19. Principal Component Analysis
Вставка
- Опубліковано 27 сер 2024
- MIT 18.650 Statistics for Applications, Fall 2016
View the complete course: ocw.mit.edu/18-...
Instructor: Philippe Rigollet
In this lecture, Prof. Rigollet reviewed linear algebra and talked about multivariate statistics.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu
if you find this lecture challenging, it might be because you forget some basic linear algebra. Don't be discouraged by the somewhat trivial algebraic calculation. the Prof does a very good job in explaining the intuition and statistical foundation for doing PCA. PCA is so commonly used in psychology studies, yet no one in the my Psy department seem to have a clue where PCA is coming from.
extremely helpful with building the basics and then moving forward
Gave me some insight, Thanks. I liked the part about how u^TSu is the variance of the X's along the u direction. Good to know for an alternative viewpoint to Singular value decomposition as a PCA.
A good opportunity to burn calories would be to wipe the blackboard properly.
For people who are whining about the lecture is too hard or can not follow. I think you guys do not have the prerequisite for the course. His lecture is trying to illustrate from the statistical prospective of PCA, anybody who is series in data science should know that statistics and linear algebra shares a lot of same ideas from different prospective.
Audio starts at 1:15
I was forwarding like crazy until I hear something and was thinking "Damn not only the first minute without audio". Just to realise my sound was mute
H is a n by n matrix, and v is a d-element column vector. H can not multiply v
He corrected the idea but didn't clean up the board. v is n-dim
But I have a doubt here n shows number of examples and d tells about how many dimension the space have so v should be of size (dx1) so it should not be feasible for Hv??
Can someone pls answer on this??
nice example of seeing matrix in perspective of stat
Shouldn't the empirical covariance matrix be divided by n-1 and not n?
both definitions works well
wonderful teacher and everything. But what's with the horrible chalk rubbing.
Clean the blackboard PROPERLY
49 min in and still hoping he'll get to PCA soon hahaha... great lecture though
Can anyone pls help me with how prof. Come up on the final result from multiplication of Hv?? Steps i am little bit confused
Is he deliberately making the writing hard to read by making the blackboards so poorly erased and specifically writing on those poorly erased boards instead of the nice black ones?
Concept of Eigenvector at 1:02
how to proof that eigenvectors are coulums of projection matrix
Great lecture. Thank so much Professor.
He is pretty good actually
In 1:08:10, those lambda's should not be eigen values of Sigma ? (or covariance matrix ?)
47:25 bottom left: How is Var(u^TX)defined? What does the "variance" of a random vector mean? Thank you so much
X is vector, not matrice in this case. So u^TX is just scalar
Try working backwards from the result U^TxU
Anyone can explain how the did he get the term in the parenthesis at 39:07? Why does Transpose(v)[1] = Transpose([1])v?
both are transpose to each other and anyway, you are going to take the expectation of those two. so it will be same
Can anyone explain how is he multiplying Identity matrix Id which is dxd with all-ones matrix which is nxn?????
Nevermind....he clears it up around 40:00 it was gigantic mess
Absolutely precious! Excellent in explaining details! Thank you.
I don't know why he let I_d rather than I_n denote n by n Identity matrix since 32:10.
oh, he correct this mistake since 40:30
for such an important concept you would think Mit would've fixed this issue by now
The only bothersome thing in this video is the dirty is the blackboard.
wtf is he writing in a messed up white board???
Absolutely great. If you have trouble getting this, maybe read a book first.
Can you share your slide please?
The lecture slides are available on MIT OpenCourseWare at: ocw.mit.edu/18-650F16. Best wishes on your studies!
horrible. Don't max out your volume. There's nothing till you get a huge surprise at 1:15.
One of the cameras is tracking the movement of the lecturer, and it makes me dizzy. The view of the blackboard is enough. Even in 2016, the camera man at OCW still can't master how to record good video lectures.
I understand nothing...
Rather watch one of the lectures on PCA by Prof Ali Ghodsi.
Link please
@@NphiniT ua-cam.com/play/PLehuLRPyt1Hy-4ObWBK4Ab0xk97s6imfC.html
This is full playlist.
He makes PCA way more complicated than it should be, wow...
Most of what he is doing is introducing the linear operator formalism. The gravy here is this side stuff, not the minimalist way to explain PCA
no
No sound?
It has sound... it's just really low. Sorry!
He should learn how to teach from Gibert Strang
Bit rude.
@@aazz7997but true
Lectures of both professors are awesome. It may be helpful to understand this course if prerequisite courses (18.600, 18.06, 18.100, etc.) are completed first. May also be helpful to study the slides first before listening to the lectures.
thanks for the video! Question: can someone explain the difference between big Sigma and S. One is covariance matrix, one is sample covariance matrix. they are not the same thing? Thanks!
Big Sigma is for the whole population. S is when selecting a sample from the population. S is an estimate of Sigma. If the sample is big enough, S would approach Sigma, but may not be exactly equal to the population parameter. I hope this is clear!
Man this video is such a torture! :D
why?
Good Lecture. But bad handling by Cameraman
11:00 There is a ghost on a board, in a right lower corner of it.
I see why this was made free.
He doesn't even cares to rub the board properly 😅😅😅😅
too much unnecessarily complicating. this is in fact not only unnecessarily complicating but also in a confusing and destructive way. however, i should still say that other lecturers up to this lecture were better in term of presentation
my computer is so smart
This guy is so cute
Is this really MIT?
this is really not the quality i expected from MIT, pretty sloppy instructor
Dude needs better erasers
Insane :)
1:13:51 v1 ZULUL
this guy is a complete mess...
He looks rather unsecure.
Winy have you published such a mess? Shame on you!
Terrible
Audio starts at 1:14
Thanks.