation (1) shows the relation satisfied by the CNN hyperparameters. Here, s represents the sliding step size of the window, and p represents the padding size of the window. k is the size of the receptive field of the convolutional layer. w is the size of the output weights.(1)w′=w+2p−ks+1.In quantitative analysis, some data is required here to process. In this study, the scale of market economic development and the form of music innovation are digitized so that the data can be input and output in the form of a matrix. Equations (2) and (3) show the representation of test data and predict data. Among them, x represents the input data, which refers to the data of the development scale of the market economy. y is the output data, which here refers to the data in the form of music innovation.(2)Test=x1,y1,x2,y2,…,xm,ym,…,xM,yM,(3)y^=y^1,y^2,…,y^m,…,y^M.In the calculation process of CNN, it generally adopts the method of gradient descent. The gradient descent method is to find the direction of gradient descent through the derivation operation. This will involve many derivation operations during each layer of the CNN. Equation (4) shows how the derivation of the weights at each layer is calculated. In the actual iterative process, it will use the automatic differentiation (AD) technique. Equation (5) shows the derivation rule for weights, which is a weighted way of equation (4). ω and δ are the weight matrix and the bias parameter, respectively. dk is the real value, yj is the optimized value.(4)E=12∑k=1mdk−fnetwk2=12∑k=1mdk−f∑j=0nωjkyj2,(5)∂E∂kijζ=∑u,vδjζuvpiζ−1uv.


### 3.3. The Market Economy Feature Extraction Based on Algorithm LSTM

In different periods, the scale of market economy development is different. The scale of market economy development is also an economic model that gradually accumulates over time. Therefore, before studying the quantitative analysis of the scale of market economy development and music innovation, it needs to extract the time characteristics of the scale of market economy development. Figure3 shows the workflow of the LSTM method. It requires the input data to be in the form of a time series. Therefore, the data of the development scale of the market economy needs to be processed into the form of time series. The input of the LSTM algorithm will contain the current state data and part of the historical state information data, which is why the LSTM algorithm can achieve temporal feature extraction. The LSTM algorithm can also implement multiple network layers in order to extract deeper data features. The LSTM sampled in this study contains a 4-layer network structure. The last layer contains a fully connected layer, which contains 256 hidden operators.Figure 3
The workflow of LSTM method.It can also be seen from Figure3 that the LSTM method has more gate structures, which are realized by assigning different weights to the data. It can optionally filter the data by the size of the weights. Equation (6) shows how the input gate of the LSTM method is calculated. The input gate will selectively input current state information data and historical state information data according to the size of the weight, where ht−1 is historical state data. W and b are the weight matrix and the bias parameter, respectively.(6)ft=σwf⋅ht−1,Pt+bf.Equations (7) and (8) show the calculation method of the forget gate of LSTM. The forgetting gate will give different weights to the historical state information data, and it will input the historical state information with greater correlation. σ and tanh represent the activation function. tanh is the activation function.(7)it=σωi⋅hi−1,Pt+bi,(8)C˜t=tanhwc⋅ht−1,Pt+bc.Equations (9) and (10) show how the output gate is calculated. The input gate will be connected to the forget gate of the next layer. It will selectively output data according to the weight. These data will be passed through an activation function. This study chose the tanh function as the loss function, which is a hyperbolic tangent function.(9)Ot=σwo⋅h⟶t−1,Pt+bo,(10)h⟶t=Ot×tanhC⟶t.The refresh gate will refresh the weights. Equation (11) shows how the refresh gate is calculated. It will give different weights to current state information and historical state information. ct is the state unit of the LSTM at time t. The tanh is the activation function.(11)C⟶t=ft×C⟶t−1+it×C⟶t.


## 3.1. The Significance of CNN and LSTM for Quantitative Analysis

This study mainly uses CNN and LSTM algorithms to achieve a quantitative analysis of the relationship between the scale of the market economy and the form of music innovation. Whether it is the scale of the market economy or the form of music innovation, both are closely related to time and space. The LSTM algorithm can be used to extract the temporal features of the scale factor of the market economy, which can form a mapping with a certain relationship to the musical innovation form. CNNs can map the complex nonlinear relationship between the size of the market economy and the form of musical innovation. The nonlinear relationship between the two is difficult to resolve by manual means. At the same time, there is a large amount of data in the factors of market economy scale and music innovation forms, which requires computers to process these complex data. In conclusion, CNN and LSTM methods can solve the cumbersome relationship between the factors of market economy development scale and the level of music innovation. This also enables quantitative analysis of data, which is not just a macro analysis.


