What the hell. One can download your book for free?! You sir are a saint. I will work thru it and if I like it I will definitely purchase it!! (I'm pretty sure I will like it, because I like all your videos so far) PS: I am so proud of you guys. You are bringing humanity forward with content like this being free. I encourage everyone who can to purchase content from sources like this

Prof. Brunton always delivers the best explanations on the subjects! His videos really help me a lot! Kudos!

The best video on PCA I could find on youtube, no messy blackboards, jokes or oversimplification, just solid explanation, great job.

You explain complicated math in a brilliant way. Thank you so much

Steve, able to explain PCA from classical statistiscal point of view. Very clear

These videos are the PCA for data driven engineering!!Thank you for bringing up these series publicly!!

I logged in just for this, which I almost never do xD I wanted to say: Thank you! Your video series is great, enjoyful, and helps getting familiar with the topic rapidly. The same applies to the book, which you link at for free. Thank you.

So far this is the best video of PCA explanation.

The alst part of the video on how SVD and PCA are related really class of its own. IT show the expert should run video lectures

Best explanation. Looking forward to video about Kernel PCA！

I've watched a lot of PCA videos and this is really the best one. You're amazing!

Amazing video. I did the MIT lectures about Linear Algebra (that talked about SVD) and the Andrew Ng's ML course (that talked about PCA). This video was the perfect bridge to connect the two things in a coherent manner. Thank you very much, Dr. Brunton!

I am a phd student learning inverse scattering, your lectures help me with understanding those concept :) greetings from naples

Finally, someone who explains statistics in a straight-forward way, whilst communicating in an adult like manner.

Love this series! Just bought your book

Correct me if I'm wrong, but B transposed multiplied by B sums up the products of mean centered values, but to get the covariation we still need to divide by number of rows in X as covariation is defined as E{(X-E(X))*(Y-E(Y))} not just sum of (X-E(X))*(Y-E(Y)) over measurements

Thank you, Prof. Brunton. I have a question: supposing I have done this series of experiments with a target measure that cannot be categorized but is a continuous value, then can I use PCA?

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

Very good explanation for each symptom and its treatment

Wow, excellent explanation. Thank you so much.

It can be helpful to use the names "features" (to refer to the 'n' different pixels in a photo, or the 'n' different characteristics of rats which may predict cancer) and "snapshots" (to refer to the 'm' different measurements (e.g. people's photos, or rats)). Then, it doesn't matter whether you have the "features" as columns or rows - Corr(feat) = feature-wise correlation matrix, where entries represent the correlation between two features, and the eigenvectors of this matrix are the "eigenfeatures". If you happen to have "features" as columns, then Corr(feat) = [X][X^T]. If you happen to have the "features" as rows, then Corr(feat) = [X^T][X]. Similarly, for the "snapshots" we have the Corr(snap) = snapshot-wise correlation matrix, where entries represent the correlation between two snapshots, and the eigenvectors of this matrix are the "eigensnapshots". Again, depending on whether the "snapshots" are in the rows or columns of X, you can find Corr(snap). This also helps when doing PCA, as you generally wish to reduce the number of "features", and are therefore interested in determining the eigenvectors of Corr(feat). No need to sweat over how your data is organized in the matrix X, or any annoying conventions for PCA. In short, it is easier to think of "features & snapshots" than "rows & columns".

Do you have a patreon? How can I help support this content? Just these materials on Ch1 and 2 have been amazing. Will it extend to addiitonal chapters?

Thank you very much for this video! Learnt quite a bit from this :)

Thank you so much. You made it really easy to understand.

Does the concept of cross-loadings exist in PCA like it does in EFA? If it does exist, what are the criteria to determine so?

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.

Is this done with a glass whiteboard and the recording is mirrored?

If I have outliers in my dataset, can this affect the PCA?, because I have tried with cases of this type and it usually identifies a single principal component

This is amazing!

Beautifully explained ~ and Thank you so much ^^

This channel is amazing!

I believe that there's a typo. The principal components are the columns of V.

Awesome! Thank you!

Excellent ,connected ,simple

Very clear, excellent

We do the last part (T=BV) in order to calculate the inner product with the principal components.

superb explanation. Thank you!

So as another way to look at this, are U the scores, sigma the eigenvalues, and V the loadings?

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).

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

Can you please share what software and equipment you're using for this presentation?

Can you also show how to get covariance matrix from a Gaussian function results from its fit on a Gaussian looking data. Any suggestion for a book to explain this kind of stuff? Cheers.

If there was a Nobel Prize in Education (which there absolutely should be), then you should absolutely win.

Still confused how do we get BV=USigma🤔🤔 since Vt doesn’t cancel with V right?

Hey Dr. Brunton. Awesome video yet again! I've been snooping around kaggle, and found a dataset on body performance given a host of variables. I thought i'd try using PCA to determine the most influential characteristics within the data and began working with it in matlab. I was able to get tons of outputs (a thrill unto itself) and a nice little scatter plot! However, when all was said and done I had difficulty understanding which variables were most influential by looking at the scatter plot and PCA breakdown. What should I be doing/thinking to gain that intuition? Thanks!

how do you write inverted letters so quick? or is it some kind of CGI?

PCA clearly explained!!!

hi doctor，really usefull to watch your lecture,but in the video,you have pointed out that T matrix is the principle components, however ,this is what confused me, my knowlage is that the col vector of loading are principle components, T is just transformed version of the data B. pls correct me if im wrong, thanks.

I started watching from SVD til here and it was super helpful! Thank you so so much.

I like your explanation. Please check equation 1.26 on your databook.

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.

