www.nature.com/scientificreports/
Corporate water information data from the annual reports, social responsibility reports, and sustainability reports of listed companies in Juchao Consulting and Hexun.com, green patent data from China "CSMAR Solu- tion V4.4", water risk assessment based on the Annual Report and Baidu News Database. Model specification. The projection tracing model was first proposed and conducted by U.S. professors Kruskal 27,28 in the 1970s as an operational model for cluster analysis to solve the problem of high-dimensional data, many of which do not satisfy the assumption of normality and need to be solved by a robust or non- parametric method. It mainly involves projecting high-dimensional data onto a low-dimensional subspace by some combination, using a projection indicator function to describe the probability size of a certain classifica- tion ranking structure of the original system, finding the projection value that makes the projection indicator function optimal, and then analyzing the characteristics of the classification structure of high-dimensional data according to that projection value 29 . This method is used in water quality evaluation, land resource carrying capacity, and enterprise accounting information quality evaluation. In this paper, a projection tracing model based on an accelerated genetic algorithm is used to evaluate the quality of corporate water information disclo- sure. The specific process of model construction is as follows 30 . Step 1: Normalization of sample indicators. Let the sample set of each indicator value be { x ∗ ( i , j ) | i = 1,2, · · · , n ; j = 1,2, · · · , p } , Among them x ∗ ( i , j ) is the value of the Jth indicator for the ith sample, N is the number of samples, and P is the number of indicators in the sample. For the larger and better indicators, the normalization criteria were applied to the indicators using Eq. (1).
x ∗ ( i , j ) − x min ( j ) x max ( j ) − x min ( j ) ,
(1)
x ( i , j ) =
which x min ( j ) , x max ( j ) are the minimum and maximum values of the Jth index value in the sample set, respec- tively, x ( i , j ) is the sequence of indicator eigenvalues normalized. Step 2: Construct the projection indicator function. The projection tracing method is to project the P-dimen- sional data { x ( i , j ) | j = 1,2, · · · , p } into the low-dimensional space, Integrated into a one-dimensional projection with a = ( a ( 1 ) , a ( 2 ) , . . . , a ( p )) as the projection direction z ( i ) .
p j = 1
(2)
z ( i ) =
a ( j ) x ( i , j ) , i = 1,2, · · · , n
Then the one-dimensional scatterplot is classified according to Eq. (2) as a unit length vector for the projec- tion function expressed as
(3)
Q ( a ) = S z D z ,
n i = 1
( z ( i ) − Ez ) 2
(4)
S z =
,
n − 1
n i = 1
n j = 1
(5)
D z =
( R − r ij ) u ( R − r ij ) ,
where S z is the standard deviation of the projection z ( i ) , D z is the local density of the projection z ( i ) ; Ez is the mean of the projection, R is the window radius of the local scatter density. r ij denotes the distance between samples, r ij = | Z i − Z j | , u ( R − r ij ) is a first-order unit step function, When R − r ij ≥ 0 , Its value is 1; R − r ij < 0 , Its value is 0. Step 3: Optimize the projection direction. After determining the sample index value, the Q ( a ) maximum direction is estimated as the best projection direction,
(6)
max Q ( a ) = s ( z ) · d ( z ) ,
p j = 1
a 2
(7)
( j ) = 1,
s.t.
Step 4: Optimal alignment of samples. According to the optimal projection direction, the projection eigen- value z ( i ) of each evaluation index combined is calculated. The genetic algorithm introduces the simulated biological evolution process into the middle algorithm, which is first converted into genetic space. After composing individuals or chromosomes according to the structure of biological evolution, the computational process is optimized by binary coding without restricting the objec- tive function and constraints. Compared with traditional and projection tracking models, its advantages are (1) accelerated genetic algorithms are able to search and improve solutions in the space of feasible solutions, thus improving the multi-dimensional spatial movement tendency of feasible solutions, exploring diverse solutions, and discovering high-quality projections, which can improve the accuracy and robustness of the model, (2) avoiding the drawbacks of traditional projection tracking models that fall into local extremes and early global
Scientific Reports |
https://doi.org/10.1038/s41598-023-39307-y
6
(2023) 13:12225 |
Vol:.(1234567890)
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