## 3.2. The Quantitative Analysis Scheme Design and CNN Algorithm

This study mainly selects three forms of music for quantitative analysis, namely classical, pop, and rap music. Pop music and rap music are the two most popular forms of music in the current economic model. Classical music is also a relatively traditional music mode, which is closely related to the development of the market economy. Figure1 shows the design of the quantitative analysis of market economic development factors and music innovation forms. In this study, the data related to the development of the market economy are processed in the form of time series and input into the LSTM layer, which is also the input data of CNN. The relevant data of the music innovation form is used as the label data and the output data of the CNN. First, this scheme takes the factor of market economy development scale as the input data of big data technology, which will be used to map the relationship between music innovation forms. The relevant data of the market factors are organized into the form of time series, which will be passed through the LSTM neural network method. The LSTM method will extract the time characteristics of the development scale of the market economy because the development scale of the market economy has a greater relationship with the changes in time. The data extracted by the LSTM neural network method will be used as the input data of the CNN method. At this time, it needs to use the data in the innovative form of music as the output data of CNN, which will form a one-to-one mapping relationship.Figure 1
Scheme design of quantitative analysis of market economy scale and music innovation form.The CNN method has been applied in many fields, and it has also been shown to have high performance for feature extraction and nonlinear relation mapping. The development scale of the market economy and the innovative form of music are both difficult to quantify research objects in the form of data. Both need to be digitized, which can then be quantitatively analyzed using CNNs. Therefore, the advantage of CNN is to deal with the nonlinear relationship between data. Figure2 shows the workflow of CNN. The work of CNN mainly relies on convolutional layers, pooling layers, and activation functions to complete. The convolutional layer is the core part of CNN, which will complete the feature extraction of the research object and reduce the amount of parameter computation. It can also be seen from Figure 2 that CNN can complete the nonlinear relationship mapping between the input data and the output data, which is also done through the feature extraction function of the convolution layer and the pooling layer. The pooling layer is mainly divided into a maximum pooling layer and an average pooling layer. The sampling method is divided into two methods: upsampling and downsampling. In this study, we sampled max-pooling layers and downsampling methods to extract relevant features.Figure 2
The workflow of the CNN method.In the operation and iteration process of CNN, the process of CNN is adjusted by many hyperparameters, such as the number of filters, step size, and other factors. However, there is a certain relationship between these hyperparameters. Equation (1) shows the relation satisfied by the CNN hyperparameters. Here, s represents the sliding step size of the window, and p represents the padding size of the window. k is the size of the receptive field of the convolutional layer. w is the size of the output weights.(1)w′=w+2p−ks+1.In quantitative analysis, some data is required here to process. In this study, the scale of market economic development and the form of music innovation are digitized so that the data can be input and output in the form of a matrix. Equations (2) and (3) show the representation of test data and predict data. Among them, x represents the input data, which refers to the data of the development scale of the market economy. y is the output data, which here refers to the data in the form of music innovation.(2)Test=x1,y1,x2,y2,…,xm,ym,…,xM,yM,(3)y^=y^1,y^2,…,y^m,…,y^M.In the calculation process of CNN, it generally adopts the method of gradient descent. The gradient descent method is to find the direction of gradient descent through the derivation operation. This will involve many derivation operations during each layer of the CNN. Equation (4) shows how the derivation of the weights at each layer is calculated. In the actual iterative process, it will use the automatic differentiation (AD) technique. Equation (5) shows the derivation rule for weights, which is a weighted way of equation (4). ω and δ are the weight matrix and the bias parameter, respectively. dk is the real value, yj is the optimized value.(4)E=12∑k=1mdk−fnetwk2=12∑k=1mdk−f∑j=0nωjkyj2,(5)∂E∂kijζ=∑u,vδjζuvpiζ−1uv.


