Method for improving precision of scatter diagram

Abstract

The invention discloses a method for improving the precision of a scatter diagram, and the method comprises the steps: carrying out the preprocessing of scatter data to be subjected to regression analysis in the scatter diagram, carrying out the standardized transformation of the scatter data, and eliminating the influence caused by the magnitude order, self variation and dimension difference among the scatter data; carrying out regression analysis on the scatter data after standardization transformation, and fitting an optimal function expression; and selecting the optimal function expression as a fitting result, converting the obtained fitting value into a fitting truth value, reusing the fitting truth value to the scatter diagram, and correcting the scatter data of the scatter diagram. According to the method, the ubiquitous problems of high goodness of fit and low fitting precision in the scatter diagram fitting process are solved, and the precision of the scatter diagram used in uranium mine geological exploration work is effectively improved.

Description

Technical Field

[0001] This invention belongs to the field of map drawing technology in geological exploration, and specifically relates to a method for improving the accuracy of scatter plots. Background Technology

[0002] Map scatter plots, based on a map, use elements such as point size and color intensity to display the size and distribution of related data. Map scatter plots are often used to display resource distribution. Geographic scatter plots display the distribution of data points in geographic space, combining the characteristics of geographic maps and scatter plots to intuitively show the relationship between data and geographical locations. Geographic scatter plots have the following characteristics: 1. Using a map (two-dimensional, three-dimensional, or satellite imagery) as the background, data points are usually represented by latitude and longitude and displayed on a geographic coordinate system, which mainly reveals spatial relationships.

[0003] 2. Each data point represents a specific attribute of a geographical location (such as population, sales, temperature, etc.). The size, color, and shape of the points can be used to represent different data dimensions.

[0004] 3. It can be dynamically expanded by combining interactive functions, such as zooming, clicking to view details, filtering, etc., to facilitate in-depth analysis.

[0005] Excel is often used to create scatter plots to check for a functional relationship between two sets of data that don't seem to have a causal relationship. If the scatter plot shows a regular trend between the two sets of data, Excel's regression analysis function (i.e., the trendline function) can be used to fit an appropriate function expression (mathematical model). Once the fit is successful, the fitted function expression can be used to predict the other variable. Fit accuracy is generally expressed as goodness of fit, which ranges from 0 to 1. The closer the goodness of fit is to 1, the smaller the error between the fitted value and the fitted value, and the higher the fit accuracy. During regression analysis, checking the goodness of fit value allows you to select the best fitting function expression.

[0006] However, during use, it was found that when using Excel's Add Trendline function to fit a data set of two variables, even though a function expression with a high goodness of fit was selected, the calculated fitted value differed significantly from the fitted value.

[0007] How to solve the problem of high goodness of fit but low fitting accuracy that is common in scatter plot fitting is a technical problem that urgently needs to be solved. Summary of the Invention

[0008] The purpose of this invention is to provide a method for improving the accuracy of scatter plots, which solves the problem of high goodness of fit and low fitting accuracy that is common in the process of scatter plot fitting, and effectively improves the accuracy of scatter plots used in uranium geological exploration.

[0009] To achieve the above objectives, the technical solution used in this invention is: Methods to improve the accuracy of scatter plots include: Preprocess the scatter data for regression analysis in the scatter plot, and perform standardization transformation on the scatter data to eliminate the influence of different orders of magnitude, self-variation, and different dimensions between scatter data. Regression analysis was performed on the standardized scatter data to fit the optimal function expression. The best function expression is selected as the fitting result. The obtained fitting value is converted into the true fitting value. The true fitting value is then applied back to the scatter plot to correct the scatter plot data.

[0010] Furthermore, the scattered data is used as sample data, and a standardization transformation is performed to eliminate the influence that is unfavorable to the fitting of scattered data. The standardization transformation formula is: In the formula: Standardized transformation value; represents the sample data; Min represents the minimum value of the sample data; Max represents the maximum value of the sample data.

[0011] Furthermore, the optimal function expression: In the formula: The fitted value obtained from the optimal function expression; Fit the true value; Maxy is the maximum value of the Y variable data column; Miny is the minimum value of the y variable data column.

[0012] Furthermore, the relative error between the true value of the dependent variable and the dependent variable data is calculated to check the fitting accuracy.

[0013] Furthermore, the formula for calculating the relative error is: In the formula: Relative error, % Sample data for the y variable.

