Randomized Singular Value Decomposition (SVD)

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This video describes how to use recent techniques in randomized linear algebra to efficiently compute the singular value decomposition (SVD) for extremely large matrices.
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
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...
Brunton Website: eigensteve.com
This video was produced at the University of Washington

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28 янв 2020

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Комментарии : 26

@user-hl5sk1oj1m 4 года назад

I can't believe that I understood this. Thank you so much Prof.

@chienthan12345 4 года назад

Very easy to understand by watching your explanation. Thank you

@chrisw3327 Год назад

Thanks Steve!!!! This is a very important approach for my desire to analyse high resolution climate model data.

@zoloojagaa9198 4 года назад

Thank you. You just saved my life

@zelexi 3 года назад

this is a fantastic explanation

@andrezabona3518 3 года назад

You are the best! I love your videos!!

@dragosmanailoiu9544 4 года назад

This prof is cool he’s interested in complex systems and fractals

@johnl4885 4 года назад

Good explanation.... not clear why it works as well as it does. Gives us some homework to get to the bottom of these ideas. Thank you

@Falangaz 4 года назад

Thanks Prof!

@nazniamul 3 года назад

Dear Prof. Your videos are fantastic and help me a lot. I just want to request you to explain (or give the numerical proof) how Sigma and V of Y matrix should be same as original data matrix X. Is there any references or documents I can go through? Your response would be a great help for all of us.

@mahan1598 3 года назад

Thank you Steve! I have a question: Suppose we have the SVD od the current matrix A. If we add a new snapshot, is there any quick way to find the SVD of the new matrix? It will be useful when we want to find the POD of time-consuming LES or DNS simulations while calculating the flow field.

@ondrejkotaba 4 года назад

Thanks!

@MoeGamm 4 года назад

Great!

@yasserothman4023 3 года назад

Thank you. but can you point out how can we compute the SVD using the QR algorithm ? i am referring to @5:29

@MohammedFarag81 3 года назад

Thanks for this interesting explanation. I have one question: How do you determine the rank r which requires pre-knowledge of the optimal threshold obtained from the Sigma matrix we are trying to compute using the rSVD? has this point been raised in related work in the literature?

@nami1540 2 года назад

Watch the videos before this one in the series

@karthikr3977 4 года назад

kool stuff]

@brunoisy 4 года назад

Why must the projection be random? From what distribution should it be generated? Couldn't I use the same projection over and over again, which means it wouldn't actually be random?

@Eigensteve 4 года назад

In principle, you could pregenerate a big random matrix and then use it over and over. Eventually, you might run into some bias problems, but it should be okay. For example, if I built a camera on these principles, my guess is that my random measurement matrix C might not change... but that would be fine, since it is highly unlikely that it would be a "bad" matrix for any real-world signals.

@butette 3 года назад

Stupid question but what is the system you use to write on the screen like that? It looks very cool.

@nazniamul 3 года назад

He use a transparent glass as a writing board and keep the background dark. Then mirror the whole video so that we can see the transformed version of whole activities. You can imagine the whole process as a transformation of space (or matrix manipulation). The whole idea is just amazing.