The Wasserstein Metric a.k.a Earth Mover's Distance: A Quick and Convenient Introduction

[@mochen9282]

The BGM is a bit annoying.

[@baaliilyes]

I totally agree...this is math, we need some silence to focus and understand

[@maxsuica6144]

"A bit" annoying. Because apparently there is some possible world where atonal fretless bass is only "a bit" annoying.

[@BobLaramee]

That's the infamous Tony Levin on bass.

[@BobLaramee]

It's the amazing Tony Levin.

[@ahmedmustahid4936]

Not a bit, VERY annoying

[@williamstephenjones3863]

Brilliant video. Ignore the comments about BGM. We are forever grateful for efforts like this.

[@BobLaramee]

Thanks for watching.

[@vanshajkhattar8373]

The explanation is very nice. Highly recommended video for someone who wants to get an intuition into Wasserstein metrics. I think the dislikes are due to music or may be his slow teaching style. I would recommend watching the video at 1.5x atleast.

[@BobLaramee]

Thanks for watching.

[@ArmanAli-ww7ml]

But i like this slow style. Everyone has different preferences

[@danielliu9616]

Speed x1.25 the video becomes normal

[@prasanthsrinivasan7709]

Thank you so much. It works ;)

[@akrammustafa3569]

Thanks, that is much better

[@kamilozdemir9772]

x2 speed is better

[@Barsay]

oh s^it it works

[@HA-zd5gx]

but with that speed the background music is not harmonic as before😢

[@lalakyadav1493]

I understood d represents the distance between two distributions. But I'm unclear about the role of dy, specifically how the height of a block (as suggested by dy) contributes to the overall distance calculation.

[@BobLaramee]

Thanks for watching. Yes, the video is not a complete explanation, more like just the beginning. For more, you'll have to do some more research. Have a look at some of the video comments and description.

[@roman6575]

The BGM is great, felt like background music of a video game, makes it easier to focus.

[@BobLaramee]

The BGM is from Tony Levin.

[@shinykaushal]

Thank you so much Sir for such a great help. On a single email you made this video & uploaded for me. I am so happy that you responded very kindly. Thanks a Ton !!! :)

[@BobLaramee]

Thanks for asking a good question.

[@amansahani2001]

Precise Explanation Sir, You are helping me in writing my master thesis. Thank You

[@BobLaramee]

Thanks for watching

[@justinchen8519]

recommend watching in x1.25 speed

[@TonyKaku-g8n]

The BGM made me think you were actually living in Antarctica with lovely penguins, I like it btw

[@BobLaramee]

Chart Denkra thanks for watching

[@yashjain8117]

Sir make a video on Kullback-leibler distance please

[@a.3659]

Thanks alot. It really helped me understand!

[@BobLaramee]

Thanks for watching

[@Dafiya445]

Thanks for your initiative in making this video. Can you please provide a link that compare images using EMD

[@ArmanAli-ww7ml]

I need further help on this? Anyone?

[@GaylordNdemboNDATORO]

The number of bins are the same for both distributions?

[@SoichiHayashi2014]

Thank you for the video. I have 2 questions. When you say to move a box from one distribution to another, how are you decide the destination of the box? In another words, how do you determine "d" ? If you are moving it to match the shape of the destination, how do you consider its size? Like.. UK is smaller than US, so how do you move all parts of US to UK? Another question is, when you are considering a distance between 2 mathmatical distribution, wouldn't there be a simple equation to calculate it using calculous? Thank you!

[@harikannantube]

Take a look at the first few pages of "Optimal transport meets graph spectra" by Shiping Liu. It is one of the many good introductions that will clarify your questions. In a simplified manner, the answers to your questions are: The moved quantities are infinitesimal in nature. They correspond to densities. The destination in the target of a source point is what one tries to obtain by solving the Monge version of the problem. In the Kantorovich version, a source point can be split and assigned to multiple target points. These transportation maps (for Monge) and transportation plans (for Kantorovich) are obtained by solving optimization problems. Existence of the solution is easier for the Kantorovich problem. The total sizes of the source and target are assumed to be normalized to one, in general. Optimal transport is a rigorous way to get the distance between distributions.

[@jjjgrp]

Nice share. Thx pal

[@alexanderyau6347]

hi the link is not available now

[@Smatema]

@@harikannantube nice explanation. I tried to read the text but this isn't available now. Could you sent to me, please?

[@harikannantube]

@Alexander Yau, @Samuel Francisco, the article title and author are mentioned now.

[@ArmanAli-ww7ml]

Anyone who have applied this technique with simple example?

[@BobLaramee]

There are some pointers in the comments.

[@ArmanAli-ww7ml]

@@BobLaramee thanks, but can i just simply say wasserestein distance as the disimilarity cost one has to pay for any deviation?

[@asifmujtaba334]

Sorry I couldn't understand the part that the distance between two small parts of hight d_y is d.dy?Could you please clarify what am I missing? By the way, it helps a lot.Thanks.

