Principal Component Analysis (The Math) : Data Science Concepts

  Рет қаралды 86,591

ritvikmath

ritvikmath

4 жыл бұрын

Let's explore the math behind principal component analysis!
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Пікірлер: 162
@loveena419
@loveena419 3 жыл бұрын
Finally, a video that explains the math behind PCA so clearly. Went through all the other videos and it helped a lot! Thank you!
@pigtowndanzee
@pigtowndanzee 4 жыл бұрын
Love your teaching style. Keep these videos coming!
@vinceb8041
@vinceb8041 3 жыл бұрын
I've been wrestling to get all intuitional and computational components for doing pca for a while, and seeing it all come together here helps tremendously! Great as always, 10/10 video :)
@qaarloshilaal2778
@qaarloshilaal2778 3 жыл бұрын
Thanks infinitely for all your videos, you're literally the best at explaining these concept in a clear and excellent way in order to continue with what we have to study/ do! Huge respect man.
@ritvikmath
@ritvikmath 3 жыл бұрын
You're very welcome!
@paulbrown5839
@paulbrown5839 3 жыл бұрын
This is a very strong video. It requires proper study. I hope you do more of this great stuff. Thank You!
@shivamkak7981
@shivamkak7981 8 ай бұрын
Such a well curated explanation of PCA, thanks so much!
@thinkingAutomata
@thinkingAutomata 2 жыл бұрын
Thanks Ritvik. Excellent explanation of PCA. Good job, well done!
@bhajman123
@bhajman123 3 жыл бұрын
Byfar the most accessible description of pca...finally was able to clearly connect the covar matrix and the eigen values to variance maximization
@nahidakhter8646
@nahidakhter8646 3 жыл бұрын
Beautifully explained! Thanks so much!
@mathematicality
@mathematicality 2 жыл бұрын
Simple and straight to the point. aBsolutely welldone!
@robertbillette4671
@robertbillette4671 2 жыл бұрын
Like everyone else has mention, amazing clarity and style.
@MaxDavidsonArgentina
@MaxDavidsonArgentina 4 жыл бұрын
Thanks for sharing your knowledge. It's great to have people like you helping out!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@martinw.9786
@martinw.9786 2 жыл бұрын
Thank you very much for the explanations - very very well done. Your references to the mathematical backround is key!
@sandeepc2833
@sandeepc2833 3 жыл бұрын
Cleared most of my doubts. Thanks a lot.
@joachimguth6226
@joachimguth6226 4 жыл бұрын
Very well presented. You are a great teacher. Hopefully you are going to cover the entire AI space.
@ritvikmath
@ritvikmath 4 жыл бұрын
That is the goal!
@warrenbaker4124
@warrenbaker4124 3 жыл бұрын
@@ritvikmath Oh wow!!! I'm so happy to see you're taking this on. I'm a huge fan and this is a real highlight for me. Thanks for all you do!!
@Moiez101
@Moiez101 Жыл бұрын
@@ritvikmath i fully support that goal! I just started with data science bro. Loving your videos, you're a great teacher.
@kakabudi
@kakabudi 2 жыл бұрын
Really great video! Thanks for explaining this concept wonderfully!
@BleachWizz
@BleachWizz 3 жыл бұрын
I'm loving your content, you're showing a part of math that is not usually shown. The part where you actually use it, where you make your choices and why are you choosing them. Like it's nice to understand the equations and why it gives you a 0 on the sweet spot, but it's also nice to remind that it not only works but it was build to work with that intention. So in the end you still need to figure out how do you get your problem to fit in one of those, what can you choose in these big generic operations to fit it into your problem.
@ritvikmath
@ritvikmath 3 жыл бұрын
Thanks for the feedback! I do try to focus a lot more on the "why" questions rather than the "how" questions.
@paulntalo1425
@paulntalo1425 3 жыл бұрын
You have made it clear. Thank you
@jaivratsingh9966
@jaivratsingh9966 Жыл бұрын
Simply excellent!