[0014] Furthermore, the scatter plot data from the regression analysis is used as sample data and copied to any two columns of an Excel worksheet; Use Excel's MIN-MAX function to find the maximum and minimum values ​​of two sample data columns; Apply Min-Max standardization to the two sample data columns. The Min-Max standardization formula is as follows: In the formula: Standardized transformation value; Sample data; Min is the minimum value of the sample data; Max is the maximum value of the sample data; Use Excel's scatter plot function to view the regular trend trajectory of two standardized data columns, and then select a function expression for fitting. The best function expression is selected as the fitting result. Then, the obtained fitted values ​​are converted into true fitted values. The best function expression is: In the formula: The fitted value obtained from the optimal function expression; Fit the true value; Maxy is the maximum value of the y variable data column; Miny is the minimum value of the y variable data column.

[0015] Furthermore, the relative error between the sample data and the fitted true value is calculated to check the regression accuracy. The formula for calculating the relative error is: In the formula: Relative error, % Sample data for the y variable.

[0016] The technical effects of this invention include: This invention solves the problem of high goodness of fit and low fitting accuracy that is common in scatter plot fitting, effectively improving the drawing accuracy of scatter plots commonly used in uranium geological exploration, providing a reference for subsequent determination of mineralization conditions and mineralization enrichment, and ensuring the orderly progress of uranium geological exploration.

[0017] Specifically addressing the common issue of high goodness of fit but low accuracy in function fitting using Excel's trendline function, this application employs a Min-Max standardization transformation to eliminate unfavorable fitting effects caused by differences in data magnitude, inherent variations, and dimensions. This significantly improves the high goodness of fit and low accuracy problem in Excel function fitting. This method can improve production efficiency and ensure the quality of data processing in uranium ore geological data. Attached Figure Description

[0018] Figure 1 This is a regression analysis graph implemented using the trendline function in Excel within a proportional representation. Figure 2 This is a regression effect diagram after the standardized transformation of the sample data group in this invention. Detailed Implementation

[0019] The following description fully illustrates specific embodiments of the present invention to enable those skilled in the art to practice and reproduce it. To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0020] The specific steps to improve the accuracy of scatter plots are as follows: Step 1: Preprocess the scatter data to be used for regression analysis in the scatter plot by standardizing the scatter data to eliminate the effects of different orders of magnitude, self-variation, and different dimensions between scatter data points. Scattered data describes scattered points on a map. In a preferred embodiment of the present invention, scattered data is used as sample data and standardized to eliminate the influence that is not conducive to the fitting of scattered data.

[0021] The standardization transformation formula is:

[0022] In the formula: Standardized transformation value; Sample data; Min is the minimum value of the sample data; Max is the maximum value of the sample data.

[0023] Step 2: Perform regression analysis on the standardized scatter data to fit the best mathematical expression; Optimal function expression: , In the formula: The fitted value obtained from the optimal function expression; Fit the true value; Maxy is the maximum value of the Y variable data column; Miny is the minimum value of the y variable data column.

[0024] Step 3: Select the best function expression as the fitting result, convert the obtained fitting value into the true fitting value, apply the true fitting value back to the scatter plot, and correct the scatter plot data. The true value of the fitted data of the y variable is obtained by substituting the fitted values ​​of the standardized transformation data of the y variable back into the standardized transformation expression of the y variable.

[0025] Step 4: Calculate the relative error between the true value of the dependent variable and the data of the dependent variable (y variable) to check the fitting accuracy.

[0026] The formula for calculating the relative error is as follows:

[0027] In the formula: Relative error, % Sample data for the y variable.

[0028] The preferred embodiment will be further described using Excel's maximum and minimum value functions as examples.

[0029] 1. Prepare an Excel workbook and copy the data (sample data) to be used for regression analysis to any two columns of the worksheet; 2. Use Excel's maximum and minimum value functions to find the maximum and minimum values ​​of two sample data columns; 3. Perform Min-Max standardization on the two sample data columns. The Min-Max standardization formula is as follows: In the formula: Standardized transformation value; Sample data; Min is the minimum value of the sample data; Max is the maximum value of the sample data; (4) Use Excel's scatter plot function to view the regular trend trajectory of the data columns after two standardized transformations, and select a function expression for fitting; (5) Select the best function expression as the fitting result, and then convert the obtained fitting value into the true fitting value, as shown in the following formula: In the formula: The fitted value obtained from the optimal function expression; Fit the true value; Maxy is the maximum value of the y variable data column; Miny is the minimum value of the y variable data column; (6) Calculate the relative error between the sample data and the true value of the fit, check the regression accuracy, and calculate the relative error using the following formula: In the formula: Relative error, % Sample data for the y variable.

[0030] Comparative Example 1 like Figure 1 The figure shown is a regression analysis chart performed using the trendline function in Excel on a proportional representation.

