Singular Value Decomposition (SVD): Matrix Approximation

Рет қаралды 231,990

4 жыл бұрын

This video describes how the singular value decomposition (SVD) can be used for matrix approximation.
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

Пікірлер: 209

@ayushsaraswat866 4 жыл бұрын

This series is by far the best explanation of SVD that I have seen.

@greenpumpkin172 4 жыл бұрын

This channel is so underrated, your explanations and overal video presentation is really good!

@dombowombo3076 4 жыл бұрын

Don't know why you think it's underrated... Everyone who is watching this videos knows how great they are.

@AdityaDiwakarVex 4 жыл бұрын

SVD was at the very end of my college LinAlg class so I never got a very good understanding of it before the final - this is truly amazing; you say "thank you" at the end of every video but it should be us saying it to you- keep doing your thing! I'm loving it.

@skilambi 3 жыл бұрын

Please keep making these high quality lectures. They are some of the best I have seen on KZfaq and that goes a long way because I watch a lot of lectures online.

@douglashurd4356 3 жыл бұрын

Superlative production! Lighting, sound, set, rehearsals, material, these videos are among the best productions on KZfaq. Even I understood some of it! :-)

@peymanzirak5400 Жыл бұрын

I find everything with these courses, even the way board arranged is just great. Many many thanks for this wonderful explanation and all your effort to make it understandable and yet complete.

@ris2043 4 жыл бұрын

The best explanation of SVD. Your videos are excellent. Thank you very much!

@alexpujoldartmouth 3 жыл бұрын

You have a talent for taking complicated topics and breaking them down into digestible pieces. That's the sign of a good teacher. Thank you.

@rajkundaliya7796 2 жыл бұрын

It doesn't get better than this. I am so thankful to you. I don't know how to repay this help.... And yes, this is a highly underrated channel

@sonilshrivastava1428 3 жыл бұрын

One of the best videos on singular value decomposition. it not only tells the maths but also the intuition. Thanks. !

@nathannguyen2041 2 жыл бұрын

This was, by far, the most compensable explanation of what the SVD is mathematically and visually. The SVD is an incredible algorithm! Amazing how so little you could keep in order to understand the original system.

@omniscienceisdead8837 2 жыл бұрын

you explain math in such a way as to not make someone feel stupid, but feel like their taking steps into understanding a larger concept, and the tools they need are the ones we already have, big ups

@zsun0188 3 жыл бұрын

I learned this in college but couldn't recall a bit after working in the industry over a year. This explanation not only helped me refresh my memory but also enhanced my understanding as well.

@AkshatJha Жыл бұрын

What a wonderful way to simplify a complicated topic such as SVD--I wish more people in academia emulated your way of teaching, Mr. Brunton.

@fabou7486 2 жыл бұрын

One of the best channels I have ever followed, appreciate it so much!

@nikosips 4 жыл бұрын

Thank you very much for those videos , they are very explanatory . Keep up the good work, we need you lessons for our academic improvement.

@bnglr 4 жыл бұрын

every time I think it's time to pause and comment this video with "awesome", it surprises me with more informative perspective. great job

@xiaoyu5181 4 жыл бұрын

This is also the best explanation of SVG I have seen! Thanks for sharing!

@smilebig3884 4 жыл бұрын

The best thing about your lectures is, u do coding implementation along with huge maths.. That makes u different from rest of the traditional instructors. Kudos to you!!!

@Eigensteve 4 жыл бұрын

It's my pleasure

@malekbaba7672 4 жыл бұрын

The best explanation of SVD i have ever seen !

@NickKingIII 4 жыл бұрын

Wonderful explanation, clear and easy to understand. Thank you very much

@tusharnandy6711 4 жыл бұрын

Gentleman, you have done a very impressive job. I have just started exploring data science and have recently completed my college course in Linear Algebra. This was quite interesting.

@zepingluo694 3 жыл бұрын

Thank you for presenting us an amazing experience to learn about SVD!

@eveninrose 4 жыл бұрын

Just started watching this playlist, excellent explanations and a great way to promote while sharing knowledge; bought your book and can't wait to revisit w/the text!

@Eigensteve 4 жыл бұрын

Awesome, thank you!

@RajeshSharma-bd5zo 3 жыл бұрын

Such a cool concept of decomposition and brilliantly explained here. Big thumbs up!!

@bryan_hiebert Жыл бұрын

Thank you so much for posting the course material. I was running through asking ChatGPT some questions about eigenvector/eigenvalues and revisiting some linear algebra when I stumbled upon transitional probability matrices or Markov Matrices, PCA and SVD as was getting back to my Data Science studies. This is very exciting stuff and your presentation is very clear and understandable.

@patf9770 3 жыл бұрын

Can't overstate how good this series is...

@din_far Жыл бұрын

this is by far the best video explaining SVD on youtube

@athanasiospliousis2654 4 жыл бұрын

Very, very nice explanation and presentation. Thank you!

