Another kind of component of the singular value

decomposition is, is known as the variance explained.

And this comes from the singular values that are in the d matrix.

Remember the d matrix, is really a diagonal matrix.

It only has elements that are on the diagonal of that matrix.

And you can think of each singular value as representing the percent of

the total variation in your data

set that's explained by that particular component.

And so, and the components are typically ordered so that the first one explains

the most variation as possible, and the

second one explains the second most, et cetera.

And so you can plot the kind of proportion of

variance explained as we have in the in this plot below.

And so here on the left hand side I've just plotted the raw singular values

and you can see that they kind of decrease in value as you go across the columns.

But of course the raw singular

value doesn't really have much meaning cause it's not on an interpretable scale.

So if I divide by the total sum of

all the singular values, then on the right hand side

I've got the, I can interpret it as the

proportion of the variance explained, and you can see that's

exactly the same plot but the y axis has

changed, and so you can see that the first singular

value if you recall it captures kind of the shift

and the mean in between the rows and the columns.

That,

that captures about 40% of the variation in your data.

Alright, so almost almost half of the variation in the

data is explained by a single kind of singular value.

Or you can think of it as a single dimension.

And then, the remaining variation in the data is explained by the other components.