@RobloxCatGirl
@RobloxCatGirl 2 ай бұрын
Thank god I found your channel. I am studying masters degree in computer science in a prestigious university and cost me a lot of money but your channel is very useful to dig deeper and understand many things. Stay on the good work!
@mashakozlovtseva4378
@mashakozlovtseva4378 4 жыл бұрын
Everything was clearly understood from math side! Thank you for your link on Medium account!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@cameronbaird5658
@cameronbaird5658 Жыл бұрын
Phenomenal video, thank you for the hard work 👏
@amaramar4969
@amaramar4969 3 ай бұрын
I had to go thru the prerequisite videos to clarify my concepts first, but after that this PCA explanation is amazing! I think you are equivalent to 10 college professors out there in terms of teaching skills. I hope you get that proportion money and the college professors feel ashamed and work harder to catchup to your standards. Again, amazing!
@christinejiang6386
@christinejiang6386 2 ай бұрын
wow! thank you! I watched all the videos before watching this one, they really helps a lot!
@shashanksundi5669
@shashanksundi5669 2 жыл бұрын
Just perfect !! Thank you :)
@resoluation345
@resoluation345 3 ай бұрын
The best series to explain the maths behind PCA
@yarenlerler67
@yarenlerler67 Жыл бұрын
Ahh such a clean explanation. I really appreciate! I will have practical statics for astrophysics exam soon, and I was having some problem with the theory part. All your videos were very helpful! I hope I am gonna get a good grade from the exam. :)
@alphar85
@alphar85 3 жыл бұрын
I stopped at 01:33 and I am going to watch the other 5 videos. you are such a blessing mate.
@133839297
@133839297 Жыл бұрын
You have a gift for teaching.
@Chill_Magma
@Chill_Magma 9 ай бұрын
Straight to the point and thorough you deserve to be subscribed from my 3 accounts
@ahmadawad4782
@ahmadawad4782 4 жыл бұрын
Watched many videos about linear algebra and PCA. You're the one who made it clear for me. Thanks!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@_arkadij
@_arkadij 4 ай бұрын
Very appreciative of the explanation why we end up with using vectors corresponding to the biggest Eigenvalues. Thanks so much
@rajathjain314
@rajathjain314 4 жыл бұрын
Very Intuitive, Great Job Ritvik!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@berkoec
@berkoec 3 жыл бұрын
Such a well-explained video - keep up the great work!
@ritvikmath
@ritvikmath 3 жыл бұрын
Thanks a ton!
@TamNguyen-qi8di
@TamNguyen-qi8di 3 жыл бұрын
Dear rivitmath, Thank you so much sir for your clear explanation. Even being in my last year of college, I am still struggling with the basics of statistics. With your help, I have been striving exponentially in class and looking to graduate from college in this semester. Your videos have been so so so helpful and i wish you an amazing health to continue with your content. I wish you could have been my professor in college. Thank you for putting out the high quality contents. Words can't describe how much I appreciate you, sir. Thank you. You have changed my life.
@ritvikmath
@ritvikmath 3 жыл бұрын
Thanks for the kind words. Wishing you much success!
@arun_kanthali
@arun_kanthali 2 жыл бұрын
Great Explanation.. Thank-you 👍
@volsurf1274
@volsurf1274 3 жыл бұрын
Concise, clear and superbly explained. Thanks!
@ritvikmath
@ritvikmath 3 жыл бұрын
Glad it was helpful!
@subhabhadra619
@subhabhadra619 Жыл бұрын
Awesomely represented..
@nuamaaniqbal6373
@nuamaaniqbal6373 2 жыл бұрын
cant thank u enough!! u r truly the boss!
