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Vectors - The Math of Intelligence #3

1708 ratings | 74052 views
We're going to explore why the concept of vectors is so important in machine learning. We'll talk about how they are used to represent both data and models. Get ready for some Linear Algebra! Code for this video (with challenge): https://github.com/llSourcell/Vectors_Linear_Algebra/tree/master Vishnu's Winning Code: https://github.com/Sri-Vishnu-Kumar-K/MathOfIntelligence/blob/master/second_order_optimization_newtons_method/second_order_optimization.py Hammad's Runner-up Code: https://github.com/hammadshaikhha/Math-of-Machine-Learning-Course-by-Siraj/blob/master/Newtons%20Method.ipynb Please Subscribe! And like. And comment. That's what keeps me going. More learning resources: http://mathworld.wolfram.com/VectorNorm.html http://www.math.usm.edu/lambers/mat610/sum10/lecture2.pdf https://www.youtube.com/watch?v=tXCqr2UsbWQ https://stackoverflow.com/questions/38379905/what-is-vector-in-terms-of-machine-learning http://www.chioka.in/differences-between-the-l1-norm-and-the-l2-norm-least-absolute-deviations-and-least-squares/ https://www.quora.com/What-is-the-difference-between-L1-and-L2-regularization Join us in the Wizards Slack channel: http://wizards.herokuapp.com/ And please support me on Patreon: https://www.patreon.com/user?u=3191693 Follow me: Twitter: https://twitter.com/sirajraval Facebook: https://www.facebook.com/sirajology Instagram: https://www.instagram.com/sirajraval/ Instagram: https://www.instagram.com/sirajraval/ Signup for my newsletter for exciting updates in the field of AI: https://goo.gl/FZzJ5w
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Text Comments (239)
Matthew Alviz (13 days ago)
I learned to appreciate math thanks to you @Siraj Raval, Thanks so much!
QUARAR LIMBU (19 days ago)
what d fcuk i would have been more serious in maths class if i had know that vectors & linear algebra had such huge importance & practical applications in physics & computer science!!!! fckkk i am doomed ! i feel like gng bk to skooll now.
Esm Famil (2 months ago)
i've learned soooo much from this series so far.. awesome job.. love you Siraj!
Ali Pardhan (2 months ago)
5:00 the linear algebra way is 6 operations, while algebra way is 3 operations. so Its 2 times SLOWER, not 3 times faster
Nitin Bhandari (2 months ago)
Did I just witness the best analogy for fit and overfit? Darn!
Nikhil Kumar M (2 months ago)
Marco Ascensio is pretty smart.
G V (2 months ago)
Why the hell would I want memes in my educational videos?
dave junges (2 months ago)
As a high performing Autist, it's very difficult to absorb your Humor. Danke
LuminaPursuit (2 months ago)
The gangnam style Pooh stayed in my mind the rest of the video. Great video though!
Nate (3 months ago)
He's talking like it's super easy to understand, but I have no clue what I just watch. Typical nerd.
Marco Flagg (3 months ago)
thank you so much for this video. :)
Skulltruck08 (3 months ago)
Please do not use memes when you are explaining something, it is VERY distracting.
Ajay Kumar (5 months ago)
Died laughing at 5:56 😂😂😂
omer sahban (5 months ago)
You pronounce Beijing perfectly
frankbraker (5 months ago)
This video is hilarious! Also, wow.
Grant King (5 months ago)
I really enjoyed the interpretive hand dance tensor music break.
Siraj Raval (5 months ago)
thanks for saying that. i'll do more soon
WTFJapantv (5 months ago)
I died laughing at I see vectors
Dom McKean (6 months ago)
I thought I knew what vectors were until I watched this! Twitter @dommckean
Kishore P. George (6 months ago)
Best explanation of 'word embedding'! Superb video!!
