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Ali Ghodsi, Lec 1: Principal Component Analysis 

Data Science Courses
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29 окт 2024

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Комментарии : 169   
@muhammadsarimmehdi
@muhammadsarimmehdi 5 лет назад
I seriously hope he teaches a lot more machine learning and those lectures get published here. He is the only teacher I found who actually dives into the math behind machine learning.
@logicboard7746
@logicboard7746 3 года назад
Agreed
@alizain16
@alizain16 2 года назад
Tou directly Statistics k professors k lecture bhi le sakty ho.
@ElKora1998
@ElKora1998 Год назад
This guy owns Databricks now, the biggest ai start up in the world. He isn’t coming back anytime soon sadly 😂
@andrewmills7292
@andrewmills7292 Год назад
@@ElKora1998 Not the same person
@ElKora1998
@ElKora1998 Год назад
@@andrewmills7292 you sure? He looks identical!
@rizwanmuhammad6468
@rizwanmuhammad6468 4 года назад
He is certainly at a level that makes you understand. Best teacher. No show off , no hand waving. Genuine teacher. Goal is to teach . Thanks you thank you
@andresrossi9
@andresrossi9 4 года назад
This professor is amazing. I'm italian so it's more difficult to follow a lesson in english than in my language. Well, it was much much easier to understand PCA here for me than in any other PCA lesson or paper in italian. And not only, but he gave a more rigorous explanation too! Outstanding, really...
@pantelispapageorgiou4519
@pantelispapageorgiou4519 3 года назад
No words to describe the greatness of this professor!
@shashanksagarjha2807
@shashanksagarjha2807 6 лет назад
If you were to take my opinion, his videos are best one on ml and deep learning on youtube
@VahidOnTheMove
@VahidOnTheMove 5 лет назад
I agree. Watch 21:00. The student repating the answer is the eigen value and the eignen vector, and the intructor says Ok this is correct but why!? In most videos on youtube I have seen, people who pretend to be expert do not know (or do not say) the logic behind their claims.
@muratcan__22
@muratcan__22 5 лет назад
@@VahidOnTheMove exactly
@nazhou7073
@nazhou7073 5 лет назад
I agree!
@leeris19
@leeris19 2 месяца назад
This is what i've been looking for! Every explanation out there just contains more question. "Get the covariance" What for ? "Do decomposition" Why ? "Use eigen vectors" Huh ??. Thank you for explaining every question I have!
@anirudhthatipelli8765
@anirudhthatipelli8765 Год назад
Thanks, this is by far the most detailed explanations of PCA
@joshi98kishan
@joshi98kishan 5 месяцев назад
Thank you professor. This lecture explains exactly what I was looking for - why principal components are the eigenvectors of the sample covariance matrix.
@ayushmittal1287
@ayushmittal1287 2 года назад
Teachers like him make more people fall in love with the topic.
@YouUndeground
@YouUndeground 4 года назад
This is the best video about this subject, including the math behind it, that I've found so far.
@Entilema
@Entilema 6 лет назад
thank you so much! I tried to see the same topic in other videos and was impossible to understand, this is so clear, ordered and intuitively explain, awesome lecturer!
@MoAlian
@MoAlian 7 лет назад
I'd won a Fields medal if I had a professor like this guy in my undergrad.
@crazyme1266
@crazyme1266 6 лет назад
i think you can do that right now... age is just a number when it comes to learning and creating :D
@pubudukumarage3545
@pubudukumarage3545 6 лет назад
Crazy || ME :) only if you are not older than 40...fields medal is given for
@crazyme1266
@crazyme1266 6 лет назад
@@pubudukumarage3545 oh thanks for the information.... I didn't knew that.... Guess I really am kinda crazy huh?? XD
@slowcummer
@slowcummer 3 года назад
Yeah, a Garfield the cat medal I'm sure you can win. Just give him Lasagne.
@godfreypigott
@godfreypigott 3 года назад
Clearly you would not have won a medal for your English ability.
