Singular Value Decomposition (SVD) and Image Compression

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In this video, we learn a very useful matrix trick called singular value decomposition (SVD), in which we express a matrix as a product of two rotation matrices and one scaling matrix.
We also show a very interesting application to image compression.
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Introduction: (0:00)
Transformations: (0:50)
A puzzle: (1:27)
A harder puzzle: (2:21)
Linear transformations: (3:50)
Dimensionality reduction: (10:50)
Image compression: (23:57)

[@AhmadBazzi]

Best explanation on SVDs. Keep it up Luis !!

[@SerranoAcademy]

Thanks Ahmad, coming from a top youtuber like you, this is great praise!

[@debashisghosh3133]

I must admit one of the simplest and efficient explanation of SVD. Loved it.

[@sampadmohanty8573]

I cannot express my happiness enough. You are inspiring many and I am going to strive to do as much as I can to make my students understand. True teachers are underappreciated. Much love.

[@rohitekka2674]

This is the most crisp, lucid, and downright amazing explanation of the concept with demonstration. I could make out the efforts you have taken in designing this video, answering every detail of the concept and covering all possible scenarios every step of the way. You're hands down brilliant, thank you for this creation!!

[@hessame9496]

This is the definition of perfect! I can't imagine anyone can explain these concepts better than him! Really appreciate it!

[@soonbinlee4049]

This is literally amazing. Please keep your work.

[@debarchanbasu768]

Luis, you are a freakin’ genius 💜 There’s no way someone would not be able to understand any math concept if taught in such a lucid way. Sir, it’s a humble request from my side (and I’m sure a lot of others would agree with me) to create an ordered playlist on math for machine learning, it’d be of great help!

[@SerranoAcademy]

Thank you Debarchan! I have some playlists on the front page of the channel (kzbin.info), on supervised/unsupervised learning, probability, etc. Also, I organized all the videos into topics here: serrano.academy. Let me know if they help, or if you have any different suggestions. Cheers!

[@bharathbhimshetty8926]

@@SerranoAcademy Nice

[@willw4096]

Much agreed. He's a genius!

[@anderslindstrom1575]

BRAVO! If anyone of you viewers wonder what "disruption" looks like when it comes to technology and business models, this video is a perfect example. If we just narrow it down to getting the knowledge of, say SVD, then why on earth would anyone pay a tuition fee, commute for hours or relocate, to sit in front of a mediocre "teacher" who do not have the interest or pedagogical skills to teach (we have all had these "teachers" and it sucks! Is that not why you are here?!?!), when you can watch a video of this quality with prefect explanations and examples at the comfort of your home as many times as you want for free(*)??? Eventually no one will!!! Education is truly democratized one video at a time...

[@muskangupta7058]

Thank You Luis Serrano for making such concepts very easy to understand.

[@user-wr4yl7tx3w]

This is the best presentation on SVD ever seen.

[@askfskpsk]

This is truly an awesome tutorial. Thanks Luis!

[@andrewchen7710]

So comprehensive yet always to the point. Amazing quality. My professor mentioned in passing that the Mars rovers perform SVD and only select the first few largest singular values to send back and you explained perfectly why this works!

[@shreesjourney4772]

That's a great explanatory video. Thank you for making it crystal clear.

[@user-or7ji5hv8y]

Wow! This is the most clear explanation on SVD.

[@Alexsemers]

I have been struggling with the concept of SVD for months and now I finally get it with this clear and friendly tutorial. Thank you!

[@korean4130]

I particularly love your explanation for image compression...just amazing! Thanks much!

[@bhaskarroy8753]

Excellent explanation Luis. Thank you very much.

[@okeuwechue9238]

Probably the best explanation of the SVD technique that I've seen so far. Good job!

[@suprabhatkumar151]

Hands down, the best video ever for svd. Thank you so much, Sir.

[@Satvikshukla0007]

You have saved me man, I had a presentation tomorrow on SVD, and now I have got everything that I need to know.

[@SM-xn9bv]

Indeed amazing demonstration of complex things!

[@wahabfiles6260]

You are most amazing person that know how to teach to make it intuitive.

[@HACKINGMADEFUN]

My professor taught this in class and I was like what is the use of this. After watching this, I realised how fascinating this stuff is. Thanks a lot for making this. Shared with my friends.

[@derjansan9564]

The first half of the video is one of the best intruductions on SVD that I could find so far. Thank you so much.

[@xiluo8714]

This video is the most intuitive way of explaining the svd, thanks!