@kaiyueli1372 2 жыл бұрын

This video series is so helpful!! Thank you Dr. Brunton!

@yasirsultani 2 жыл бұрын

These are the best videos out there. Biggest fan Steve, keep it up.

@alek282 4 жыл бұрын

Amazing lectures, immidiately bought the book, thank you!

@LusidDreaming 3 жыл бұрын

The book is great, but relatively terse for someone like me who needs to brush up on his linear algebra. These video lectures are an excellent compliment to the book and really help drive home the concepts.

@douglasespindola5185 2 жыл бұрын

Gosh, what a class! As mr. Ayush said, this was indeed by far the best SVD explanation I've seen. You've made a such complicated subject way more affordable! I wish you all the best, Steve! Greetings from Brazil!

@Eigensteve 2 жыл бұрын

Thanks so much! That is great to hear!!

@saitaro 4 жыл бұрын

It was pleasure to watch. You should do more educational videos, mr. Brunton.

@carlossouza5151 4 жыл бұрын

You are a very very gifted teacher! Thank you for sharing this! :)

@HuadongWu 3 жыл бұрын

the best lecture of SVD I have ever seen!

@Nana-wu6fb 2 жыл бұрын

Literally the best svd explained, so meaningful

@PunmasterSTP Жыл бұрын

Matrix approximation? More like "Magnificent explanation!" I really can't convey in words how absolutely outstanding *all* of your videos are.

@dhoomketu731 3 жыл бұрын

This one's a brilliant explanation. Simply loved it.

@garrettosborne4364 3 жыл бұрын

This is answering a lot of my questions on SVD.

@kansasmypie6466 3 жыл бұрын

Can you do a series on QR decomposition as well? This is so useful!

@YYchen713 2 жыл бұрын

Thank you for making the linear algebra less boring and really connected to data science and machine learning, this series is so much more interpretable than what my professor explains

@PunmasterSTP Жыл бұрын

Hey I know it's been nine months but I just came across your comment and was curious. How'd the rest of your class go?

@btobin86 2 жыл бұрын

You are so talented at teaching, great explanations!

@alwaysaditi2001 3 ай бұрын

Thank you so much for this easy to understand explanation. I was really struggling with the topic and this helped a lot. Thanks again 😊

@Eigensteve 2 ай бұрын

Glad it was helpful!

@wackojacko1997 Жыл бұрын

Not an engineer/student, but I'm watching this to get a better understanding of PCA in statistics. I'm going to check the book and research this, but my only complaint (nit-picky) is trying to tell the difference when Steve speaks between "M" and "N" which I know refers to the number of rows or columns of the matrix. But really, this was great and I am thankful that this is something I can study on my own. Much appreciated.

@patrickgilbert6170 3 жыл бұрын

Great video. Should be required viewing for anybody learning the SVD!

@billandrews6291 3 жыл бұрын

13:41 The way I like thinking about is, for example, two vectors in R^3 that are orthogonal are not necessarily orthogonal when projected into R^2, which is essentially what is being done by dropping some of the dimensions. Love the videos though, has me thinking about SVD again.

@user-hp1zj6hk5c Жыл бұрын

really really nice explanation！you are really a great teacher！

@mkhex87 Жыл бұрын

To the point. Answers all the important questions. I mean you should come to the party knowing some lin alg but great for intermediate level

@deepthikiran8345 3 жыл бұрын

The explanation is really wow !! Very intuitive ... thank you so much !!

@kiaranr 2 жыл бұрын

I've read about and even used SVD. But I never really understood it in this way. Thank you!

@liuhuoji 3 жыл бұрын

love the video, well explained and aesthetically good.

@guitar300k 2 жыл бұрын

I like your series also the dark background make my eye feels ease than white background like other channels did

@juangoog 2 жыл бұрын

Wow, what a wonderful presentation. Congratulations.

@khim2970 Жыл бұрын

really appreciate your efforts. wish u all the best

@Streamoon 2 жыл бұрын

Thank you Prof. Brunton, excellent explanation! Just come from MIT 18.06.

@Aditya-ne4lk 4 жыл бұрын

Just in time for the new semester!

@ARSHABBIR100 4 жыл бұрын

Excellent explanation. Thank you very much.

@arne9518 3 жыл бұрын

This is a gold mine! thanks for your videos

@chenqu773 3 жыл бұрын

Good explanation! Many thanks ! how could one manage to get these stuffs explained in such an elegant way.

@parnashish1910 2 жыл бұрын

Beautifully explained.

@FezanRafique 3 жыл бұрын

Steve is magician of explanation.

@Eigensteve 3 жыл бұрын

Thanks so much!

@wudiNB Жыл бұрын

best teacher that l have ever met

@MassimoMorelli 3 жыл бұрын

Extremely clear. Just want to point out a fact which at first did not seem obvious to me: the outer product has rank 1 because all the column are proportional to the first vector of the outer product, hence they are linearly dependent.