Foxy (6 months ago)
What is the source of your memes?
duckmeharder (7 months ago)
"hearth rate" - 1:13
Eric Sparkman (7 months ago)
awesome edutainment
Glauter Coelho (7 months ago)
Amazing explanation ! Congratulations
ajay sharma (7 months ago)
2:10 what he think i got it i doesn't
picsag com (7 months ago)
A very concise summary of Vectors and Linear Algebra for Machine Learning can be found at: www.picsag.com/2018/04/20/linear-algebra-for-machine-learning/
Samitha Randeniya (7 months ago)
Brother your descriptions are really really great!! keep it up.. Congrats
Jeffrey Ely (8 months ago)
1:08 What is a hearth rate lmao jk
Value Py (8 months ago)
LOL! wtf Kevin?
Eliot McLellan (9 months ago)
Emil Konstantinovitz (9 months ago)
Thumbs up for moderat
it is great keep making videos!!!
anurag mishra (9 months ago)
Who discovered vectors,was it Isaac Newton?
Shaswat Sood (10 months ago)
Awesome style
Mariel Toledo (10 months ago)
Thanks for making this video, it is awesome!
nicholas williams (11 months ago)
A vector space is a set that obeys the 8 vector space axioms. A vector is an element of that set.
Younis Mohammed (11 months ago)
Damn the way you've moved from Scalar-to-Vector by Algebra-to-Linear algebra, so Array-to-Matrix. You're a professional Educator, Siraj. Thank you very much.
Y. Aakash (1 year ago)
awesome is less for this video :D where can i find that matrix multiplication visual tool at 4:37and... you can't divide matrices :P
David P (1 year ago)
Crap you are convincing me to take the two vector calculus courses at my college. In addition to the multivariable course. Okay so which foundational papers in the field should I read and which major books for class, for amateurs and professionals.
David P (1 year ago)
Off to math on Reddit, Quara, and mathexchange forums.
TatTvamAsi (1 year ago)
Hey, I find your memes to be distracting. The one with spongbob at :50 didn't really carry the point you were making. Don't get me wrong, I love that you use memes, but I feel they should be included only to solidify the point rather than a quick joke - or after your point is made so it's not distracting.
Spandan Madan (1 year ago)
Would be great to see someone actually point out the mistakes in this video. I begin by pointing out 5:31. By reshaping your input you don't take it to a new vector space. An mXn dimensional vector space and a 1Xmn vector space are homeomorphic. Anyone want to add to this list?
Spandan Madan (1 year ago)
Adding on as I watch, 6:00 word2vec was not a single neural net. It was an ensemble of models. And no it can't learn the embedding for a new word. There's no training/testing split there. There's only an embedding.
Matthijs M (1 year ago)
Random pic of a new unlabeled eye-pic......... haha
vignesh sivakumar (1 year ago)
*Da Fuk* :O + :P = 69 lol.........😂😂😂😂😂😂😂😂😂😂😂😂😂😂😂
MrKaryerist (1 year ago)
Brilliant demo of how vectors can be used in real life. Helps me to put it in the context of my linear algebra course👍
mounika reddy (1 year ago)
hello siraj..really nice videos..I have some doubts in ML .. do u have any mail.id? to contact? .. that will be really helpfull for me.
Doctor RohitSharma (1 year ago)
I have to Pause, repeat, Pause Google, Play again, Pause, Repeat, Pause, Google, Play Again... In each Video..
Mario Delagarza (1 year ago)
7:30 xD Oh, My God, I love your videos
Alex B. (1 year ago)
What you explained: 11 minutes of precious and resourceful information What I got: :O + :P = 69
vignesh sivakumar (1 year ago)
I feel you Bro... I feel you........
Prasenjit Giri (1 year ago)
Thank you for the explanation, but one thing I'm still not clear on is how does Word2Vec finds similar words from sentences. For eg. 1. Mercedes is a German legacy 2. Honda on the other hand is pretty new 3. But nothing beats Toyota reliability In this context, how will Word2Vec get to cluster {Mercedes, Honda, Toyota} as one group - can you please help explain this. I do get calculating distance, vectorizing the position of each word and selecting the dimension randomly but how does Word2Vec works. Thank you again Siraj from a software developer.