## 3.3. The Market Economy Feature Extraction Based on Algorithm LSTM

In different periods, the scale of market economy development is different. The scale of market economy development is also an economic model that gradually accumulates over time. Therefore, before studying the quantitative analysis of the scale of market economy development and music innovation, it needs to extract the time characteristics of the scale of market economy development. Figure3 shows the workflow of the LSTM method. It requires the input data to be in the form of a time series. Therefore, the data of the development scale of the market economy needs to be processed into the form of time series. The input of the LSTM algorithm will contain the current state data and part of the historical state information data, which is why the LSTM algorithm can achieve temporal feature extraction. The LSTM algorithm can also implement multiple network layers in order to extract deeper data features. The LSTM sampled in this study contains a 4-layer network structure. The last layer contains a fully connected layer, which contains 256 hidden operators.Figure 3
The workflow of LSTM method.It can also be seen from Figure3 that the LSTM method has more gate structures, which are realized by assigning different weights to the data. It can optionally filter the data by the size of the weights. Equation (6) shows how the input gate of the LSTM method is calculated. The input gate will selectively input current state information data and historical state information data according to the size of the weight, where ht−1 is historical state data. W and b are the weight matrix and the bias parameter, respectively.(6)ft=σwf⋅ht−1,Pt+bf.Equations (7) and (8) show the calculation method of the forget gate of LSTM. The forgetting gate will give different weights to the historical state information data, and it will input the historical state information with greater correlation. σ and tanh represent the activation function. tanh is the activation function.(7)it=σωi⋅hi−1,Pt+bi,(8)C˜t=tanhwc⋅ht−1,Pt+bc.Equations (9) and (10) show how the output gate is calculated. The input gate will be connected to the forget gate of the next layer. It will selectively output data according to the weight. These data will be passed through an activation function. This study chose the tanh function as the loss function, which is a hyperbolic tangent function.(9)Ot=σwo⋅h⟶t−1,Pt+bo,(10)h⟶t=Ot×tanhC⟶t.The refresh gate will refresh the weights. Equation (11) shows how the refresh gate is calculated. It will give different weights to current state information and historical state information. ct is the state unit of the LSTM at time t. The tanh is the activation function.(11)C⟶t=ft×C⟶t−1+it×C⟶t.


## 4. Result Analysis and Discussion

### 4.1. Analysis of LSTM Algorithm in Extracting Market Economic Features

This study selects data from several music creation institutions in Beijing and the development scale of Beijing’s market economy for quantitative analysis. Generally speaking, the development scale of the market economy in relatively large cities varies greatly, and the level of music innovation in this region is also relatively high. Moreover, the music innovation mode here is also changing rapidly. Therefore, this study selected the relevant data of Beijing as the research object of quantitative analysis. This research will process the data related to the development of the market economy and the form of music innovation into the data of uniform distribution and the same interval using the normalization method.For the prediction of the development scale of the market economy, this study selects the neural network method with and without the LSTM method for relevant quantitative analysis. In this study, algorithms with LSTM layers refer to hybrid LSTM-CNN algorithms and algorithms without LSTM layers refer to CNN algorithms. Figure4 shows the errors of the two methods in predicting factors related to the size of market economic development. From Figure 4, it can be seen that the neural network method with the LSTM layer has better accuracy than the method without the LSTM layer. For the method with LSTM layers, the maximum prediction error is only 2.85%. The largest prediction error is 3.08% for the method without LSTM layers. The forecast error of factors related to the development of the market economy decreased by 0.23%. This shows that the neural network method with the LSTM layer has higher performance in extracting factors related to the development of the market economy. At the same time, this also shows that the development of the market economy has a great correlation with time.Figure 4
The prediction errors of factors related to market economic development using with and without the LSTM method.From the above description, it can be seen that the neural network method with the LSTM layer has higher performance in quantitative analysis of market economic development factors and music innovation forms, which is due to the fact that the prediction errors with LSTM are lower than those without LSTM layers. Therefore, in the quantitative analysis of the three forms of music innovation, this study chooses the neural network method with the LSTM layer to carry out the correlation analysis. Figure5 shows the prediction errors for three forms of musical innovation, which refer to classical music, pop music, and rap music. Overall, CNN and LSTM methods have small errors in quantitative analysis of the market economy and music innovation forms, and all prediction errors are within 3%. This error is reliable enough to quantitatively analyze innovative forms of music. The largest prediction error is only 2.93%, and this part of the error comes from the prediction of popular music. Pop music is a more popular form of music in today’s society. It has a greater relationship with the development scale of the market economy. When the market economy develops better, the creative mode of pop music will also change. The variability of the development scale of the market economy has led to the variability of popular music forms. This leads to a large error in predicting popular music. The creative mode of classical music is relatively stable, and it is less affected by the development scale of the market economy. This resulted in a small error in predicting classical music, with a prediction error of just 1.78%. For the prediction of rap music features, this part of the error is only 2.23%. This is also a small and acceptable margin of error for a similar study of musical innovation. In conclusion, the CNN and LSTM methods have sufficient capabilities to quantitatively analyze the relationship between the size of market development and the form of music innovation.Figure 5
The prediction errors of musical innovative forms using LSTM methods.