[@firstkaransingh]

Wow.... You took a very complex topic and turned it easy-peasy. Thank you.

[@mayurgite4050]

Thank you so much for making SVD simpler, loved it,

[@jameslaurie6300]

I've watched several videos trying to explain what linear transformations are and this one hit home for me...thank you!

[@shantanubapat6937]

One of the finest explanation of singular value decomposition. Thank you!

[@baurks]

This is hands down the best explanation of SVD on the internet. Thank you

[@MrZidane1128]

By far this is the most clear explanation about SVD ! Greatly appreciate your work and efforts

[@chrysanthi6562]

Having to compose a mathematical essay about the usage of SVD in image compression, without having been taught about the concept of linear algebra, I had to look for appropriate sources that would help me understand the theory. After hours of online research I managed to find your video and I have to admit that I'm impressed. Your analysis is both thorough and comprehensive in the simplest way possible. Thank you so much for your help! Keep up the good work!

[@nzambabignoumba445]

Mr. Luis Serrano you are the BEST.

[@tyrelhess6605]

This explanation was absolutely amazing. Thank you so much for your help!

[@HazemAzim]

Best Explanation for intuition underlying SVDs

[@sherkoalamer538]

Awesome awesome awesome illustration. Thank you, you made the idea very clear and simple

[@shamshersingh9680]

By far the best explanation I have seen for SVD. It could not be better than this. Thanks a lot Luis for this excellent video.

[@ricardoraymond9037]

Amazing! All so plain and simple to see and understand the full concept of ML.

[@ulugbekdjuraev3833]

Thank you very much for such a nice and simple-to-understand explaintion!

[@CanDoSo_org]

Wow, you explained SVD in such a nice and clear manner! Love it. Thank you so much.

[@isaacjohnson8752]

You did a phenomenal job on this concept and video! This is the best explanation I have seen as to why we can drop smaller singular values and end up with a reasonable approximation!

[@kumarvis01]

One of the best explanation for SVD .. To good.

[@harperbye]

One of the best and simple explanation of svd, thank u!

[@beketmyrzanov1979]

Luis, you are a talented teacher. Thank you for this great explanation!

[@vicentevivanco77]

This explanation is genius. After watching a few videos on the subject, I got to this one and wow, everything I just saw made sense. A few people have this talent, and it’s awesome that you’re helping others with it. Keep up with your content!

[@ishitharajapakse9675]

Best video in KZbin about SVD. Need more ML related videos. Keep it up :)

[@googlesong8679]

this is the best explanation on SVD ive seen thank you! you really explain the logic behind it well

[@tpz1474]

Easily the best explanation on youtube by far - I've been going all over trying to understand what SVD actually means. This video provided that and so much more, will catch your other videos and hopefully they're as good!

[@NinadDaithankar5]

This is extraordinary! Thanks a lot for simplifying the visual intuition behind SVD so clearly.

[@kmrudula777]

Such a detailed video. Many thanks for sharing!

[@604_jassimshaji8]

I'm so happy to finally find you....the best...it was like you were answering my questions while I'm asking you in a live...hoping for more similar videos ❤️

[@recepyldrm3608]

I've spent 3 hours finding this amazingly clear explanation instead of studying messy course notes and it worthed it:) Thank you, Mr. Serrano.

[@vijaymaraviya9443]

Excellent. crisp and comprehensive👌

[@ssitakiran]

You are one of the best teachers i have ever come across. Please keep helping people like me with awesome explanations. May god bless you !

[@piyukr]

This is the best, the best, the best explanation of SVD, image compression I could find on youtube. Thank you so much Mr. Serrano!

[@TheWaWeL37]

Great video, it's really nice to see that kind of explanation out there :) Keep it up

[@SC-ss8vb]

By far the best SVD explanation!

[@mikee8785]

Thank you sir for simplifying the depth of topic with such visuals under 30 mins 🙏. Now I have practical intuition of SVD

[@bm-ub6zc]

This IS the best explanation of ANYTHING (no matter what field, what topic) I've ever got in my life about something. Incredibly visual didactic style. Grandioso!

[@grjesus9979]

Wow! Seriusly this is perfect! You go direct to the root of it. Thank you a lot for making it easy to understand 😀😀

[@mosammatarifaakther2304]

Thanks a lot, Luis. It's very easy to understand the content and I love it.

[@achyuthvishwamithra]

One of the best explanations ever!