[0031] Figure 1In the table, columns C and D are the data columns for the two variables x and y. The Excel scatter plot shows that the two data columns have a regular trend. A cubic polynomial regression was selected, and the goodness of fit R2 is as high as 0.9997. The regression values ​​calculated according to the fitted function expression are shown in column E. The relative error between the regression values ​​and the values ​​of the y variable (column F) is as high as 110.59%-577.52%. Such a high calculation error indicates that this regression has failed.

[0032] Figure 1 The sample data model is representative and has universality. It only reveals the existing problems, without introducing solutions.

[0033] Example 1 like Figure 2 The figure shown is a regression effect diagram after the standardized transformation of the sample data group in this invention.

[0034] Here it is still used Figure 1 We will use sample data as an example.

[0035] First, use Excel's functions to find the maximum and minimum values ​​of the x and y data columns. Then, use the Min-Max standardization formula to standardize the x and y data columns. Figure 2 Then, after standardizing the data for variables x and y, apply Excel's scatter plot function to view the regular trends in the two data columns. Selecting the best cubic polynomial regression, the goodness-of-fit R² is still as high as 0.9997. At this point, the fitted function expression becomes... Figure 2 As shown, the standardized transformed data fitting values ​​of the y variable obtained using the function expression are shown below. Figure 2 Column G in the table. Substitute the fitted values ​​of the standardized transformation of the y variable back into the standardized transformation expression of the y variable to obtain the true fitted value of the y variable. Figure 2 (Column H in the middle). Calculate the relative error between the true value of the fitted y variable and the value of the y variable ( Figure 2 (Column I) As can be seen from the calculated relative error, except for the first row of data which has a relatively large relative error (-6.19%), the relative errors of most data are between -3.73% and 2.19%. The fitting accuracy is sufficient for prediction.

[0036] The terminology used in this invention is descriptive and exemplary, not restrictive. Since this invention can be embodied in many forms without departing from the spirit or essence of the technical solution, it should be understood that the above embodiments are not limited to any of the foregoing details, but should be interpreted broadly within the spirit and scope defined by the appended claims. Therefore, all variations and modifications falling within the scope of the claims or their equivalents should be covered by the appended claims.

Claims

1. A method for improving the accuracy of scatter plots, characterized in that, include: Preprocess the scatter data for regression analysis in the scatter plot, and perform standardization transformation on the scatter data to eliminate the influence of different orders of magnitude, self-variation, and different dimensions between scatter data. Regression analysis was performed on the standardized scatter data to fit the optimal function expression. The best function expression is selected as the fitting result. The obtained fitting value is converted into the true fitting value. The true fitting value is then applied back to the scatter plot to correct the scatter plot data.

2. The method for improving the accuracy of scatter plots as described in claim 1, characterized in that, Using scattered data as sample data, a standardization transformation is performed to eliminate the influence that is unfavorable to the fitting of scattered data. The standardization transformation formula is: In the formula: Standardized transformation value; Sample data; Min Minimum value of sample data; Max is the maximum value of the sample data.

3. The method for improving the accuracy of scatter plots as described in claim 1, characterized in that, Optimal function expression: In the formula: The fitted value obtained from the optimal function expression; Fitting the true value; Maxy The maximum value of the dependent variable data column; Miny is the minimum value of the dependent variable data column.

4. The method for improving the accuracy of scatter plots as described in claim 1, characterized in that, Calculate the relative error between the true value of the dependent variable and the dependent variable data to check the fitting accuracy.

5. The method for improving the accuracy of scatter plots as described in claim 4, characterized in that, Formula for calculating relative error: In the formula: Relative error, % Variable sample data.

6. The method for improving the accuracy of scatter plots as described in any one of claims 1-5, characterized in that, Copy the scatter plot data from the regression analysis as sample data to any two columns of an Excel worksheet; Use Excel's MIN-MAX function to find the maximum and minimum values ​​of two sample data columns; Apply Min-Max standardization to the two sample data columns. The Min-Max standardization formula is as follows: In the formula: Standardized transformation value; Sample data; Min Minimum value of sample data; Max Maximum value of sample data; Use Excel's scatter plot function to view the regular trend trajectory of two standardized data columns, and then select a function expression for fitting. The best function expression is selected as the fitting result. Then, the obtained fitted values ​​are converted into true fitted values. The best function expression is: In the formula: The fitted value obtained from the optimal function expression; Fitting the true value; Maxy The maximum value of the dependent variable data column; Miny is the minimum value of the dependent variable data column.

7. The method for improving the accuracy of scatter plots as described in claim 6, wherein the relative error between the sample data and the fitted true value is calculated, the regression accuracy is checked, and the formula for calculating the relative error is: In the formula: Relative error, % Dependent variable sample data.

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