### 4.2. Quantitative Analysis of Predictive Accuracy of Musical Innovation Patterns and Market Economy Development

For the three musical innovations, pop predictions are the hardest. This is mainly due to the close correlation between the creation of popular music and the development scale of the market economy. Figure6 shows the distribution of predicted and actual values for popular music. The yellow area represents the prediction error between the predicted value of pop music and the actual value. It can also be seen from Figure 6 that the values of different groups of popular music fluctuate greatly, which is also related to the variability of popular music. However, CNN and LSTM methods can also better predict the trend and value of popular music. If there is a small correlation between the development scale of the market economy and popular music, this will lead to a large error in the prediction of popular music. This is because the data of the market economy development scale is the input data of CNN and LSTM. However, from the results in Figure 6, it can be found that although the development scale of the market economy is relatively large, it still has a relatively large correlation with popular music. Most pop music predictions are larger than they actually are. This may have a greater relationship with the ideal prediction environment of the algorithm. From the yellow prediction error area in Figure 6, it can also be seen that the CNN and LSTM methods have better accuracy in quantitatively analyzing the scale of market economic development and the form of music innovation.Figure 6
The distribution of predicted and actual values of popular music.Rap music is a music innovation model that has developed rapidly in recent years. This is also closely related to rapid economic development. Since rap music is a relatively new form of music, this leads to huge challenges in quantitative analysis of rap music. Figure7 shows the prediction error for rap music. Generally speaking, the error of the error scatter plot does not exceed 5%, which indicates that the prediction accuracy has met the needs of the prediction. In this study, the input and output of the CNN and LSTM algorithms are the data related to the development of the market economy and the related data of rap music, respectively. If the model cannot well map the relationship between the market economy and rap music, it means that there is a small relationship between the development of the market economy and rap music. However, from the prediction error of rap music in Figure 7, it can be seen that the development scale of the market economy and rap music also have a greater correlation because this part of the error is relatively small. Overall, all forecast errors are within an acceptable range. Most forecast errors are within 3%. At the same time, it can also be seen from Figure 7 that there is a relatively large fluctuation in the prediction error of the rap music form, which also shows that rap music is greatly affected by the scale of market economic development. Only a small part of rap music has a prediction error of more than 3%, but this part of the error is also within 4%. This further illustrates that the CNN and LSTM methods have high confidence in predicting the form of rap music.Figure 7
The prediction error distribution for rap music.Classical music is a relatively stable musical art form, and it is less affected by the scale of market economic development. However, in today’s rapid economic development, the development of classical music has been affected to a certain extent. In terms of quantitative analysis of the development scale of the market economy and the form of music innovation, it also analyzes the impact of traditional music forms. Figure8 shows a box plot of the distribution of predicted and actual values for classical music forms. It can also be seen from Figure 8 that the change of classical music is relatively small with the change of the scale of market economy development. Overall, there is a small error between the predicted and actual values for classical music. CNN and LSTM methods can better perform quantitative analysis and prediction tasks on the changing forms and numerical values of classical music. There is also a small difference in cabinet shape and size between the predicted and actual values for classical music. This shows that the CNN and LSTM methods can more accurately quantitatively analyze the relationship between the development scale of the market economy and classical music. Figure 9 shows the linear correlation of predicted values for classical music. In Figure 9, the red line represents the 95% confidence band, and the blue line represents the linear function y = x. It can also be seen from Figure 9 that classical music has a good linear correlation. The closer the linear correlation coefficient is to 1, the better the prediction efficiency is. Generally speaking, the linear correlation coefficient exceeds 0.95, which means that the prediction effect is better. The numerical values of classical music are distributed on both sides of the linear function, and the distance between these data values and the linear function is relatively close.Figure 8
Predictive distribution box plot for classical music.Figure 9
Linear correlation of predicted values for classical music.


