Singular Value Decomposition (SVD): Mathematical Overview
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- Опубліковано 18 січ 2020
- This video presents a mathematical overview of the singular value decomposition (SVD).
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/Data-Driven-Sc...
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
Brunton Website: eigensteve.com
This video was produced at the University of Washington - Наука та технологія
Why are comments disabled on other videos?! We all want to say thank you to this dude
this man is such a great teacher
a legend
You are so right. He skips straight through things but he brings you along. I have met some good teachers but SB is incredible!
He also works as a teacher (the two things are not related, just saying he also works as a teacher).
@@romanemul1 a god
@@abeke5523 A myth
I don't know how they do it, but Steve Brunton and 3Blue1Brown can explain stuff in a very impressive comprehensive way
Steve Brunton is saving my masters as he saved my undergraduate. What a guy!
I feel so lucky that I can see your videos and your channel, your lessons are amazing, it make me feel deep happy. I can feel that you would love to share your knowledge to everyone. Thank you so much Steve Brunton.
Relating SVD to Fourier series is the most enlightening sentence I had ever heard. Thank you.
Yeah that blew my mind too!
The fact that I'm seeing this video 2 years after it was posted makes me feel that I'm about two years behind the best in what exists in machine learning and data science. =(
Well, better late than never! Haha! Great class, Steve! You're an awesome teacher! Greetings from Brazil!
A great lecturer. Some people are born teachers.
A great lecturer and I am buying their book to show my appreciation and thanks to Mr Brunton - and his colleague.
From downtown London, UK.
Great stuff! You explain the story the mathematics is trying to say in such a clear and understandable way!
You’ve now become the only channel I’m subscribed to where I’ve also hit the bell - I really appreciate your approach
Awesome!
I haven't finished the video but it is so great to have a preamble explaining what is what, especially something very simple but sometimes ambiguous like what is the direction of the matrix vectors! It might seem obvious to some but in my experience this is often confusing, I tend to make an assumption but often halfway through I have to backtrace the whole calculation trying to evaluate the alternative interpretation.
Amazing! Well explained! I've had to watch a few times tbh, because I kept getting distracted by how Impressively he writes backwards. He doesn't even get distracted by the effort!! Just keeps on talking, teaching, and drawing while writing tidy, informative, concise notes... backwards! Amazing!! Thank you!!
Mr. Brunton certainly understands how to take the students along in the lecture and not leave them at sea. Also, I believe the video is a mirror reflection of Mr Brunton actions which would produce the same effects.
i am doing an elective about this and you are practically saving my life
I've used PCA, but have never heard of SVD. After this video I can see how they are related and wonder how I never heard of it. Looking forward to the rest of the series!
Thank you so much, you are great at explaining!
Same for me, it`s like your told to use some math(PCA) but they left out the foundation(SVD). The lectures and the book together are really really good and that you get the material for free is awesome.
This guy is like the greatest teacher ever!!
Dude you and some other UA-cam teachers have been make my life great and helping me love studying again, thank you truly
Outstanding and brilliant with the intuition. A great teacher, and the best set of videos, bar none, on the topic.
This is the best video on SVD i have ever come across. Just wow.
I think i have found a corner of youtube that brings me true joy. Thank you.
This is the first time I learn about SVD and I can fully understand. Thank you!!!
Every time I see a tutorial video for professors in the US universities I envy their students, they don't have to learn eveything twice, once from the classroom from a bad teacher then again on UA-cam from amazing teachers like Steve or others
Not all US universities are like that. These are the guys at top schools who really mastered their subject's state-of-the-art. At ordinary state universities, students can not even get a proper education in basic subjects, and professors are too busy, depressed, and pressured with research to be able to have any sanity to teach properly.
@@robensonlarokulu4963even at great schools, not all professors are equally good at teaching.
I cannot thank you more for the splendid elucidation of SVD
Awsome explanation, before coming to this channel watched other videos and got a bit confused but here the concept is explained so smoothly. Thanks!!
Incredible production! Congrats from Spain!
This is the best explanation I have seen so far! Great explanation!!
You obviously can see this through your viewership, but holy smokes you have an amazing delivery style. Thank you
Amazing content, amazing explanation, amazing videography. Thank you so much for your work. I am truly grateful and I wish I could be your student in my lifetime. I watched one video and immediately knew that I have to hit the subscribe button. Thank you once again
Such smooth and intuitive understanding saving me from perplexity of the topics. Thanks Sir!! May God bless you! Love from students from Bharat!
Oh my God. What a teacher. Thank you sir. I needed to learn this mid career and you are God send...
Keep up the great work! Excellent channel!
Thank you so much. Simple, clear and with examples, it's nice 👌
I cannot thank you enough for the awesome explanation! Thank you!
wow. when you strated describing the meaning of U sigma and V, I could see how it was of similar concept of that of fourier series and transform
Great video, love the different real world examples
Thank you for all the awesome lectures.We wish you all the best..