@najme9315
@najme9315 2 года назад
Iranian Professors are fantastic! and Prof. Ali Ghodsi is one of them
@mu11668B
@mu11668B 3 года назад
Wow. This IS what I'm looking for!! Thank you SO much! BTW the explanation for 20:21 is simple if you already have some experience of manipulating with linear algebra. Just decompose the matrix S into EΛ(E^-1) and the sum will turn into sum of ratios of eigenvalues, with the ratios sum up to 1. (assume that the data are already standardized, which is crucial.) Thus you have to put the ratio of corresponding eigenvector to 1 to get the max sum, which is the maximum eigenvalue.
@هشامأبوسارة-ن7و
@هشامأبوسارة-ن7و 5 лет назад
Good lecture. PCA tries to find the direction in the space, namely a vector, that maximises the variance of the projected points or observations on that vector. Once the above method finds the 1st principal component, the second component is the vector orthogonal to the first component.
@vamsikrishnakodumurumeesal1324
@vamsikrishnakodumurumeesal1324 4 года назад
By far, the best video on PCA
@usf5914
@usf5914 4 года назад
know we see teacher with clear and open mind
@alpinebutterfly8710
@alpinebutterfly8710 2 года назад
This lecture is amazing, your student are extremely lucky ...
@김성주-h1b
@김성주-h1b 3 года назад
This is the best pca explanation I've ever seen!! 👍👍
@jaivratsingh9966
@jaivratsingh9966 6 лет назад
Dear Prof, at 28:46 you say that tangent of f and tangent of g are parallel to each other - possibly you meant to say that gradient ie normal of f and normal of g are parallel to each other. Anyways it effectively means the same thing. Excellent video!
@ferensao
@ferensao 4 года назад
This is a great tutorial video, I could grasp the idea behind PCA with easy and clear thoughts.
@jeffreyzhuang4395
@jeffreyzhuang4395 Год назад
43:03 The entries in Σ are not eigenvalues of A transpose A, but square roots of eigenvalues of A transpose A.
@zhaoxiao2002
@zhaoxiao2002 2 года назад
At time 1:03:26, [U, D, V] = svd (X). Question: shall we do svd(X - E(X)), since X contain pixel values in [0, 255] and the data points X is not centered to E(X)?
@hassanebouzahir2653
@hassanebouzahir2653 12 дней назад
3:30 We can always reduce the dimensionality of the features by projecting them onto an optimal subspace.
@kamilazdybal
@kamilazdybal 5 лет назад
Great lecture! Tip to the camera person: there's no need to zoom in on the powerpoint. The slides were perfectly readable even when they were at 50% of the video area but it is much better to see the lecturer and the slide at the same time. Personally, it makes me feel more engaged with the lecture than just seeing a full-screen slide and hearing the lecturer's voice.
@xuerobert5336
@xuerobert5336 6 лет назад
This series of videos are so great!​
@srishtibhardwaj400
@srishtibhardwaj400 6 лет назад
That was an amazing lecture Sir! Thank you!
@rbr951
@rbr951 6 лет назад
Wonderful lecture thats both intutive as well as mathematically excellent.
@muratcan__22
@muratcan__22 5 лет назад
everything is explained crystal clear. thanks!
@sudn3682
@sudn3682 6 лет назад
Man, this is pure gold!!
@alirezasoleimani2524
@alirezasoleimani2524 Год назад
Amazing lecture. I really enjoyed every single second ....
@oguzvuruskaner6341
@oguzvuruskaner6341 4 года назад
There is more mathematics in this video than a data science curriculum.
@suhaibkamal9481
@suhaibkamal9481 4 года назад
not a fan of learning through youtube videos , but this was an excellent lecture
@slowcummer
@slowcummer 3 года назад
He's an astute mathematician with virtuoso teaching skills.
@josephkomolgorov651
@josephkomolgorov651 3 года назад
Best lecture on PCA!