## 4.1. Analysis of LSTM Algorithm in Extracting Market Economic Features

This study selects data from several music creation institutions in Beijing and the development scale of Beijing’s market economy for quantitative analysis. Generally speaking, the development scale of the market economy in relatively large cities varies greatly, and the level of music innovation in this region is also relatively high. Moreover, the music innovation mode here is also changing rapidly. Therefore, this study selected the relevant data of Beijing as the research object of quantitative analysis. This research will process the data related to the development of the market economy and the form of music innovation into the data of uniform distribution and the same interval using the normalization method.For the prediction of the development scale of the market economy, this study selects the neural network method with and without the LSTM method for relevant quantitative analysis. In this study, algorithms with LSTM layers refer to hybrid LSTM-CNN algorithms and algorithms without LSTM layers refer to CNN algorithms. Figure4 shows the errors of the two methods in predicting factors related to the size of market economic development. From Figure 4, it can be seen that the neural network method with the LSTM layer has better accuracy than the method without the LSTM layer. For the method with LSTM layers, the maximum prediction error is only 2.85%. The largest prediction error is 3.08% for the method without LSTM layers. The forecast error of factors related to the development of the market economy decreased by 0.23%. This shows that the neural network method with the LSTM layer has higher performance in extracting factors related to the development of the market economy. At the same time, this also shows that the development of the market economy has a great correlation with time.Figure 4
The prediction errors of factors related to market economic development using with and without the LSTM method.From the above description, it can be seen that the neural network method with the LSTM layer has higher performance in quantitative analysis of market economic development factors and music innovation forms, which is due to the fact that the prediction errors with LSTM are lower than those without LSTM layers. Therefore, in the quantitative analysis of the three forms of music innovation, this study chooses the neural network method with the LSTM layer to carry out the correlation analysis. Figure5 shows the prediction errors for three forms of musical innovation, which refer to classical music, pop music, and rap music. Overall, CNN and LSTM methods have small errors in quantitative analysis of the market economy and music innovation forms, and all prediction errors are within 3%. This error is reliable enough to quantitatively analyze innovative forms of music. The largest prediction error is only 2.93%, and this part of the error comes from the prediction of popular music. Pop music is a more popular form of music in today’s society. It has a greater relationship with the development scale of the market economy. When the market economy develops better, the creative mode of pop music will also change. The variability of the development scale of the market economy has led to the variability of popular music forms. This leads to a large error in predicting popular music. The creative mode of classical music is relatively stable, and it is less affected by the development scale of the market economy. This resulted in a small error in predicting classical music, with a prediction error of just 1.78%. For the prediction of rap music features, this part of the error is only 2.23%. This is also a small and acceptable margin of error for a similar study of musical innovation. In conclusion, the CNN and LSTM methods have sufficient capabilities to quantitatively analyze the relationship between the size of market development and the form of music innovation.Figure 5
The prediction errors of musical innovative forms using LSTM methods.