[@BobLaramee]

Don’t rely on this video for the exact details of the computation. You can check out the paper references in the description.

[@taco9453]

Try to apply Wasserstein k means to financial market, thanks for this explanation.🙌

[@mahmudzaman9107]

Is it possible to give the explanation with an example a = (1,2,3, 4, 6, 11,18) b = (2,6, 18) c= (2,3,4) what is the earth mover distance between a,b and a,c

[@JackLe1127]

there are a lot of seagulls where you live...

[@BobLaramee]

Yes there are.

[@jay-xj1om]

What is the last song?

[@BobLaramee]

It is by Tony Levin on an obscure album called world diary

[@tejasduseja]

Hi, sorry if this sounds like a dumb question but how is the distance between two pieces is dy*d? Does distance metric is defined in such a way?

[@BobLaramee]

Hi Tejas. It's a fine question. I didn't explain the mathematics very well in the video. I would need to make a follow up video to present the mathematics better. In the meantime, you can have a look at the references made in the comments.

[@tejasduseja]

@@BobLaramee Thanks for the quick reply and for nice explanation in video ^^. It really helps students like us.

[@yehdhihanna6114]

the background sound is so anoying (can't focus)

[@BobLaramee]

It was just an experiment. My other videos have no background music.

[@marvinpeng1930]

Super amazing explanation. Thank you so much!

[@BobLaramee]

Thanks for watching.

[@jaskarankaur4971]

Am I wrong, or the music is the cliché US movies's Indian music?

[@BobLaramee]

The music is from Tony Levin's World Diary album. Not a very popular one but I really like it.

[@BobLaramee]

Where are you studying?

[@AredioVani]

Fantastic video, thank you

[@reynaldo2232]

Great explanation, thank you

[@BobLaramee]

Thanks for watching.

[@leemun41]

Greate thanks from Brazil!

[@jonathanballoch]

6:19 for the math 7:28 for the computing

[@TammyZhen]

Thank you! Great video, and a very clear explanation.

[@BobLaramee]

Thanks for watching

[@durandsinclair5338]

Thanks for your explanation. It really helped me understand things!

[@BobLaramee]

Durand Sinclair Thanks for watching.

[@lujia]

Do I need a controller for this video? Because I feel like I have to fight a final fantasy boss at some point. Besides the music great video. Btw I am reading the original paper right now and are the little boxes you drew "signatures" from the paper?

[@BobLaramee]

Yes, you need a good controller to watch these videos. Probably I should have read the papers I refer to more carefully before making the video.

[@JuliusG73]

Can Wasserstein be nondeterministic? It seems the Python implementation is giving me very similar values but there are tiny perturbations when I rerun the calculation on the same distributions.

[@BobLaramee]

I think the result will depend on the implementation. Thanks for watching

[@rahuldeora5815]

You could have added a bit more dept into this

[@BobLaramee]

True. i had no idea how much demand there is for this material. A follow-up is on my todo list.

[@rahuldeora5815]

Is there anyway I can contact you( maybe email)? I was planning on doing a research paper walkthrough(kinda like my first but not exactly) of WASSERSTEIN AUTO-ENCODERS: openreview.net/pdf?id=HkL7n1-0b This paper was named one of the top 5 papers for deep learning in 2018. My goal with these videos is to get more more familiar with research papers.

[@BobLaramee]

Sure. A skype call is also fine. My email is r.s.laramee at swansea.ac.uk. My skype name is rlaramee.

[@rahuldeora5815]

Awesome I will definitely contact you

[@shivampadmani_iisc]

I am also from Indian Institute of Science Banglore, India

[@BobLaramee]

Thanks for watching.

[@AC-dn7xp]

Is the wasserstein distance symmetric?

[@fvguerino]

Aneeshaa Chowdhry yes

[@kb777md]

Thank you

[@BobLaramee]

Thanks for watching.

[@Merajmohdkhan]

Perfect explanation ...thumps up for ur effort dude

[@BobLaramee]

thanks for watching.

[@squat200]

This is amazing. Thank you.

[@BobLaramee]

Thanks for watching.

[@sanek-kisliy]

Aweome video, thanks!

[@BobLaramee]

Thanks for watching.

[@Ferguson02871]

Well done sir thank you.

[@BobLaramee]

Thanks for watching.

[@alexanderyau6347]

You have a big cup!

[@BobLaramee]

Big cup for big mouth 😉

[@imranrashid2890]

what's with this annoying background music? I just want to learn!

[@BobLaramee]

High standards.

[@sydneystriker5355]

How is the difference between those boxes is dy *d. It was a bad decision to watch your video you just ended up confusing me

[@BobLaramee]

I agree it's not perfect

[@carlossoto7083]

save yourself some time; the real video starts around 2 minutes in

[@angelorf]

"Computing is the best subject." haha

[@MaxLevill]

Pésimo el fondooo jaja distrae mucho

[@UgurA0]

Great explanation, thanks.

[@BobLaramee]

Thanks for watching.