What is Sparsity?

Ғылым және технология

Here, I define sparsity mathematically.
Follow @eigensteve on Twitter
These lectures follow Chapter 3 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com/Data-Driven-Science-Engineering-Learning-Dynamical/dp/1108422098/
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
Brunton Website: eigensteve.com
This video was produced at the University of Washington

Пікірлер: 43

  • @toastrecon
    @toastrecon3 жыл бұрын

    When I was 10, I got up early on a Saturday for the Smurfs. Now, I get up early for Sparsity. No commercial interruptions. All that's missing is some Lucky Charms.

  • @TheMazyProduction

    @TheMazyProduction

    3 жыл бұрын

    For me it was spongebob how it’s generative models.

  • @samre3006
    @samre30063 жыл бұрын

    Life would be so much better when they teach about applications before dry theory as motivation. I am very thankful for these amazing videos.

  • @Eigensteve

    @Eigensteve

    3 жыл бұрын

    Couldn't agree more!

  • @shanesteinberg8161
    @shanesteinberg81613 жыл бұрын

    Thank you Steve. Your KZread videos are a great balance of accessibility of quick bite-sized concepts without the lowering of discussion to menial examples.

  • @matveyshishov
    @matveyshishov Жыл бұрын

    Thank you so much, Steve! You're connecting the practical implementations with the underlying math incredibly seamlessly, almost a work of art!

  • @nahashonosinde9163
    @nahashonosinde91633 жыл бұрын

    Thank you Professor Steve. Just what I was looking for! Your tutorials have helped me in my masters in Control engineering, and this new series is a helping hand at the start of my PhD.

  • @ATXMEG
    @ATXMEG3 жыл бұрын

    Many thanks indeed for providing such great lectures and sharing it with us. :)

  • @ShashwatPandeyindia
    @ShashwatPandeyindia3 жыл бұрын

    Dear Steve... your lectures are a blessing. Thank you so much 🙏

  • @andrezabona3518
    @andrezabona35183 жыл бұрын

    Omg, I'm completely in love for signals because of you!! Hope doing something cool soon with all this!

  • @koukous95
    @koukous95 Жыл бұрын

    Thank you very much for these amazing and well detailed videos, I'm actually working on my Master's degree thesis about cognitive radio and these videos helped a lot in the compressed sensing chapter!

  • @andersonsen1989
    @andersonsen19893 жыл бұрын

    Thank you so much for the lectures!

  • @SRIMANTASANTRA
    @SRIMANTASANTRA3 жыл бұрын

    Hi Professor Steve, Thanks for the nice idea shear with us.

  • @sat1915
    @sat1915 Жыл бұрын

    You just made it super interesting. Hats off.

  • @MaksymCzech
    @MaksymCzech3 жыл бұрын

    Thank you for the video, great as usual

  • @JoaoVitorBRgomes
    @JoaoVitorBRgomes3 жыл бұрын

    Obrigado, Steve! Things make more sense now.

  • @user-qp2ps1bk3b
    @user-qp2ps1bk3b3 жыл бұрын

    love those lectures

  • @symbolxchannel
    @symbolxchannel3 жыл бұрын

    Dimensionality reduction is simply awesome!

  • @mehrabzamanian581
    @mehrabzamanian5812 жыл бұрын

    Useful and concise

  • @mosaicspark2372
    @mosaicspark23723 жыл бұрын

    Holy shit man, I just discovered your channel and it feels like I have found a gold mine! There are soo many useful videos that I don't even know where to begin. Is there any way to support your work so you can continue creating this wonderful content? Patreon, Paypal, Donations?

  • @anangsuwasto8678
    @anangsuwasto86783 жыл бұрын

    Amazing explanation!! :)

  • @kidconnitv9774
    @kidconnitv97743 жыл бұрын

    What a time to be alive!

  • @sumant9189
    @sumant91893 жыл бұрын

    Thanks professor.

  • @Victor-dh5us
    @Victor-dh5us3 жыл бұрын

    Thank You !

  • @kane_8t
    @kane_8t4 ай бұрын

    Man u look like HG Wells from flash series ....luv ur videos ❤

  • @omar_5352
    @omar_53523 жыл бұрын

    I just wish this was available 30 years back when I worked on video compression. Great material and well presented indeed. But as far as I recall JPEG relied on DCT, not DFT.

  • @Andres186000

    @Andres186000

    2 жыл бұрын

    I think JPEG may have originally relied on DFT and then was updated to DCT to deal with gibbs phenomena when compressing images with sharp edges

  • @msoulforged
    @msoulforged3 жыл бұрын

    7:30 When the metalhead in you kicks in \\m// :) One question, what is a quantitative measure of sparsity? Like how much percentage of elements should be zero to count a matrix as sparse?

  • @dixshants1227
    @dixshants1227 Жыл бұрын

    Thank you for the video! very helpful! is it possible that some basis gives us a more sparse result than others? Like here the DFT may give us 10 non-zero entries of a 1mil entry image, but what happens if we use a different transform that gives us 5 or 20 non-zero entries? Does that make a difference and is it in our interest to look for transforms that keep increasing the sparsity?

  • @doctorpoosa
    @doctorpoosa3 жыл бұрын

    Thanks for these amazing videos! I really appreciate if you could talk a little bit about L0 norm also. Thank you!

  • @subhadeepmandal3092
    @subhadeepmandal3092 Жыл бұрын

    In Tailored Basis what is epsilon r and Vr?

  • @zrmsraggot
    @zrmsraggot2 жыл бұрын

    Is the the sum of the values in the sparse S 'equals to 100%' like they are the whole values that play a role in the equation ?

  • @lucaborgese96
    @lucaborgese963 жыл бұрын

    Thank you very much

  • @Eigensteve

    @Eigensteve

    3 жыл бұрын

    You are welcome

  • @prashantsharmastunning
    @prashantsharmastunning3 жыл бұрын

    super super interesting

  • @Garganzuul
    @Garganzuul3 жыл бұрын

    I suspect sparsity and structure might be the same thing. I think that translates to a high degree of linear independence being more informative. Then information is something which is less dependent on circumstance.

  • @brandonwilson8115
    @brandonwilson81153 жыл бұрын

    Just out of curiosity, are you writing backwards, or are you flipping the image with software? Very interesting and effective video making setup.

  • @SridharNag

    @SridharNag

    3 жыл бұрын

    same here, even i would like to know the same

  • @yosily

    @yosily

    2 жыл бұрын

    I had the same question

  • @miguelfernandesdesousa7784
    @miguelfernandesdesousa77843 жыл бұрын

    steve brunton in 1440p oh my god

  • @gammygoogur
    @gammygoogur2 жыл бұрын

    for what its worth jpeg uses discrete cosine transform and not discrete fourier transform - awesome vids tho

  • @mysterylearning4181
    @mysterylearning41812 жыл бұрын

    But how is he writing everything backwards so easily...?