Principal Component Analysis (PCA) 1 [Python]

This video describes how the singular value decomposition (SVD) can be used for principal component analysis (PCA) in Python (part 1).
Book Website: databookuw.com
Book PDF: databookuw.com/...
These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com...
Brunton Website: eigensteve.com
This video was produced at the University of Washington

[@yenunadeesaselviento]

The code cuts off at the edge of the video. Where can we download it. Thanks for sharing this!

[@sheiladespard8861]

I tried to download the code from the website, but Python code folder includes only Matlab code :(

[@NiKogane]

Hi, it was corrected - I downloaded it today !

[@EladM8a]

Why the division in B/np.sqrt(nPoints)?

[@anirbanbhattacharjee8093]

In PCA literature, the covarience matrix B*B is normalized by nPoints (or the bessel correction (nPoints -1), but doesn't matter here because nPoints is large). So if you normalize B by np.sqrt(nPoints) instead, B* also gets normalized by np.sqrt(nPoints) and you end up getting the C normalized by nPoints

[@anirbanbhattacharjee8093]

where C = (B*)B, & B* is the transpose of B

[@jbhsmeta]

Hi Mr. Steve, I have one question, why are you dividing the "B by np.sqrt(nPoints)" U, S, VT = np.linalg.svd(B/np.sqrt(nPoints),full_matrices=0) dividing mean centered data by sqrt of no.of data -?? Could not understand.

[@melvinlara6151]

Actually i have the exact same question. Could you figure it out?

[@JoaoVitorBRgomes]

@@melvinlara6151 I didn't see the whole lecture yet, but I guess B is data with mean =0 and np.sqrt(nPoints) probably is the standard deviation (variance squared). So he first standardize the data then he applies SVD ...

[@melvinlara6151]

@@JoaoVitorBRgomes hey! actually i figured the same thing out. But, thank you;

[@JoaoVitorBRgomes]

@@melvinlara6151 no problem Melvin Lara, I am a student of Data Science too. If you have a kaggle profile and want to exchange knowledge my alias is " topapa .

[@anirbanbhattacharjee8093]

In PCA literature, the covarience matrix (B*)B is normalized by nPoints (or the bessel correction (nPoints -1), but doesn't matter here because nPoints is large). So if you normalize B by np.sqrt(nPoints) instead, B* also gets normalized by np.sqrt(nPoints) and you end up getting the (B*)B normalized by nPoints

[@muhammadmuneeburrahman1262]

You said in the video that each row of X will represent an example/or record, and column will represent the feature. In your code, X.shape = (2, 1000) where each column represent one data point and. B is passed to the SVD with same shape. Hence the VT matrix size is (2,1000) which means that there are 1000 principle Componenets, that is not possible of 2D data??? Am I right or wrong?? Please explain?

[@1PercentPure]

i kneel............................................................

[@subramaniannk3364]

Great lecture Steve! You explained that "u" in svd represents principal direction, "sigma" represents loading. What does "v" represents ?

[@sambroderick5156]

There’s a whole series a lectures explaining this (and a book.

[@NiKogane]

Thank you so much for providing all of this knowledge online for free !

[@kanacaredes]

excellent video!!! Thks

[@Eigensteve]

You are welcome!

[@tomlane6590]

A brilliant set of videos. Thank you so much.

[@nguyenvan-hau9577]

Beautiful code!

[@charlespatterson8412]

I would prefer to do this in my head because I can visualize it and move it around. I am not a mathematician but many of these are terms for things I am already familiar with. Perhaps I should have kept my TRS80 and took Bill's Class at Juanita High. I decided to concentrate on 'Salmon Enhancement' and 'European History' instead. It's probably just as well, I find writing code quite boring because I am more into Concepts... "Keep up the Good work!"

[@saitaro]

Math is fully about concepts. And how would you visualize something that is higher than 3 dimension?

[@charlespatterson8412]

@@saitaro Extrapolation

[@user-iiii234a5gc]

add a time term? or 4dimension more is exist just at theorical expression

[@yaseenmohammad9600]

this technique is generally used when large amounts of higher dimensional data are there. like in image processing for example if u take 50(50*50) images it will become 50,2500 dimensional data resulting in covariance of 2500*2500 matrix where pca is used to extract eigen faces. now i don't think there are people who can solve eigen value equation for 2500 * 2500 matrix in head

[@charlespatterson8412]

@@yaseenmohammad9600 Maybe if the variables are 'round' enough I could 'take a shot' at it...