What is Sparsity?

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-Sc...
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
Brunton Website: eigensteve.com
This video was produced at the University of Washington

[@toastrecon]

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]

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

[@samre3006]

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]

Couldn't agree more!

[@ATXMEG]

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

[@matveyshishov]

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

[@shanesteinberg8161]

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

[@nahashonosinde9163]

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.

[@andrezabona3518]

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

[@ShashwatPandeyindia]

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

[@koukous95]

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!

[@MaksymCzech]

Thank you for the video, great as usual

[@SRIMANTASANTRA]

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

[@andersonsen1989]

Thank you so much for the lectures!

[@sat1915]

You just made it super interesting. Hats off.

[@mosaicspark2372]

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?

[@user-qp2ps1bk3b]

love those lectures

[@JoaoVitorBRgomes]

Obrigado, Steve! Things make more sense now.

[@anangsuwasto8678]

Amazing explanation!! :)

[@kidconnitv9774]

What a time to be alive!

[@symbolxchannel]

Dimensionality reduction is simply awesome!

[@mehrabzamanian581]

Useful and concise

[@sumant9189]

Thanks professor.

[@kane_8t]

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

[@Victor-dh5us]

Thank You !

[@msoulforged]

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?

[@omar_5352]

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]

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

[@lucaborgese96]

Thank you very much

[@Eigensteve]

You are welcome

[@doctorpoosa]

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

[@dixshants1227]

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?

[@Garganzuul]

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]

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

[@SridharNag]

same here, even i would like to know the same

[@yosily]

I had the same question

[@prashantsharmastunning]

super super interesting

[@zrmsraggot]

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 ?

[@subhadeepmandal3092]

In Tailored Basis what is epsilon r and Vr?

[@gammygoogur]

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

[@miguelfernandesdesousa7784]

steve brunton in 1440p oh my god

[@mysterylearning4181]

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