Jie Wang (1 year ago)
Although it's just one word, I can see your Chinese mandarin pronunciation is quite good. :)
Siraj Raval (1 year ago)
+Gai Wang Xie xie
i think they get it ya we got it moving onto ...... 😂😂😂
Amit Saroj (1 year ago)
Hey SIraj what's your secret, how are you learning so fast?
jkm (8 months ago)
he has a video explaining how to speed learning.
adoniyas girma (1 year ago)
Great video siraj!your videos aren't just informative but entertaining as well, keep making them. big fan here
rpbp (1 year ago)
you are a wonderful teacher
rpbp (1 year ago)
this is an awesome explanation of math we have learned in college thanks Siraj god bless
Dean S (1 year ago)
Symetry,  your videos have a flair for more than just symbols on a chock board, excellent.
paulwillisorg (1 year ago)
Unfortunately I can't watch these videos with my 13 year old daughter because you keep saying F*#K!!!!!!!!!!!!
Siraj Raval (1 year ago)
hmm. interesting point Paul. I will keep the F word out since i am trying to reach kids. thanks
Robin Ranabhat (1 year ago)
no matter what people say about your fast paced teaching , i am in love with your style .
Philius (1 year ago)
2:58 :O + :P = 69 I see what you did there ;)
Mark Carbonaro (1 year ago)
1:20 If a hearth rate of 70 is consider healthy, I'm not sure how I'm alive. I have neither a fireplace nor a hearth.
Anis Matar (1 year ago)
Excellent but maybe if this was broken into 2 vids of 10 mins each lots of concepts would be more clearly explained.
Sri Vishnu K (1 year ago)
Hi Siraj, This is my submission to this week's contest. https://github.com/Sri-Vishnu-Kumar-K/MathOfIntelligence/tree/master/regularization_linear_regression Hope you like it. :)
Sri Vishnu K (1 year ago)
Thanks a lot Siraj :)
Siraj Raval (1 year ago)
vishnu great work here!
Ogunleye Pius (1 year ago)
thank you so much for this
Dan Peci (1 year ago)
Siraj, I jumped into Deep Learning about a year ago and am a huge fan of your videos; this would have been a fantastic resource when I first started out and I think it's so cool that you're taking the time to get through the foundational stuff so everyone can enjoy your other, awesome videos! Thanks :)
Siraj Raval (1 year ago)
Carson McManus (1 year ago)
It's a weird feeling to cringe and learn at the same time.
Carson McManus (1 year ago)
the random winnie the pooh dancing and you talking to Elon Musk
Siraj Raval (1 year ago)
which part was the cringiest? Love any feedback thanks :)
Param Bhavsar (1 year ago)
hey siraj,this is my submission for this week coding challenge https://github.com/param087/the_math_of_intelligence_week3_challenge/blob/master/demo.ipynb
Mitch Spano (1 year ago)
siraj, what do you do professionally? I'm curious because I have a bachelor of science in mathematics, and a masters of science in software engineering and have been working as a salesforce.com developer/architect. I miss the mathematics side of software, and love the content of your videos, maybe I should find my way into your field...
hammad shaikh (1 year ago)
Siraj, this is my homework submission for this week. My jupyter notebook illustrates how using L2 regularization reduces overfitting of high degree polynomials in the context of linear regression. https://github.com/hammadshaikhha/Math-of-Machine-Learning-Course-by-Siraj/tree/master/Regularization%20in%20Linear%20Regression
hammad shaikh (1 year ago)
Thanks Siraj, I will try my best to keep up with this course. Keep these nice quality videos coming!
Siraj Raval (1 year ago)
great job Hammad
Rajdeep Purkayastha (1 year ago)
can we implement tensor concept in java ? I am asking because Java includes "Vector class".
Tejas Chandrasekar (1 year ago)
Awesome vid Siraj. One question - at 8:56 when you show the 4 types of norms, is there a norm that you recommend developers should use most often? Or does it depend on the type of ML model you're building?
Benjamin Akera (1 year ago)
Hey Siraj, please consider making a video on Object detection, the deep learning approach perharps with Fast-RCNN, YOLO, SSD or The tensorflow object detection API..please....
