How to Perform Singular Value Decomposition (SVD) in R - Step by Step Examples

How to Perform Singular Value Decomposition (SVD) in R ?

Answer

To perform Singular Value Decomposition (SVD) in R, you can use the svd() function. This function decomposes a matrix into three matrices representing the singular vectors and values.

✐ Examples

1 Performing SVD on a 3x2 Matrix

In this example,

We start by creating a 3x2 matrix named mat using the matrix() function. This matrix represents the data we want to decompose.
Next, we use the svd() function to perform SVD on the matrix mat. We assign the result to a variable named svd_res.
We extract the matrices representing the singular vectors from svd_res using the $u and $v attributes and assign them to variables named u and v respectively.
We also extract the singular values from svd_res using the $d attribute and assign them to a variable named d.
We print the matrices u and v, as well as the vector d to the console to see the results. This allows us to verify the decomposition.

R Program

mat <- matrix(c(1, 2, 3, 4, 5, 6), nrow = 3, byrow = TRUE)
svd_res <- svd(mat)
u <- svd_res$u
v <- svd_res$v
d <- svd_res$d
print('Matrix U:')
print(u)
print('Matrix V:')
print(v)
print('Vector D:')
print(d)

Output

[1] "Matrix U:"
           [,1]       [,2]
[1,] -0.2298477  0.8834610
[2,] -0.5247448  0.2407825
[3,] -0.8196419 -0.4018960
[1] "Matrix V:"
           [,1]       [,2]
[1,] -0.6196295 -0.7848945
[2,] -0.7848945  0.6196295
[1] "Vector D:"
[1] 9.5255181 0.5143006

2 Performing SVD on a 4x3 Matrix

In this example,

We start by creating a 4x3 matrix named mat using the matrix() function. This matrix represents another set of data we want to decompose.
Next, we use the svd() function to perform SVD on the matrix mat. We assign the result to a variable named svd_res.
We extract the matrices representing the singular vectors from svd_res using the $u and $v attributes and assign them to variables named u and v respectively.
We also extract the singular values from svd_res using the $d attribute and assign them to a variable named d.
We print the matrices u and v, as well as the vector d to the console to see the results. This allows us to verify the decomposition.

R Program

mat <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), nrow = 4, byrow = TRUE)
svd_res <- svd(mat)
u <- svd_res$u
v <- svd_res$v
d <- svd_res$d
print('Matrix U:')
print(u)
print('Matrix V:')
print(v)
print('Vector D:')
print(d)

Output

[1] "Matrix U:"
           [,1]        [,2]       [,3]
[1,] -0.1408767 -0.82471435  0.5418041
[2,] -0.3439463 -0.42626394 -0.6625522
[3,] -0.5470159 -0.02781353 -0.3003078
[4,] -0.7500855  0.37063688  0.4210560
[1] "Matrix V:"
           [,1]        [,2]       [,3]
[1,] -0.5045331  0.76077568 -0.4082483
[2,] -0.5745157  0.05714052  0.8164966
[3,] -0.6444983 -0.64649464 -0.4082483
[1] "Vector D:"
[1] 2.546241e+01 1.290662e+00 2.503310e-15

Summary

In this tutorial, we learned How to Perform Singular Value Decomposition (SVD) in R language with well detailed examples.

◀ Previous Next ▶