High technology industries are playing an increasingly important role in the optimization of regional industrial structure. Spatial statistics is an analytical method to analyze statistical information through spatial position. Compared with traditional statistical methods, spatial statistical analysis has its own advantages in understanding the geographical location characteristics and spatial pattern by considering the spatial position and neighborhood relationship according to correlation analysis. This paper combines the principal component analysis method of statistics and spatial analysis, uses R language [1] to make the analysis results intuitively expressed on the spatial map based on the research results.

Spatial statistical analysis was originally proposed by South African geologist Krige, many foreign scholars carried out extensive and in-depth research on it. From 1970s to 1990s, Cliff and Griffith in the analysis [2] not only conducted many meaningful explorations on the verification of spatial autocorrelation, but also establish spatial model. Anselin and Getis in the analysis [3] and [4] conducted research on Local Spatial Statistical Indicators, including ESDA (Exploratory Spatial Data Analysis), LISA (Local Indicators of Spatial Analysis), Moran scatter map, etc. J.R. Friedman in the analysis [5] based on the theory of unbalanced regional economic development, divided the spatial structure of the economic layout into two systems, center and periphery, emphasizing that innovation elements gradually spread to the periphery while strengthening the development capacity and vitality of the “center”. Since the 1990s, regional economic research has entered the stage of new spatial economics, in which new economic geography theories such as P.R. Krugman [6], Masahisa Fujita [7], and A. J. Venables [8] have become mainstream. In 2000, Okabe [9] et al. discussed spatial interpolation, spatial model and spatial point pattern analysis from the perspective of spatial mosaic, and Lloyd [10] et al. systematically summarized the statistical analysis of local models and spatial point patterns. Wu Yuming in the analysis [11] and [12] uses the spatial constant-coefficient spatial autoregressive model, spatial error model, and geographic weighted regression model of spatial statistical analysis to conduct a quantitative analysis of the overall R & D and innovation in China’s provinces. Chen Hongchuan in the analysis [13] built a high-tech industry technology innovation capability evaluation index system, used data mining method (K-means clustering) to evaluate the high-tech industry technology innovation capacity. Zheng Shuwang and Xu Zhenlei in the analysis [14] used partial least squares regression model to analyze the influencing factors of the high-tech industries’ technological innovation capability in the three northeastern provinces, and established a comprehensive evaluation index system for technical innovation capability. Fan Decheng and Du Mingyue in the analysis [15] used the TOPSIS grey relation projection method to calculate the close degree of grey relation projection, introduced coordination degree model to evaluate regional coordination development level and conducted quadratic weighted calculation. Wu Yanxia and Zhou Chunguang in the analysis [16] used spatial panel Dubin model to test the relationship between financial agglomeration and its spatial overflow and the development of high-tech industries. The results show that the Guangdong-Hong Kong-Macao Greater Bay Area financial agglomeration has the ability to promote the development of high-tech industries.

1) In this paper, we conduct comprehensive evaluation of the high tech industry development under principal component analysis (PCA) combined with spatial analysis to find the scientific way to develop high-tech industry.

2) The research results of this paper will be applied in the management and decision-making of high-tech industry in China. Through the research on industrial structure and regional distribution, some feasible countermeasures and suggestions are put forward.

3) This paper introduces the spatial correlation effect analysis for the first time in the domestic industrial statistical analysis research by using the theoretical method of spatial statistical analysis and the integrated statistical model. We systematically and multi-dimensionally conduct empirical test and analysis on the overall research of China’s high-tech industry.

To conduct comprehensive analysis, it is necessary to construct the evaluation index system. Generally speaking, the principles to be followed in constructing the comprehensive evaluation index system are as follows:

1) Principle of system comprehensiveness.

2) Principle of stable comparability.

3) Principle of scientific simplicity.

4) Principle of flexibility and operability.

In order to fully reflect the situation of national high-tech industry and understand the impact of regional differences on industrial development, it is necessary to conduct classification research according to the similarity of the development situation of high-tech industry in various regions. On the basis of collecting and collating the relevant data released by the country, we selected 10 evaluation indexes in 4 categories, including production and operation conditions as shown in Table 1.

According to the four types of statistical indicators, we establish the astrological map of the development data of each province in 2019.

Principal component analysis (PCA) is a powerful tool for dimensionality reduction of variables, and its basic idea is to try to recombine correlated indicators into a new set of independent comprehensive indicators to replace the original ones. The mathematical solution is to take the original p indices as a linear combination of the new indices. The first linear combination, namely the first composite index, is denoted as y₁. In order to make this linear combination unique, it is required that the variance of y₁ is the largest among all linear combinations. If the first principal component is not enough to represent all the information of the original p indexes, then consider selecting the second principal component y₂, and require the existing information of y₁ not to appear in y₂, that is, Cov (y₁, y₂) = 0. Figure 11 shows schematic diagram of principal component analysis.