The professor has so patiently explained every individual part of the whole equation with so much of attention and beauty, he literally made me "feel" the entire concept!
Sir, kindly teach others on how to teach as well. We need a lot more people like you in this world.
Brilliant approach. So intuitive.
This man is the Guru of so many topics. His explanation is so good even I can understand the material.
Thanks!
Wow I can clearly visualise it in my head how the multidimensional data is stacked and matched across time.
This is so useful and clearly explained. Thank you
You're a star , Mr Brunton. Thanks !
OMG this is exactly what I was looking for! And you have explained it in the clearest way possible. Thank you! Instantly subscribed.
You are amazing. Thank you .. The explanation was really clear and your way of teaching is great.
Awesome!! I'm not really good at it but learning it or listening enhances and adds to others skills that are relevant to this almost... if that makes scense...
Amazing teacher! Great work!
Thank god you made this video, sir. Awesome!
Thank you very much for explaining these in very simple words
Such an amazing explanation. Thank you so much.
Thanks for your great video! I will read your book as well.
you explain very well. thank you man
Brillant explanation! Thank you!
That's a great lecture on svd.Hope for getting more initiative videos
WOOOOWW ! Amazing teacher! Thanks Professor, I'll get the book.
Thank you so much Steve Brunton
@steve Brunton! Amazingly explained !! Ite super clear now in my head
A good UA-cam rule of thumb is to never read the comments. An caveat to that rule is if the poster is a skilled educator. Thank you so much for your wonderful video!
What a fantastic teacher!
great explanation... should be distributed to all universities worldwide including to my own professors at my uni :)
you helped me a lot, thank you. 🇧🇷❤
Fantastic video, really well explained
Great explanation! Thank you so much.
Very nicely explained!! Thanks!
This is the best SVD lecture I have ever known! and I have a question why SVD always give first come first serve importance to each vector? if X is a random matrix, how does SVD decide/know the first vector is the most important one and the importance of other vectors decreasing in order. thank you
You are a legend, Steve
Incredible videos, thanks so much!
Welcome back ♡
Thank you professor for the wonderful lecture
Thanks a lot teacher, I didn't knew SVD is so simple to understand..
Please have a lecture on Wavelet decomposition you are the best. The time and effort you have put in is so clearly seen, please also have lecture on how to give good presentations like yours and how to prepare for it 🤓🤓
you made it so easy to understand.
Thanks!
In my first semester of graduate school for ML, was starting to think this wasnt for me based on how lost I have been on this topic. You saved me from imposter syndrome, thank you
Happy to help and thanks for watching!
RtoL writing behind a glass is revolutionizing online teaching, the 1st of which seems to be that on Nancy's channel on calculus. Super cerebrum-cerebellum-hand axis👍
Thanks for sharing these wonderful videos Steve.
Are you also planning to cover MCMC, Gibbs sampling etc in future?
Great suggestions -- on my (long) list!
What a great teacher, thank you!!! 🇧🇷❤
verdade
Thank you! Really clear explanations!
Glad it was helpful!
This guy is awesome. This is the Full SVD not the reduced SVD FYI
This is how you teach. Thank you.
Really sir, how can someone explain like this, thanks for your efforts.
Amazing stuff!👍
Thank you so much for this gem
Excllent introduction of SVD, it looks very similar to EOF.
It was a great explanation, Thank you Sir.
Probably the best explanation I've seen. At least I understood it))
amazing series! New subscriber here! Love the aesthetics and how clearly you explain everything.
Awesome, thank you!
sir you are the best,too good explanation and material
thank you so much for this series! I just started and have a stupid question, what does it mean when you say eigen something? I know eigenvectors are the vectors that remain the same direction after matrix transformation, but eigen-flows/faces?
Good question. I use this to mean "characteristic" or "latent" (which is what it means for eigenvalues/vectors too). But eigenflows and eigenfaces are eigenvectors of a large data correlation matrix. So in a sense, they are eigenvectors of a particular linear algebra problem.
Specifically, if I stack images as column vectors in a matrix X, then the "eigen-images" of X are the eigenvectors of X^T * X.
Much respect from a mathematics teacher
This is pure genius.
Beautiful lecture
Great video series...I don't understand this maths part here...can u advise what topic should I be studying to understand this better?
Amazing explanation！！！
blew my mind with the explanation of each of the three elements. thanks!
Awesome, great to hear!
Awesome explaination sir
excellent lessons
great explanation
You are amazing! Thank you so much!
Beautiful talk
I cannot understand why SVD of a matrix is unique.
Thanks for your great explanation.
Dear Professor: May God bless you for your kindness of teaching us!!!
One question: in some country which has a huge population, by scanning a person's face, the authority can identify him/her in a couple of seconds. Considering the 'face library' is so huge, then the matrix will be huuuuge. There must be additional trick(s) to do this. Could you hint a little bit on it? Thank you very much!