## 4.2. Quantitative Analysis of Predictive Accuracy of Musical Innovation Patterns and Market Economy Development

For the three musical innovations, pop predictions are the hardest. This is mainly due to the close correlation between the creation of popular music and the development scale of the market economy. Figure6 shows the distribution of predicted and actual values for popular music. The yellow area represents the prediction error between the predicted value of pop music and the actual value. It can also be seen from Figure 6 that the values of different groups of popular music fluctuate greatly, which is also related to the variability of popular music. However, CNN and LSTM methods can also better predict the trend and value of popular music. If there is a small correlation between the development scale of the market economy and popular music, this will lead to a large error in the prediction of popular music. This is because the data of the market economy development scale is the input data of CNN and LSTM. However, from the results in Figure 6, it can be found that although the development scale of the market economy is relatively large, it still has a relatively large correlation with popular music. Most pop music predictions are larger than they actually are. This may have a greater relationship with the ideal prediction environment of the algorithm. From the yellow prediction error area in Figure 6, it can also be seen that the CNN and LSTM methods have better accuracy in quantitatively analyzing the scale of market economic development and the form of music innovation.Figure 6
The distribution of predicted and actual values of popular music.Rap music is a music innovation model that has developed rapidly in recent years. This is also closely related to rapid economic development. Since rap music is a relatively new form of music, this leads to huge challenges in quantitative analysis of rap music. Figure7 shows the prediction error for rap music. Generally speaking, the error of the error scatter plot does not exceed 5%, which indicates that the prediction accuracy has met the needs of the prediction. In this study, the input and output of the CNN and LSTM algorithms are the data related to the development of the market economy and the related data of rap music, respectively. If the model cannot well map the relationship between the market economy and rap music, it means that there is a small relationship between the development of the market economy and rap music. However, from the prediction error of rap music in Figure 7, it can be seen that the development scale of the market economy and rap music also have a greater correlation because this part of the error is relatively small. Overall, all forecast errors are within an acceptable range. Most forecast errors are within 3%. At the same time, it can also be seen from Figure 7 that there is a relatively large fluctuation in the prediction error of the rap music form, which also shows that rap music is greatly affected by the scale of market economic development. Only a small part of rap music has a prediction error of more than 3%, but this part of the error is also within 4%. This further illustrates that the CNN and LSTM methods have high confidence in predicting the form of rap music.Figure 7
The prediction error distribution for rap music.Classical music is a relatively stable musical art form, and it is less affected by the scale of market economic development. However, in today’s rapid economic development, the development of classical music has been affected to a certain extent. In terms of quantitative analysis of the development scale of the market economy and the form of music innovation, it also analyzes the impact of traditional music forms. Figure8 shows a box plot of the distribution of predicted and actual values for classical music forms. It can also be seen from Figure 8 that the change of classical music is relatively small with the change of the scale of market economy development. Overall, there is a small error between the predicted and actual values for classical music. CNN and LSTM methods can better perform quantitative analysis and prediction tasks on the changing forms and numerical values of classical music. There is also a small difference in cabinet shape and size between the predicted and actual values for classical music. This shows that the CNN and LSTM methods can more accurately quantitatively analyze the relationship between the development scale of the market economy and classical music. Figure 9 shows the linear correlation of predicted values for classical music. In Figure 9, the red line represents the 95% confidence band, and the blue line represents the linear function y = x. It can also be seen from Figure 9 that classical music has a good linear correlation. The closer the linear correlation coefficient is to 1, the better the prediction efficiency is. Generally speaking, the linear correlation coefficient exceeds 0.95, which means that the prediction effect is better. The numerical values of classical music are distributed on both sides of the linear function, and the distance between these data values and the linear function is relatively close.Figure 8
Predictive distribution box plot for classical music.Figure 9
Linear correlation of predicted values for classical music.


## 5. Conclusions

Music is an important part of people’s life and production activities. The development of music art has a lot to do with the factors related to the development scale of the market economy. However, it is difficult to quantitatively analyze the relationship between the development scale of the market economy and the form of music innovation in an artificial way.This study uses CNN and LSTM algorithms in big data technology to achieve a quantitative analysis of music innovation forms. LSTM can better extract the time characteristics of the development scale of the market economy, which is beneficial to the quantitative analysis of music innovation forms. This study mainly analyzes three types of music: classical music, pop music, and rap music. Overall, CNN and LSTM methods can quantitatively analyze the relationship between the scale of market economic development and the form of music innovation. The largest prediction error is only 2.93%, and this part of the error mainly comes from the prediction in the form of popular music. The smallest prediction error is only 1.78%, which mainly comes from the prediction of classical music. The linear correlations for classical music also all exceed 0.955. All prediction errors for the rap music form are within 3%. This shows that CNN and LSTM methods are sufficient to quantitatively analyze the relationship between the scale of market economic development and the form of music innovation.



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*Source: 4524811-2022-07-11.xml*