As shown in Figure 11, the indexes (scatter points) with x₁-x₂ as the axis have a large projection on x₁ and x₂, so both indexes contain the necessary information of the data. However, if we find out there is a strong correlation between x₁ and x₂, and the data could be distributed along y₁, then we can carry out simple transformation.

{ y 1 = cos θ x 1 + sin θ x 2 y 2 = − sin θ x 1 + cos θ x 2 (1)

After this transformation, the information of the original data is mainly contained on the y₁ axis under the new coordinate axis, while the information projection on the y₂ axis is very small, which can be ignored. If only y₁ is selected for study, we can successfully achieve the dimensionality reduction processing.

The case of multidimensional variables is similar to that of two-dimensional

variables, but we can only imagine the abstract space, such as a multidimensional ellipsoid with high fluctuation. In order to reduce the dimension, the principal component analysis is basically completed by first finding out each principal axis of the ellipsoid. Then calculate the new axis standard which can represent most of the principal axis information as a new variable. Similar to the two-dimensional case, the spindles of the higher dimensional ellipsoid are also required to be perpendicular to each other, and these new spindles that are orthogonal to each other are linear combinations of the original spindles, which are the principal components. The fewer principal components can be selected for study, the better the dimensionality reduction effect will be. Most researchers believe that the criterion for selecting principal components is that the sum of the principal axes represented by the new principal components should account for most of the sum of the original principal axes. Some scholars suggest that the total length of the spindle selected accounts for more than 80% of the total length of all spindles. This principle can be used as a basic treatment principle.

Principal component analysis process:

1) Find the eigenvalues and eigenvectors of the correlation matrix;

2) Calculate variance contribution rate and cumulative variance contribution rate: the contribution rate of each principal component represents the percentage of the total information of the original data;

3) Determine the principal components: let comp.1, comp.2 ... comp.p be p principal components, in which the total amount of data information contained by the first m principal components (i.e. their cumulative variance contribution rate) is not less than 80%, the first m principal components should be used to reflect the original evaluation object.

4) Use the linear combination of the original indexes to calculate the scores of each principal component: take the eigenvector as the weight, represent each principal component as the linear combination of the original indexes, and the meaning of the principal component is determined by the comprehensive meaning of the indexes with greater weight in each linear combination.

Comp . j = u j 1 x 1 + u j 2 x 2 + ⋯ + u j p x p       j = 1 , 2 , ⋯ , m (2)

The formula is called principal component score function, which is used to calculate the principal component score of each sample. If m = 2, then the p variables of each sample can be substituted into the above equation to calculate the principal component scores of each sample, then they can be used as scatter plots of principal component scores on the plane so that the samples can be classified.

5) Take the variance (characteristic value) of each principal component as weight, obtained comprehensive score.

Comp = λ 1 Comp .1 + λ 2 Comp .2 + ⋯ + λ m Comp . m λ 1 + λ 2 + ⋯ + λ m = ∑ j = 1 m W j Comp . j (3)

where W_j is the weight of the principal component, the ranking can be obtained by using the total score.

The principal component analysis function is used to analyze data, where X is the data box, m is the number of factors, whose default is 2. Plot is the main component graph. When these parameters are TRUE, the function program will automatically calculate and output the result. When the parameter value is FALSE, it is not calculated.

Next, due to the fact that there are many years, we will take the data of year 2019 as an example for principal component analysis.

1) find the principal components of the correlation matrix

2) determine the principal component

From Table 4, according to the principle that the contribution rate of cumulative variance is greater than 80% and the variance is greater than 1, two principal components are selected, and the contribution rate of cumulative variance is 97.72%. In this case, m = 2.

3) principal component coefficient

Obtained from Table 5

y 1 = 0.251 x 1 + 0.25 x 2 + 0.251 x 3 + 0.25 x 6 + 0.25 x 7 + 0.247 x 9 + 0.249 x 12

y 2 = 0.266 x 13 + 0.241 x 14 + 0.346 x 15 + 0.312 x 16 + 0.324 x 17 + 0.382 x 18 + 0.415 x 19

Choosing only two principal components, the main two components should be production management, research and development investment. Therefore, the first principal component (y₁) can be regarded as technology research and production. Under the condition that other conditions remain unchanged, whenever x₁ means that the number of high-tech enterprises increases by 1 unit, the corresponding y₁ increases by 0.251 units; whenever x₂ means that average annual employee increases 1 billion, the corresponding y₁ increases by 0.25 units; whenever x₃ means that the main business income of high-tech enterprises increases by 1 billion, the corresponding y₁ increases by 0.251 units. The second principal component (y₂) is the fixed capital investment. Under the condition that other conditions remain unchanged, whenever x₁₄ means that the number of patent applications increases by 1 unit, the corresponding y₂ increases by 0.241 units; whenever x₁₈ means that the project investment increases by 1 unit, the cor-responding y₂ increases by 0.346 units; whenever x₁₉ means that the new fixed assets increases by 1 unit, the cor-responding y₂ increases by 0.415 units.

