What is the purpose of svd?

You asked us the following:

Compute an svd.

This is my question:

What is the purpose of svd?

I ran the following code to attempt to understand the value of the svd function on a basic level:

a <- matrix(
c(1, 2, 3, 10, 20, 30),

s <- svd(a)


I got the following output:

[1] 37.60319 0.00000

[,1] [,2]
[1,] -0.2672612 -0.5345225
[2,] -0.5345225 0.7745419
[3,] -0.8017837 -0.3381871

[,1] [,2]
[1,] -0.09950372 -0.99503719
[2,] -0.99503719 0.09950372

I don't understand what value those numbers bring to a basic dataset like this:

[,1] [,2]
[1,] 1 10
[2,] 2 20
[3,] 3 30

Answers and follow-up questions

Answer or follow-up question 1

Dear student,

'What is the purpose of svd?'

SVD is explained In Section ' Text Mining', subsection 'Dimension reduction'.

As the title says, the purpose of SVD is to reduce the number of dimensions.
The firsts sentence in that subsection reads:
'In order to further reduce the number of columns in our document-by-term matrix (dtm)
we use Latent Semantic Indexing (LSI)'. In the same paragraph you'll read:
'Our approach to LSI is Singular Value Decomposition (SVD)'.
Please note that a dtm is simply a matrix (rows and variables).

As to your example:
d is a measure of the information contained in the resulting singular vector (concept; linear combination).
As you can see, the second singular vector has d=0. This means it does not contain information.

Therefore we can drop that singular vector in subsequent analyses (i.e., we reduce the number of
dimensions from 2 variables to 1 variable).

As further explained in the code Section ' Text Mining':
u contains the singular vectors (instance-concept matrix).
v contains the loadings of variables on concepts (variable-concept matrix)
d contains how much information is contained in the concepts (concept vector)

Michel Ballings

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