@NirajKumar-hq2rj
@NirajKumar-hq2rj 3 года назад
Around 44:50 , u explained M as set of mean values of x_i data points, shouldn’t mean (xi) = 1/d rather than 1/n *sum of xi over i = 1 to d
@YashMRSawant
@YashMRSawant 5 лет назад
Sir I have one question @1:01:50. If I had only one face image with each pixel distribution independent of other but mean corresponds to original face value at that pixel. I think first, second and so on PCs are noise dominant and we are still able to see the face.?
@purushottammishra3423
@purushottammishra3423 5 месяцев назад
I got answers to almost every"WHY?" that I had while reading books.
@qasimahmad6714
@qasimahmad6714 3 года назад
Is it important to show 95% confidence ellipse in PCA? why it is so? If my data is not drawing it then what should i do ? can i used PCA score graph without 95% confidence ellipse?
@abdelkrimmaarir5104
@abdelkrimmaarir5104 4 месяца назад
Thank you for this lecture. Where can we find the dataset used for the noisy faces?
@haideralishuvo4781
@haideralishuvo4781 3 года назад
Amazing lecture , Fabulous
@Amulya7
@Amulya7 2 года назад
43:20, aren't they the square roots of eigenvalues of XTX or XXT?
@ksjksjgg
@ksjksjgg 2 года назад
concise and clear explanation
@ardeshirmoinian
@ardeshirmoinian 4 года назад
so using SVD is it correct to say that columns of U are similar to PC loadings (eigenvalue scaled eigenvectors) and V is the scores matrix?
@GebzNotJebz
@GebzNotJebz 4 месяца назад
Amazing lecture
@yuanhua88
@yuanhua88 4 года назад
best video about pca math thanks
@chaoyufeng9927
@chaoyufeng9927 5 лет назад
it's amazing and it really made me understand clearly!!!!!!!!!
@streeetwall3824
@streeetwall3824 6 лет назад
Thank you prof Ghodsi, very helpful
@asmaalsharif358
@asmaalsharif358 5 лет назад
thanks for this explanition.please how can i contact with you?i have inquiry
@bhrftm5178
@bhrftm5178 4 года назад
دم شما گرم. عالی بود.
@lmurdock1250
@lmurdock1250 4 года назад
mind blown in the first two minutes
@debayondharchowdhury2680
@debayondharchowdhury2680 5 лет назад
This is Gold.
@fish-nature-lover
@fish-nature-lover 7 лет назад
Great lecture Dr. Ali...Thanks a lot
@iOSGamingDynasties
@iOSGamingDynasties 3 года назад
Great video! Really nice explanation
@lavanya7339
@lavanya7339 3 года назад
wow....great lecture
@bhomiktakhar8226
@bhomiktakhar8226 3 года назад
Oh what an explanation!!
@MSalman1
@MSalman1 3 года назад
Excellent explanation!!
@godfreypigott
@godfreypigott 3 года назад
Why has lecture 3 been deleted? How do we watch it?
@husamatalla8912
@husamatalla8912 7 лет назад
ALL Thanks Dr.Ali
@mariasargsyan5170
@mariasargsyan5170 5 лет назад
he is great
@ayouyayt7389
@ayouyayt7389 2 года назад
At 17:25 sigma should be sigma squared to call it variance if not we say standard deviation.
@jimm9465
@jimm9465 6 лет назад
the best ever, thanks!
@PradeepKumar-tl7dd
@PradeepKumar-tl7dd 7 месяцев назад
best video oh PCA
@rajeshreddy3133
@rajeshreddy3133 4 года назад
Amazing lecture..
@Dev-rd9gk
@Dev-rd9gk 6 лет назад
Amazing lecture!
@kheireddinechafaa6075
@kheireddinechafaa6075 3 года назад
at 18:03 I think "a square times sigma square" not sigma?
@alexyakyma1479
@alexyakyma1479 3 года назад
Good lecture. Thank you.
@obsiyoutube4828
@obsiyoutube4828 5 лет назад
We need code and application areas of PCA?