4) Principal component score

From Table 6, we can see the top four provinces with the highest score in the first principal component C1 are Jiangsu, Shandong, Zhejiang and Guangdong.

The research input and output level of these regions is far higher than that of other regions. Jiangsu and Shandong are significantly ahead of other regions. The level of research input and production output is relatively low in Tibet, Qinghai and Ningxia. The second principal component indicates that Jiangsu, Shandong, Zhejiang and Sichuan spend more on fixed assets. It can also be seen from the scatter map that Guangdong and Jiangsu are in the leading position in the development of high-tech industry, followed by Shandong, Zhejiang, Shanghai, Beijing and Sichuan, other regions have relatively low scores, and it is difficult to make intuitive distinctions due to the impact of image size. For composite scores, Jiangsu, Guangdong and Zhejiang have highest score. Tibet, Gansu, Ningxia and Xinjiang score in the end of the country. Therefore, Jiangsu, Guangdong, Zhejiang and Shandong are the four provinces in the national front row of high technology industry development while Tibet, Gansu, Ningxia and Xinjiang fall behind in high technology industry development.

Finally, the comprehensive score was estimated by the weighting method, and the proportion of each principal component’s variance contribution to the total variance contribution of the two principal components was used as the weight to make the weighted summary, and the comprehensive score and ranking of the provinces were obtained.

In terms of comprehensive scores from Table 7, Guangdong and Jiangsu scored the highest, Shandong, Zhejiang and Henan ranked 3rd, 4th and 5th, and Ningxia, Qinghai, Xinjiang and Tibet ranked last in the country. In terms of development of high-tech industry, it is true that Guangdong, Jiangsu, Shandong, Zhejiang and other coastal areas are in the leading position of development, while the vast western region lags behind, the central region is relatively backward, but Sichuan is a relatively high point in the central and western regions.

From Figure 12, uses the results of spatial statistical function analysis, we

got this picture, which is very intuitive to reflect the various provinces in 2019 of high technology industry in China. Guangdong, Jiangsu and Zhejiang are the best, south China, east China and Sichuan is of high value, the whole picture presents the characteristics of the southeast of China is more advanced while the northwest part of China falls behind.

From Table 8 based on the principal component analysis of the first-level indicator, it can be seen that the scores of Guangdong and Jiangsu have been stable in the first and second positions, and the scores of these two provinces are relatively close. The two provinces have their own advantages in the development of high-tech industries. Shandong and Zhejiang have been in the third and fourth place, relatively stable; Hebei province has made progress; however, the scores of Beijing, Shanghai, Tianjin and Sichuan have been declining. Hubei province has the most obvious decline, falling from the 8th place to the 30th place. Ningxia, Xinjiang, Qinghai are at the bottom of the list. Tibet made little progress. From 2016 to 2019 Guangdong, Jiangsu, Shandong, Zhejiang scored the highest on the first principal component C1, which is the research level of input and output. Jiangsu significantly ranks ahead of other areas. The level of research input and production output is relatively low in Tibet, Qinghai and Ningxia. The second principal component indicates that Jiangsu, Shandong, Zhejiang and Sichuan spend more on fixed assets. It can also be seen from the scatter map that Guangdong and Jiangsu are in the leading positions in the development of high-tech industry. Shandong, Zhejiang, Shanghai, Beijing and Sichuan

follow. Other regions have relatively low scores, and it is difficult to make intuitive distinctions due to the impact of image size. For composite scores, Guangdong, Jiangsu and Zhejiang have high score. Tibet, Gansu, Ningxia, Xinjiang score at the end of the country. Thus, Jiangsu, Guangdong, Zhejiang, Shandong are in the national front row of high technology industry development. With the high level of research and development investment, patent number, fixed assets, high technology industry development is relatively high. In the economically backward western regions, the number of new product patents is reduced due to the low investment in high-tech research and development. In addition, the fixed asset investment in northwest regions is small, that is why the development of high-tech industries in these regions falls behind.

Through space comparison of annual statistics (Figure 13), we can clearly see that China’s high-tech industries have continuously to be concentrating in the coastal and southern part of the country. Guangdong province in the Pearl River delta coastal areas has remained number one from 2016 to 2019. Jiangsu province in the Yangtze River delta coastal area remains steadily in the second place

from 2016 to 2019. Shandong and Zhejiang provinces have remained third and fourth in recent years. Sichuan province is an important support for the continuous rise of central China. The development of high-tech industries in central regions such as Hunan, Jiangxi is relatively slow. Northeast China, such as Heilongjiang and Jilin, are declining, while western regions, such as Xinjiang, Qinghai, Gansu, are lagging far behind.