@alexyang6755 3 жыл бұрын

it covers a lot.Thanks for beautiful teaching!

@pilmo11 11 ай бұрын

superinformative series of SVD

@sanaomar2182 Жыл бұрын

This is the best explanation ever

@nicholashawkins1017 2 жыл бұрын

Lightbulbs are finally going off when it comes to SVD cant thank you enough!

@Multibjarne 2 жыл бұрын

Explanations like this for a dummy like me makes my life so much easier

@LyndaCorliss Жыл бұрын

Top rate education, I'm happily learning a lot. Nicely done. Thank you

@mohammedal-khulaifi7655 2 жыл бұрын

you are at the tip-top i like your explanation

@andrezabona3518 3 жыл бұрын

for mn ? (For example, what happen if my dataset is composed by 5000 images of 32x32?)

@jonathanschwartz7256 4 жыл бұрын

Watch out Kahn Academy, Steve Brunton is coming for ya! Seriously though, these videos are fantastic :)

@inazuma3gou 3 жыл бұрын

Excellent, excellent content. Thank you so much!

@maydin34 3 жыл бұрын

Sir. Just thank you for making me be your student in here for free! Great performance, great job!

@neurochannels Жыл бұрын

I never *really* appreciated SVD until I saw this video. Mind blown!

@mr.jizhouwubs7256 3 жыл бұрын

Great video in linear space point of view. One naive question: can we make use of Lanczos algorithm such that we can pick up the most significant eigenvalues for approximation in order to circumvent the full diagonalization of the whole large matrix?

@mohiuddinshojib2647 3 жыл бұрын

This is everything that I need. Thanks for nice explanation .

@Eigensteve 3 жыл бұрын

You are welcome!

@mdmamunurrashid2945 3 жыл бұрын

Love his explanation style

@katieadamczyk937 Жыл бұрын

This is a fantastic video!!

@fabiopadovani2359 4 жыл бұрын

Thank you very much. Excellent explanations.

@opencast1819 2 жыл бұрын

Great lecture Steve, really enjoyed it! I have a couple of questions: is it better to have longer or shorter time series for the SVD? And is a tall skinny matrix you mentioned speaking about the "economy" SVD only matter for the memory and time savings, or is it generally recommended to have such an input matrix? Thank you in advance and best greetings from Austria) Alexander

@maipyaar 3 жыл бұрын

Thank you for this video series.

@hugeride 3 жыл бұрын

Just amazing explanation.

@arthurlee8961 13 күн бұрын

That's so helpful! thank you!

@zhichaozhao172 2 жыл бұрын

Prof.Steve, Thanks for your explanations. But what is the difference between the POD and SVD for aerodynamics analyeses?

@lekshmynair3355 3 жыл бұрын

Thank you too so much sir for this explanation its truely amazing

@adelheidgang8217 Жыл бұрын

incredicle explanation!

@regbot4432 3 жыл бұрын

Wow, you are really good teacher.

@raven5165 9 ай бұрын

In the example, m is the number of images you have, n is their pixel values. So m doesn't have to be enough to represent your data. It is like saying, if you have 2 photo, 2 dimensions are enough to represent image features.

@namex26 2 жыл бұрын

Great lectures. Thanks so much. Kind of hard to distinguish the m's and n's sometimes. Hoped you'd use some other letters :D

@johnberry5275 3 жыл бұрын

I'm glad he made it clear that *outer products* were taking place.

@sachingarg4385 3 жыл бұрын

Part 2 of the Eckard Young theorem is that this video is the best explanation of the theorem's part1 :P

@franciscojavierramirezaren4722 4 жыл бұрын

Thanx amaizing as always👍

@Phi1618033 Жыл бұрын

This all sounded like gibberish until I started to think of the first term of the expansion (Sigma1*U1*V1T) as the (strongest) "signal" and the rest of the terms as ever decreasing amounts of "signal" and ever increasing amounts of "noise". So the last term (Sigmam*Um*VmT) is essentially all background "noise" in the data. Thinking of it that way, it all makes perfect sense.

@JCatharsis 2 жыл бұрын

Thank you so much professor.

@nolanzheng7810 2 жыл бұрын

I cant believe I am watching this for free. Thank you!

@harrypotter1155 2 жыл бұрын

Mindblowing!

@aryanshrajsaxena6961 2 ай бұрын

Thank You Professor. Respects from India

@Eigensteve 2 ай бұрын

You're welcome :)

@maciejmikulski7287 Жыл бұрын

The assumption n >> m is contrary to what we have quite often in data sciences. In many problems, the number of samples (here m) is bigger than number of features (here n). In such a case, we just take the transpose and keep going the same way? Or there are some additional considerations (of course except of swapping interpretations of eigen vectors etc)?