在 R 编程中将缩放矩阵转换为其原始形式 - 使用矩阵计算

在 R 编程中，可以使用scale()函数对矩阵进行缩放和居中。但是，没有内置函数可以将缩放矩阵转换回原始矩阵。在本文中，我们将学习使用一些简单的计算将缩放矩阵转换回原始矩阵。

使用矩阵属性

缩放矩阵的属性可用于将矩阵缩放回其原始矩阵。

R

# Create matrix
mt <- matrix(c(1:20), ncol = 5)
  
# Print original matrix
cat("Original matrix:\n")
print(mt)
  
# Scale the matrix
scaled.mt <- scale(mt)
  
# Print Scaled matrix
cat("Scaled matrix:\n")
print(scaled.mt)
  
# Unscale the matrix
unscaled.mt <- t(apply(scaled.mt, 1, 
                function(r) r * attr(scaled.mt, 'scaled:scale') + 
                                attr(scaled.mt, 'scaled:center')))
  
# Print Unscaled matrix
cat("Unscaled matrix:\n")
print(unscaled.mt)

输出：

Original matrix:
     [, 1] [, 2] [, 3] [, 4] [, 5]
[1, ]    1    5    9   13   17
[2, ]    2    6   10   14   18
[3, ]    3    7   11   15   19
[4, ]    4    8   12   16   20
Scaled matrix:
           [, 1]       [, 2]       [, 3]       [, 4]       [, 5]
[1, ] -1.1618950 -1.1618950 -1.1618950 -1.1618950 -1.1618950
[2, ] -0.3872983 -0.3872983 -0.3872983 -0.3872983 -0.3872983
[3, ]  0.3872983  0.3872983  0.3872983  0.3872983  0.3872983
[4, ]  1.1618950  1.1618950  1.1618950  1.1618950  1.1618950
attr(, "scaled:center")
[1]  2.5  6.5 10.5 14.5 18.5
attr(, "scaled:scale")
[1] 1.290994 1.290994 1.290994 1.290994 1.290994
Unscaled matrix:
     [, 1] [, 2] [, 3] [, 4] [, 5]
[1, ]    1    5    9   13   17
[2, ]    2    6   10   14   18
[3, ]    3    7   11   15   19
[4, ]    4    8   12   16   20

使用均值和标准差

在此示例中，我们将使用原始矩阵的均值和标准差对缩放矩阵进行缩放。

R

# Create matrix
a <- rnorm(5, 5, 2)
b <- rnorm(5, 7, 5) 
  
mt <- cbind(a, b)
  
# get center and scaling values 
m <- apply(df, 2, mean)
s <- apply(df, 2, sd)
  
# Print original matrix
cat("Original matrix:\n")
print(mt)
  
# Scale the matrix
scaled.mt <- scale(mt, center = m, scale = s)
  
# Print Scaled matrix
cat("Scaled matrix:\n")
print(scaled.mt)
  
# Unscale the matrix
unscaled.mt <- t((t(scaled.mt) * s) + m)
  
# Print Unscaled matrix
cat("Unscaled matrix:\n")
print(unscaled.mt)

输出：

Original matrix:
            a          b
[1, ] 5.552301  1.9865159
[2, ] 3.936486 17.5327829
[3, ] 5.379720 15.0981877
[4, ] 3.546333  0.5230305
[5, ] 5.043194  2.0930855

Scaled matrix:
               a         b
[1, ]  0.01543556 -2.062174
[2, ] -0.69057233  5.252016
[3, ] -0.05997146  4.106591
[4, ] -0.86104456 -2.750713
[5, ] -0.20701146 -2.012036
attr(, "scaled:center")
       a        b 
5.516974 6.369655 
attr(, "scaled:scale")
       a        b 
2.288663 2.125494 

Unscaled matrix:
            a          b
[1, ] 5.552301  1.9865159
[2, ] 3.936486 17.5327829
[3, ] 5.379720 15.0981877
[4, ] 3.546333  0.5230305
[5, ] 5.043194  2.0930855
attr(, "scaled:center")
       a        b 
5.516974 6.369655 
attr(, "scaled:scale")
       a        b 
2.288663 2.125494