Principal Component Analysis (PCA)

Best explanation by a head and pair of arms ive ever seen

Video must be left-right inverted after shot.

The best video ever made on PCA

dude！he is writing backwards while explain everything flawlessly

Please do not translate the videos into Spanish!! many technical words translated into Spanish are wrong

Thank you for the great explanation!

Should the mean not be over each column instead of row?

Sorry but almost every book and tutorial regurgitates the same stuff about max variance. So let us say if I have just one variable (a male is the variable) and I make hundred measurements of his 100 body features then what is PCA going to give me? Or if I have hundred males (males is still the variable) then if I measure many features of each individual then what is PCA going to give me in terms of variance?

At 5:13, are we supposed to shift each row by the mean? In the video, X_bar should be [x_bars]*[1;1;1;...], right?

As far as I understand it from several other ressources (and my own thoughts), T would be the original data points projected onto the principal components, which in turn are the eigenvectors of the covariance matrix (i.e., V). That would also make sense when considering that the dimensionality of T is the same as of X. Or am I completely confused now?

In my class, we used BB^T for the covariance matrix, why is this?

Yes the best explanation of PCA on the web, as long as you are not a complete novice to PCA. Don't get me wrong: Prof. Brunton is the teacher every student deserves; it must be said that in order to follow this beautiful course on SVD you must have some basic Linear Algebra 101 at undergraduate level, at least.

perfect

First of all, thank you for all the amazing lectures you've made available, they've helped me so much in my data science journey. I was reviewing the information you shared at 6:00, and then on the book, where you mention that the row-wise covariance matrix is given by B*B, whereas in your video Singular Value Decomposition (SVD): Dominant Correlations you mention this is the column-wise correlation matrix.

Could you check if I'm missing something? I feel like the latter should be the correct one (which would give us a matrix nxn).

Thank you so much!

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Lewis George Taylor Shirley Rodriguez Jose

So V comes from C?

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Johnson Patricia Lopez Margaret Wilson Betty

Thank you Dr. Brunton! I just bought your book and am reviewing the PCA chapter. There is a difference in your definition of principal components between this video and your textbook. Can you please clarify?

In the textbook (2nd edition) in Section 1.5, after Eq 1.40, you state that "the columns of the eigenvector matrix V are the principal components". However, in this video, you define principal components as the mean-centered data matrix multiplied by your eigenvector matrix V, which in this video are defined as "loadings" that describe how much of each of the principal components each row in X has.

Which definition is more accurate? Or are they both accurate? Please clarify if possible. Thank you so much!!

Amazing explanation, went through a lot of videos but this one is the best

Amazing lecture! But in previous videos you also said that the rows represent experiments so that was a little strange

PCA clearly explained!!!

Why eigen?

This is so technically correct, and simultaneously so obtuse, that my intuition fuse has melted. Please consider redoing this as 3D pseudo visualizations of data subsets.

Dear Steve bu video da neden altyazılarda türkçe yok. Anlayamadim

Fundamental !!!

IS HE WRITING IN MIRROR IMAGE? HE'S BEHIND THE GLASS RIGHT? SO WHAT LOOKS LIKE PCA TO US, IS HIM ACTUALLY WRITING PCA FROM THE BACK??

PCA is best used on a well researched and confirmed theory otherwise the numbers are not interpretable

Very good explanation for each symptom and its treatment

Thank you

covariance should be C=1/n*BB`

How to film such kind of tutorial videos?

Best math content is always the serious and straightforward ones.. Fuck the jokers, you are the king dude

In some implementations, I find that along with mean centering, standard deviation division is followed (Z-scores), does this make a difference? I believe standard deviation division is important to keep the features on the same scale (Unit Variance).

very good, thanks a lot 😅

Principal Component Analysis (PCA) is a technique in statistics that simplifies complex data by identifying and emphasizing the most important patterns or features. It does this by transforming the original variables into a new set of uncorrelated variables called principal components, allowing for a more efficient representation of the data.

How does prof write like that??

This guy is super good at writing backwards

Should #3 be the covariance matrix of the columns rather than the row ?.
It seems to me that leads to V rows = B columns

2023-11-17

i hate it when people write on some board, because it is barely readable and the writing costs useless time for nothing. but thanks anyway

Note @ 7:50 regarding CV = VD. The D here is a matrix where all the eigenvalues are on the diagonal.