@Rk40295
@Rk40295 2 года назад
بالتوفيق ان شاء الله
@msrasras
@msrasras 6 лет назад
Great lecture, thank you sir
@bodwiser100
@bodwiser100 2 года назад
Awesome!
@monalisapal6586
@monalisapal6586 3 года назад
Can I find the slides online ?
@yuanhua88
@yuanhua88 4 года назад
great lecture thanks!!!
@Anil-vf6ed
@Anil-vf6ed 7 лет назад
Dear Prof, Thanks for the lecture. Is it possible to share the lecture materials? Thank you!
@bosepukur
@bosepukur 6 лет назад
excellent lecture
@mayankkhanna9644
@mayankkhanna9644 3 года назад
how??? How is the variance of the projected data = u^(T)SU
@mayankkhanna9644
@mayankkhanna9644 3 года назад
Got it
@venkatk1591
@venkatk1591 3 года назад
I am not clear on this .can you explain
@mayankkhanna3284
@mayankkhanna3284 3 года назад
@@venkatk1591 you can see the explanation here - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WpYoKsWKS7w.html
@aravindanbenjamin4766
@aravindanbenjamin4766 3 года назад
Does anyone know the proof for the second pc ?
@rabeekhrmashow9195
@rabeekhrmashow9195 4 года назад
Thank you it’s fist time I understand PC but I am studying master financial mathematics sorry I just want to do every step manual is that possible
@ProfessionalTycoons
@ProfessionalTycoons 6 лет назад
AMAZING!
@BelkacemKADRI-u6d
@BelkacemKADRI-u6d 10 месяцев назад
c'est un grand
@betterclever
@betterclever 6 лет назад
Lecture is great but that struggle to find image size though.
@mojtabafazli6846
@mojtabafazli6846 6 лет назад
Thats great , can we have access to that noisy dataset ?
@abhilashsharma1992
@abhilashsharma1992 4 года назад
at 19:32 why is var (u_1 transpose x)=u__1 transpose s u)
@khubaibraza8446
@khubaibraza8446 4 года назад
S is just a notation. S is covariance matrix of original matrix X , u1 is constant(We can say) . In variance constant become square but in the case of vectors form you write u1 u1_transpose. final expresssion is u1 X u1_transpose
@CTT36544
@CTT36544 5 лет назад
1:14 Be careful that this example is not that proper. Note that PCA is basically a system for axis rotation and hence it usually does not have good applications for those data with "donut" (or, swiss roll) structure. A better way is either to use kernel PCA or MVU (maximum variance unfold).
@YashMRSawant
@YashMRSawant 5 лет назад
I think this is not about PCA but the fact that distributions in higher dimensions can be projected to lower dimensions such that there is one to one correspondence between higher dimensional and lower dimension counterparts as much as possible.
@anilcelik16
@anilcelik16 3 года назад
He already mentions that, the assumption is that the data is aligned close to a plane like a paper
@rampage14x13
@rampage14x13 5 лет назад
Around 22:00 can someone explain why the function is quadratic?
@yannavok7901
@yannavok7901 5 лет назад
t=transpose ^2= square This function is quadratic because of u and ut: Quadratic function for one variable has the following form : ax^2 + bx + c Quadratic function for two variables has the following form ax^2 + bxy + cy^2 + dx + ey + g Let's consider an example: 1- Suppose vector u=[x1] [x2] then ut = [x1 x2] matrix S=[1/2 -1] [-1/2 1] 2- ut S gives us the following vector: ut S = [ 1/2*x1-1/2*x2] [ -x1 + x2 ] 3- ut S u gives the following function which will be a scalar if the vector u is known: ut S u = 1/2 * x1^2 + x2^2 -3/2 * x1 * x2 ut S u is quadratic
@rbzhang3374
@rbzhang3374 5 лет назад
Definition?
@maurolarrat
@maurolarrat 7 лет назад
Excellent.