@kaeruuuu_
@kaeruuuu_ 2 жыл бұрын
Necessary videos: 1. kzbin.info/www/bejne/jmibpX94jph1g80 (Vector Projections) 2. kzbin.info/www/bejne/nZ3EmoNoZ5d9jaM (Eigenvalues & Eigenvectors) 3. kzbin.info/www/bejne/bKC9hWpoYtOhr6s (LaGrange Multipliers) 4. kzbin.info/www/bejne/m2iWYWZpn7-Heas (Derivative of a Matrix) 5. kzbin.info/www/bejne/Z2aVpYaPqc6EmNk (Covariance Matrix)
@ShubhamYadav-ut9ho
@ShubhamYadav-ut9ho 22 күн бұрын
Amazing explanation as always
@proxyme3628
@proxyme3628 Жыл бұрын
Brilliant explanation of why eigen vector is the one from maximum optimisation, never saw such great explanation before. Wish your course is in Coursera. I do not think any text book explains the eigen value as Lagrangian Multiplier and eigen vector as maximising variance. Thanks so much.
@Sriram-kj6kl
@Sriram-kj6kl 2 жыл бұрын
Your videos help a lot man.. Thank you 👍
@Tankwell-cq5ky
@Tankwell-cq5ky Жыл бұрын
Very well presented - well done!😊😊
@deplo
@deplo 3 жыл бұрын
Hi Ritvikmath, thank you for your super informative videos! I took all courses on this topic but I was wondering if you could expand it with factor analysis and correspondence analysis. It would be interesting to know how different methods work and relate to each other because it would provide a deeper perspective. Thanks
@santiagolicea3814
@santiagolicea3814 Жыл бұрын
This is a great explanation, thanks a lot. It'll be great if you can also make a video showing a practical example with some data set, showing how you use the eigenvectors projection matrix to transform the initial data set.
@DeRocks1607
@DeRocks1607 12 күн бұрын
You are great teacher.. ultimately I understood
@543phi
@543phi 4 жыл бұрын
Thanks for this video! As a Data Science student, your lecture helped to clarify a lot....I appreciate your teaching style.
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@simranjoharle4220
@simranjoharle4220 Жыл бұрын
Your videos are extremely helpful! Thank you!
@ritvikmath
@ritvikmath Жыл бұрын
Glad you like them!
@mmarva3597
@mmarva3597 2 жыл бұрын
Thank you very much !! really helpful
@muhammadghazy9941
@muhammadghazy9941 Жыл бұрын
thank you man appreciate it
@nandhinin799
@nandhinin799 4 жыл бұрын
Clearly explained, helped me greatly in understanding the basis of PCA.
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@Chill_Magma
@Chill_Magma 9 ай бұрын
Seeing your videos increases my confidence on math stuff :DDD
@aravindsaraswatula2561
@aravindsaraswatula2561 3 күн бұрын
Awesome video
@cll2598
@cll2598 2 күн бұрын
Epic explanation
@Cybrean1
@Cybrean1 3 жыл бұрын
Excellent presentation and delivery … wish you all the success!
@ritvikmath
@ritvikmath 3 жыл бұрын
Thank you! You too!
@vinceb8041
@vinceb8041 3 жыл бұрын
12:20 Quick note on why going down the list of eigenvalues is legit, the covariance matrix is a symmetric matrix, and it can be shown that if such a matrix has more than one eigenvalues that are not the same, the corresponding eigenvectors will be orthogonal.
@erfanbayat3974
@erfanbayat3974 Ай бұрын
this video is amazing
@gc6327
@gc6327 4 жыл бұрын
Hi Ritvik- Can you do a video on factor analysis. That would be huge! Thanks buddy!
@herberthubert6828
@herberthubert6828 3 жыл бұрын
you rock, thank you
@georgegkenios486
@georgegkenios486 3 жыл бұрын
Amazing work mate!
@ritvikmath
@ritvikmath 3 жыл бұрын
Thanks a lot!
@user-xw5cg7by6t
@user-xw5cg7by6t Жыл бұрын
This video is super great! I was wondering why Covariance matrix is used to compute PCA, but this video made my doubts clear!!
@ritvikmath
@ritvikmath Жыл бұрын
Glad it was helpful!
