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PCA - principal component analysis

Anonymous Fri 17 Dec 21:49:14 2021 No.13975393 View Reply Original Report

Quoted By: >>13975601 >>13975904 >>13975912 >>13979192 >>13980809 >>13981917

I get that it groups variables together. Why not just run a correlation matrix, though? Does this thing have any real world use in a business context?

Anonymous

Anonymous Fri 17 Dec 2021 23:05:11 No.13975601 Report

Quoted By: >>13975885

>>13975393
PCA mainly:
1. transforms the data to an uncorrelated version of itself
2. projects it to a lower dimensional space
Its main use is representing data in a lower dimensional space, so that further analysis can be performed, or can be easier interpreted.

Anonymous

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Anonymous Sat 18 Dec 2021 00:12:22 No.13975885 Report

Quoted By: >>13978662

>>13975601
So are pc1 and pc2 “bundled” variables that are “uncorrelated”?

Maybe it’s the output of these PCA calcs that I can’t understand

Anonymous

Anonymous Sat 18 Dec 2021 00:16:51 No.13975904 Report

Quoted By: >>13976577 >>13984628

>>13975393
>I get that it groups variables together.
Not what it does. It's a dimension reduction method, the whole point is that it lets you take a dataset in n dimensions and squeeze it down to 2-3 while preserving some structure. It does this by taking the eigenvectors of the covariance or correlation matrix and projecting the dataset onto them.
>doesn't this lose information?
yes it does, which is why you check the cumulative variance of the PCs you end up using in your projection. if it's like 90%, there's a good chance that any clusters you see in the visualization really exist. if it's like 50% or less, might as well be divining tealeaves.

Anonymous

Anonymous Sat 18 Dec 2021 00:18:31 No.13975912 Report

Quoted By: >>13976155

>>13975393
It tells us europeans, asians and africans are distinct races

Anonymous

Anonymous Sat 18 Dec 2021 01:16:15 No.13976155 Report

Quoted By: >>13980707

>>13975912
This is your brain on 4chan

Anonymous

Anonymous Sat 18 Dec 2021 03:21:07 No.13976577 Report

Quoted By: >>13984660

>>13975904
Okay but if you narrow down to the two most important variables why not name them instead of calling them PC1 and PC2?

Anonymous

Anonymous Sat 18 Dec 2021 18:17:56 No.13978662 Report

Quoted By:

>>13975885
What PCA does is take the eigenvectors of the covariance matrix, and sorts them by eigenvalues in a matrix A. A*X results in an uncorrelated version of X. Now, let’s say that X has three dimensions, we would get three eigenvectors. If we took away the eigenvectors with the lowest eigenvalue, we’d have a 2x3 matrix A consisting of the other two eigenvectors. Now the operation A*X results in a two dimensional projection of X. Information is indeed lost (calculated by sum of used eigenvalues divided by sum of all eigenvalues) but it’s usually small enough that the operation has a net benefit.

Anonymous

Anonymous Sat 18 Dec 2021 20:45:38 No.13979192 Report

Quoted By:

>>13975393
>Why not just run a correlation matrix
if you have many dimensions you will get a huge covariance matrix that can be difficult to interpret. PCA compresses n-dimensions into 2 or 3 dimensions, making it easier to visualize and study relationships and groups.

Anonymous

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Anonymous Sun 19 Dec 2021 03:10:49 No.13980707 Report

Quoted By: >>13980775

>>13976155
Then what does this show?

Anonymous

Anonymous Sun 19 Dec 2021 03:32:09 No.13980775 Report

Quoted By: >>13980874

>>13980707
>y axis
>Captcha: ASMRV

Anonymous

Anonymous Sun 19 Dec 2021 03:45:21 No.13980809 Report

Quoted By: >>13981476

>>13975393
It's one of many methods for dimension reduction. You could also just be a SME and know shit like variable y is just variable x multiplied by 3. Or make a robust statistical model and reduce regressors one by one.

When you have a lot of variables, those kind of things can be difficult though so PCA is pretty useful for that. In most use cases, you're probably never going to use it though. If you have only like 10 or so variables you should just be investigating relationships alone without resorting to PCA imo.

It's a cool technique though (and very elegant imo).

Anonymous

Anonymous Sun 19 Dec 2021 03:59:58 No.13980874 Report

Quoted By:

>>13980775
So?

Anonymous

Anonymous Sun 19 Dec 2021 08:17:11 No.13981476 Report

Quoted By:

>>13980809
>It's a cool technique though (and very elegant imo).
agreed.
it's good also to build tree diagrams with a grouping algo

Anonymous

Anonymous Sun 19 Dec 2021 11:17:35 No.13981917 Report

Quoted By:

>>13975393
It is a correlation matrix. That's what your step 3 is. Did you read your own image?

Anonymous

Anonymous Sun 19 Dec 2021 23:10:43 No.13984628 Report

Quoted By:

>>13975904

>if it's like 50% or less, might as well be divining tealeaves

That is not true at all.

Anonymous

Anonymous Sun 19 Dec 2021 23:18:09 No.13984660 Report

Quoted By:

>>13976577

It doesn't 'narrow down to the most important variables' from the original data. The principal components returned are transformations of the original variables. Each original variable will be represented more/less in each component depending on the data (this is what the Eigenvectors show).

Imagine fitting a linear model to a dataset. Is the line that results from least squares a variable from the untransformed data? No. That's literally what PC1 is.

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