[@hardikrajpal2410]

This video deserves more recognition!

[@salmabarakat9457]

Thank you so much, i have been struggling to understand SVD and finally I understood it well.

[@user-or7ji5hv8y]

This is pretty amazing explanation. So insightful.

[@kiranchowdary8100]

World needs more people like you.

[@dragon5038]

So informative and easy to follow. I love this. Thank you so much for taking the time to create this video. It's so important to know how the concepts we learn in class can be applied in real life. This has changed everything for me. Thank you again.

[@devchandan6161]

Your video made help us made our entire presentation for college - Thanks a tonne!

[@user-wb5wd2rs2h]

great video on SVD, helped me understand the concept really well, thank you very much 🙏

[@saurabhsinha2026]

Amazing explanation. Thank you so much Luis.

[@shenge5347]

Just found your channel. I need to understand SVD for my work and this is great.

[@siyizheng8560]

This video is so amazing and I finally understood SVD! Thank you so much!

[@emsdy6741]

Thank you so much this. I am really happy I found your channel. I have been struggling to understand SVD.

[@Laura-xd6ry]

Thank you ! You´re explaining this concept in such a perfect way with so many good examples and visiuals. Keep up the good work :)

[@ishaantonk159]

i have been finding study material to learn SVD and in this journey I went through several PDFs, slides and few books but this video is the best and crisp explanation of this algorithm. Thanks!

[@trianaprietogalvan5881]

The best visual explanation of SVD.

[@fgh680]

Thank you, Mr. Luis Serrano. Much appreciated: the entire effort to put out the video with so much dexterity...AWESOME!!

[@SerranoAcademy]

Thank you Viswapriya!

[@aeonsalgado4329]

El mejor video de la vida para entendelo todo! SVD y PCA los aprendi gracias a los videos de este canal. Muchas Gracias.

[@mahimanzum]

this was an awesome explanation. please do more of these . thanks a lot. please do one on Independent Component Analysis (ICA)

[@iJamesGuo]

Wow! Great explanation on SVD! Thank you!

[@RajeshSharma-bd5zo]

A big thank you for such a great explanation

[@its_me7363]

I really love the way you explain these Maths topics which I never understand in Linear Algebra classes as theory but here I got in this one video with clear visualization and moreover we can always follow in python code which is really cool to see. Thanks for effort and time for strangers like me. Just Keep going.

[@mathman1475]

Thanks for the video. It is an excellent explanation of SVD and image compression.

[@prashant381]

Absolutely brilliant. My brain absorbed it like a sponge. Will buy the book. Looks just fine for application without assuming any background

[@Saikumar-yamjala]

Wow! Now this topic is so clear for me, thank you.

[@jorovifi89]

What a great content, very much appreciated. Thank you

[@cagatay6259]

The best explanation of svd ever !

[@samaustin7952]

This video was amazing! Best explanation of the SVD I've seen so far.

[@electric_sand]

After searching for this topic, I had a list of videos to choose from, then I remembered the great explanations I had gotten from this channel, so I selected this video... wasn't disappointed.

[@souravdey1227]

Sheer brilliance. Your clarity of thought is mind bending. Luis serrano, statquest, ritvickmath, krish naik and codebasics - this is pretty much my holy grail for datascience

[@shahryarhabibi7187]

Very well explained! please upload some practical videos including coding as well.

[@arminkashani5695]

Excellent explanation! Thank you so much for the great video.

[@nagadevisanthanakrishnan3070]

Wow .it's so crazy and the mathematics representation was expressed in the pictorial representation of the beginning of this video is so awesome...keep rocking

[@scapri1000]

Amazing explanation. Thank you so much

[@AshishRanjan-jn7re]

Wow... Much much better than any book or professor's explanation..

[@generationgap416]

You are Democratizing quality technical education and making it accessible to all.

[@stefanm2864]

Pretty cool! I forgot a lot of my math studies in the last year, but your explenations were so precisely, but also simple that I understood nearly everything. Thank you (and sorry for my bad english :-) )

[@mfatihaydogdu7]

Perfect explanation, thank you.

[@astaragmohapatra9]

This video is great and clear explanation.

[@susmitislam1910]

You're an excellent teacher, Luis. Can't thank you enough for the amazing explanations for these hard-to-grasp concepts. Hope you and your family are doing well during this pandemic.

[@SerranoAcademy]

Thank you! Hope you and your family are well too!

[@nazniamul]

Brilliant explanation. Great work. keep it up.