@masor17utm86
@masor17utm86 5 лет назад
why is var (u_1 transpose x)=u__1 transpose s x)
@yannavok7901
@yannavok7901 5 лет назад
t= transpose ^2= squared In ordrer to demonstrate that Var(ut X) = ut S u I will use - the könig form of the variance Var(X)= E(X^2) - E^2(X) - and this covariance matrix form COV(X)= E(X Xt) - E(X) [E(X)]t So let's start: We will use the köning form to define the variance: 1- Var(ut X) = E((ut X)^2) - E^2(ut X) * We know that (ut X)^2=(ut X) [(ut X)]t so the first quantity becomes: E((ut X)^2) = E( (ut X) [(ut X)]t ) The second quantity becomes: E^2(ut X)=E(ut X) [E(ut X)]t And we get: 2- Var(ut X)= E( (ut X) [(ut X)]t ) - E(ut X) [E(ut X)]t * We know that [ut]t = u and [(ut X)]t= (Xt u) (notice that the transpose has changed the multiplication order) so the first quantity will change like this: E( (ut X) [(ut X)]t ) = E( (ut X) (Xt u) ) And we get: 3-Var(ut X) = E( (ut X) (Xt u) ) - E(ut X) [E(ut X)]t * We know that Expectancy of a vector(or matrix) filled with scalars gives the same vector(or matrix) and Expectancy of a vector(or matrix) filled with random variables gives Expectancy of that vector(or matrix) In others words: E(u)=u, E(ut)= ut , E(X Xt)=E(X Xt) and E(X)=E(X) So the first quantity becomes E( (ut X Xt u) ) = E(ut) E(X Xt) E(u) = ut E(X Xt) u and the second quantity becomes E(ut X) [E(ut X)]t = E(ut) E(X) [E(ut) E(X)]t = ut E(X) [ut E(X)]t = ut E(X) [E(X)]t u And we get: 4-Var(ut X) = ut E(X Xt) u - ut E(X) [E(X)]t u * let's factorize by ut And we get: 5-Var(ut X) = ut [ E(X Xt) u - E(X) [E(X)]t u ] * let's factorize by u And we get: 6 -Var(ut X) = ut [ E(X Xt) - E(X) [E(X)]t ] u * We know that COV(X)= E(X Xt) - E(X) [E(X)]t And we get: 7-Var(ut X) = ut COV(X) u * Here S = COV(X) And finally, we have: 8-Var(ut X) = ut S u
@chawannutprommin8204
@chawannutprommin8204 6 лет назад
This gave me a moment of epiphany.
@logicboard7746
@logicboard7746 2 года назад
Jump @17:20 then @29:30 @42:10
@usf5914
@usf5914 4 года назад
tanks.
@VanshRaj-pf2bm
@VanshRaj-pf2bm 6 месяцев назад
Ye lecture kis bachhe ke liye h
@raduionescu9765
@raduionescu9765 3 года назад
WITH THE HELP OF GOD WE ADVANCE IN A STRAIGHT LINE THINKING SPEAKING BEHAVIOR ACTIONS LIFE TO THE HIGHEST STATE OF PERFECTION GOODNESS RIGHTEOUSNESS GOD'S HOLINESS EXACTLY AS WRITTEN IN THOSE 10 LAWS
@arnoldofica6376
@arnoldofica6376 5 лет назад
English subtitles please!
@aayushsaxena1316
@aayushsaxena1316 7 лет назад
perfect :)
@andrijanamarjanovic2212
@andrijanamarjanovic2212 3 года назад
👏👏👏👏👏👏👏👏👏👏👏👏👏
@arsenyturin
@arsenyturin 4 года назад
I'm still lost :(
@nazhou7073
@nazhou7073 5 лет назад
太神奇了!
@berknotafraid
@berknotafraid 5 лет назад
ADAMSIN
@mortezaahmadpur
@mortezaahmadpur 6 лет назад
viva Iran
@ProfessionalTycoons
@ProfessionalTycoons 5 лет назад
2
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