Wow, I saw n videos before this, beautiful explanation¡

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

are you writing in the reverse order (right to left) on the board?

Is it important to show 95% confidence ellipse in PCA? If my data is not drawing then what should i do ? can i used PCA score graph without 95% confidence ellipse?

The data matrix is a wide matrix, so if it is already zero mean, then in this case the PC XV is equal to XU (Considering U from the SVD lecture)?

I am confused with SVD of B in step 4 , Isn't we do SVD or Eigen decomposition of C the covariance matrix? i.e. T=CV=UE, C=UEV' ? thank you

Hi professor, Just one question. If your X matrix has samples in the rows and sample features in the columns, then the correct shouldn't be to calculate the column-means(X), instead of row-means(X), and subtract each column-value by its respective column-mean? So, each X column (feature) has mean = 0.

Why did we calculate covariance matrix?

Can someone explain to me, why covariance matrix is just the inner product of B transposed B?

Please could you make a video about singular spectrum analysis?

Thanks for the great explanation! In your next video, can you please explain how you are writing backward!?

Hello, can you show with examples how to curvilinear component analysis?

4:45 here you’re summing over the elements of each row, but in the book on page 21 it say x_j = sum_i X_ij so you’re building the sum of each column. Is it a typo ?

How does he write in reverse?

Hi Steve, There may be a tiny typo in Page#22 in your Data Driven Science book. The equation(1.26) is supposed to be $B = X - \bar X$ to represent demeaned data $X$ while it shows $B = X - \bar B$ on the book. Please correct me if I am wrong.

Excelent teaching. I have one question tho. When you wrote the covariance matrix of the rows (6:00) because each row is a measurement vector I thought its the covariance between the measurements but then you wrote C=(BT)(B) which is the covariance of the features. Can you explain please.

You only said about the data should have 0 mean, but what about the standard deviation? Don't we need to scale the data first by dividing each measure by its standard deviation to make sure the PCA doesn't easily overfit to direction with the largest magnitude?

Thank you

If the images of X are not all independent, then X is not full rank matrix.then will we have only rank number of eigen faces?

Amazing! Thank you!

I was following ok until the part that started with writing the lambdas. I got lost there. Also, how is this and the nipals algorithm related?

At the 13’45 ‘’ mark why is the equation CV=VD? Should it be CV=DV?

good explanation in general. but you really should play with matrix dimension during explanations.

If we do row-wise correlation with respect to B, should it be C=B * B_T instead of B_T * B?

Nice lecture

this is more than Awesome!! i want to ask you one question and it is here a1=[1,23,4,51,62,7,8,43,1,29] a2=[5,45,32,51,60,7,8,35,10,31] a3=[13,3,64,35,36,37,48,3,31,1] a4=[3,3,1,5,6,3,8,3,1,3] a5=[0,3,0,5,0,0,8,0,0,1] how can i figure out important columns (features) with eigenvalues and eigenvectors? As we can see here , importance of a4 and a5 is negligible! but how can i find out with this concept? I have eigenvalues and eigenvectors of this but do not know how to use them in this context ? after finding eigenvalues and eigenvectors , i know how to find PC.Because i have seen your videos . As i have seen in the comment section someone already asked this question . But i was not able to understand the Ans! kindly help me out.

2:09 I just don't get it: Let's say we measured 1600 samples. Each sample measurement resulted in a concentration value for each of 26 Elements. How would that look like in the matrix? So my matrix would have 1600 rows and 26 columns, right?

Can somebody explain to me why it's B'B not BB' since the data were stored row-wise.

Thank so much. Please, can you make a video on Invariant coordinate selection (ICS) method ??? It will be very helpful. Thank in advance.

BtB seems to calculate the cariance matrix of cols of B.

@6:08, Can anybody confirm that C=B*BT instead of C=BT*B. That is because each row of B represents the measurement of a variable (0 mean).

The following are measurements on the test scores (X, Y) of 6 candidates for two subject examinations: (50, 55), (62, 92), (80, 97), (65, 83), (64, 95), (73, 93) Determine the first principal components for the test scores, by using Hotelling's iterative procedure. Sir how to .....???

Thank you for the lecture, its been very helpful. On an unrelated note, how do you write backwards with such ease?

Amazing video. To the point and efficient.

How to film such kind of tutorial videos?

He just knows it all.

Can you please make a video on OLPP?

Steve love your work, and your production values are fantastic - fyi, you can likely fix a lot of the contact noises from your lav mic with some relatively simple filtering and processing, and lowering the levels a bit during the recording could help avoid the distortion that crops up sometimes. If you'd like to discuss, let me know and I'll get you my contact details.

you are my idol now =vvvvvvvvvvvvvvvvvvvvvvvvvv

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

doesn't C has to be B*B^T ? B^T * B is the covariance of the columns if I get this correctly

This guy is super good at writing backwards

In the mean center part you are calculating row averages? As you described each row can be have "sex, age, demographics, and so on", these are not of the same category. Shouldn't it be column means?

very good, thanks a lot 😅

Best Illustration of PCA, I searched a lot for the explanation of equation till I find it in your video. I have outer question what are using in your presentation to appear on the screen and the board you use ?

Great video, but conventionally the principal components are the eigenvectors V instead of T, 8:15

Wouldn't we need to divide by N or N-1 for the covariance matrix? I know covariance as sij = 1/(N-1)* sum (n=>N) (v_in*v_jn)

Hi sir, The approach of explanation is good but the clarity of the main mathematical concept (eigenvalue and eigenvectors) lags. Thanks for sharing this awesome content. Love and respect from India.

Dear Steve bu video da neden altyazılarda türkçe yok. Anlayamadim