AnteConfig (1 year ago)
whoa, you said "also useful for preventing overfitting" and I realized I needed to take notes. I'm glad I stumbled upon your youtube videos sir.
WBits Me (1 year ago)
pls remove the f bombs... it doesn't serve any purpose other than limiting and alienating your viewers
Daniel Dick (1 month ago)
What purpose does vulgarity have but to exclude people who are offended by it? Should one use racist terms to exclude people of a color or nationality? Should one use hateful terms toward various religions to exclude them? About 60 or so years ago, my mom took an English course at a local community college and found that the professor's language was full of genitalia and cursing and dirty jokes. Then when the final day came to drop the course or stay, he said, "Good. Now that we have gotten rid of all the Christians, we can get down to business." What if he had said, "Good. Now that we have gotten rid of all the black people or Mexicans or Jews or Homosexuals or Muslims..."? If we were in Hitler's Germany, people would likely defend this stand. Today we seem to feel we have matured and outgrown the nonsense of racism and bigotry. And yet in some situations bigotry seems merely redirected rather than eliminated. In a sense, one might feel that asking that people abstain from vulgarity is more like a single religion imposing its values onto society, such as Muslims forcing women of all religions to wear head coverings or Sikhs forcing all to wear turbins and carry the small religious knife they carry and so on. But the offense vulgarity brings is not limited to one religion, it comes across as a staking of a claim of ones right to offend anyone of their choosing or to offend all except those who chime in and agree. It is almost a symbol of their own religion--the atheist's turbin or the Unitarian's cross. And then the rest of us are expected to be open minded or tolerant and not exclude those who use such seemingly unnecessary vulgarity. And yet to those who use this vulgarity, the prohibition against it seems so arbitrary. To some it may seem better to inoculate the world of its offense by using vulgarity often. But if it is benevolent to do this, then why wouldn't it also be benevolent to use racist or "homophobic" terms to inoculate people from the sting of that terminology? Maybe we should take into consideration what the terms actually mean and use them for their intended purpose. For instance, the f word for fornication, the s word for defecation, and then you wouldn't have such nonsense as fornicating phones or envelopes which are supposedly cursed by God as if they had committed a grave injustice. I think we all have a good grasp of how ridiculous most vulgarity is and how the words used are not there to communicate any sensible meaning but rather to ad offensiveness to the language whether as a weak attempt to add emphasis or whether to promote a sense of bigotry against those offended by it and perhaps unity with other like minded bigots who hate those offended by that language. Perhaps that's harsh. But perhaps the harshness is in that it justly, honestly, and fairly calls for clarification of the motives behind the use of gratuitous or unnecessary or meaningless vulgarity.
hammad shaikh (1 year ago)
I agree with this comment, mainly because I think Siraj unique style of teaching can make teenagers interested into data science. It might make it difficult for high school teachers to recommend these videos because of inappropriate language.
Siraj Raval (1 year ago)
hmm ok. thanks for the feedback!
Hi, I have a general query. Which algorithm is good to detect anomaly neural network or multi variable linear method ?
you speak mandarin?
JAI SHAH (1 year ago)
Hey Siraj can you take a video on this paper : https://cs.stanford.edu/people/karpathy/cvpr2015.pdf ... Generating description from images
Julio argumedo (1 year ago)
Moderat :3
Sarath T S (1 year ago)
Awesome man.., (y)
Pratik Gujral (1 year ago)
That's too much of information to digest at once.
Chase Graham (1 year ago)
Siraj, you sound like a human. It's weird. XD Really though your pacing is perfect. Also, what's that music at 3:02?
Jean-Jacques de Balzac (11 months ago)
Mr Crash (1 year ago)
So how does matrix multiplication work programmaticly in numpy? I thought matrix multiplication is done the algebraic way in a loop like you showed in the algebra example and numpy is just faster because its doing its looping calculations in C. (4:52)
Siraj Raval (1 year ago)
will explain this in-depth next week promise
bitcoinmeetups (1 year ago)
Loved this video. Very interesting subject. It reminds me of stuff I have been thinking about myself independently for years. Thank you Siraj, this video was great.
Siraj Raval (1 year ago)
dope np
Yamaa Oh (1 year ago)
hi can you answer this for me sir? 😶 " given the line x+3y+5=0 and a circle x^2+y^2-6x-4y+3=0 find the equation of the tangent to the circle which are parallel."
alemmat (1 year ago)
very good videos Siraj you are the best
AE (1 year ago)
Linear algebra, vectorization, word2vec, cost functions, gradient descent, TPUs, tensorflow, tensorboard, neural networks, vector norms, regularization, and feature vectors in 11 minutes!!
Mikhail Angela (1 year ago)
Just found Welch Labs on youtube as another spot for good youtube videos on introducing ml, you guys should collab
Aidan Gomez (1 year ago)
GREAT visuals and production and perfect explanation. you just keep getting better at this.
Aidan Gomez (1 year ago)
Siraj Raval 🅱️🅱️🅱️🅱️🅱️🅱️
Siraj Raval (1 year ago)
thanks Aidan for following my progress
Paula M (1 year ago)
what horoscope are you?
Siraj Raval (1 year ago)
Valentin Ganchev (1 year ago)
Too many memes, which distract from the core topic of the video. While I appreciate your deep knowledge into the meme ecology and your grasp of the matter, I'd prefer them to be less in the future.
Siraj Raval (1 year ago)
thanks for the feedback
Sayak Paul (1 year ago)
This video is really powerful, very well put.
Le fyziks guise (1 year ago)
A vector is simply a multidimensional value. That is all. We are so used to giving things singular values that the concept of assinging a... Thing that has more than one number seems strange. But that's how it is. That's literally all there is to vectors. Once you understand that, vector concepts will become clear. This video overcomplicates things.
Siraj Raval (1 year ago)
hmmm. sure ok, good point actually. will remember this
Maike Fischer (1 year ago)
You are so cute when you explain stuffff 😜
Siraj Raval (1 year ago)
thanks so sweetu
matthew cooper (1 year ago)
Hey Siraj! How come no vim? :( Also please make a behind the scenes so we can see how you edit and make these vids.
bitcoinmeetups (1 year ago)
I also wonder what tools are used for all the background graphics and stuff.
Larry Lawrence (1 year ago)
thank you for math and intelligence video
Luan Brito (1 year ago)
Why Python is used to do this? It isn't slower than other languages?
Luan Brito (1 year ago)
Eduardo Rasgado yeah, I am in the first period of mechatronic engineering and I only had a introduction on programming.
Eduardo Rasgado (1 year ago)
Luan Brito i think you have to take some time to read more about the topic. there are huge good things about python such as another lenguajes like C.
Ong Jia Rui (1 year ago)
Hi Siraj, here's my code for this week's challenge: https://github.com/jrios6/Math-of-Intelligence/tree/master/3-Regularization
Ong Jia Rui (1 year ago)
Thanks! You can work on improving it by trying a polynomial function (: then we can show it to the white house together
hammad shaikh (1 year ago)
Solid work, I liked the application to global warming. I wonder if 98% of the data scientists agree with the rise in global temperatures?
Swanand Kulkarni (1 year ago)
Really nice code. Explanation is great as well.
Sem Shimla (1 year ago)
what the fuck kevin? auuw
ayush sharma (1 year ago)
2:09 that was epic"stop they get it".
hammad shaikh (1 year ago)
Great video Siraj, high quality content! I think you might need to update the syllabus on github because it says week 3 is K-means clustering algorithm. Also I reorganized my github repository so it has a folder for each week for this course so the runners up link in your description wont work anymore. The new link to the runners-up code should now be: https://github.com/hammadshaikhha/Math-of-Machine-Learning-Course-by-Siraj/blob/master/Newtons%20Method%20for%20Optimization/Newtons%20Method.ipynb
Jake Roosenbloom (1 year ago)
Amazing!! The audio was the best on any video yet. Thanks for making this :')
Siraj Raval (1 year ago)
thanks Jake
Frenchpet (1 year ago)
tfw no qt ai gf

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