@pratik.patil87
@pratik.patil87 6 ай бұрын
Thanks Ritvik, I went through multiple resources to figure out this exact questions " why does eigen vectors and eigen values of a covariance matrix represent the direction and strength of the biggest increase in variance" . Thanks your video clarifies it beautifully. One question still though, I understand the equation we use to maximise but why do we need the constraint(uT u =1)?
@Rockyzach88
@Rockyzach88 Жыл бұрын
Just finished the LA section in the Deep Learning book and I can tell this is going to help supplement and fill in this gaps of understanding. Good vid.
@ritvikmath
@ritvikmath Жыл бұрын
I hope so!
@ajanasoufiane3903
@ajanasoufiane3903 4 жыл бұрын
Great video, it would be nice if you could show the big picture through the SVD decomposition :)
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@fahimfaisal4660
@fahimfaisal4660 2 жыл бұрын
Excellent
@user-kw6ib6ks1q
@user-kw6ib6ks1q 3 ай бұрын
great explanation. Really appreciate it. thanks
@ritvikmath
@ritvikmath 3 ай бұрын
Glad it was helpful!
@sidddddddddddddd
@sidddddddddddddd Жыл бұрын
What you've called the closed form of the covariance matrix is actually the biased estimator of the covariance matrix \Sigma. And if you divide by (N-1) instead of (N), you get the unbiased estimator of \Sigma. Awesone video! Thanks :D
@jhonportella5618
@jhonportella5618 3 жыл бұрын
Great, great video I really appreciate your effort and good methodology to teach. I have a question on the projection math. on your projection video you obtained P=XUU but here you used P=U*XU. Maybe this is a silly question but I would really appreciate if you can tell me why this equivalence is possible. Many thanks
@ernestanonde3218
@ernestanonde3218 2 жыл бұрын
great video
@rabiizahir2885
@rabiizahir2885 2 жыл бұрын
Thanks a lot.
@MohamedMostafa-kg6gk
@MohamedMostafa-kg6gk 3 жыл бұрын
Thank you for this great explanation .
@ritvikmath
@ritvikmath 3 жыл бұрын
You are welcome!
@seetaramdantu3190
@seetaramdantu3190 3 жыл бұрын
excellent...well explained
@ritvikmath
@ritvikmath 3 жыл бұрын
Glad it was helpful!
@darshansolanki5535
@darshansolanki5535 4 жыл бұрын
Best video!!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@odysseashlap
@odysseashlap 4 жыл бұрын
Really appreciate this! Any good book suggestion for PCA mathematical Framework in greater depth? Maybe another video (hard maths of pca)?
@chinaminer
@chinaminer 3 жыл бұрын
Hello, thanks for this video and also for the others, well done! On this video I have a doubt to ask. Where can I submit the question in order to not mess comments here?
@fabianwinkelmann3931
@fabianwinkelmann3931 3 жыл бұрын
Thank you:)
@alejandropalaciosgarcia2767
@alejandropalaciosgarcia2767 3 жыл бұрын
Bro, you are awsome
@akrylic_
@akrylic_ 4 жыл бұрын
There's a property of transposes around 6:45 that you could have mentioned, and I got tripped up for a second. The reason why you can write u^T*(xi-xbar) as (xi-xbar) ^T*u is because (AB)^T =(B^T)(A^T) It's a cool trick, but not obvious
@ritvikmath
@ritvikmath 4 жыл бұрын
Very true, thanks for filling in the missing step!
@zechengchang3444
@zechengchang3444 3 жыл бұрын
Can you explain more? How does (AB)^T =(B^T)(A^T) have anything to do with u^T*(xi-xbar)? Thanks.
@AshishKGor
@AshishKGor 2 жыл бұрын
Thanks sir.
@PR-ud4fp
@PR-ud4fp Жыл бұрын
Thanks 😊
@brofessorsbooks3352
@brofessorsbooks3352 4 жыл бұрын
Good!
@zilezile4942
@zilezile4942 4 жыл бұрын
Good morning If you have difficulty understanding the statistical models and programming them with the R software; You have difficulty understanding where the main components come from when you do principal component analysis; You need to discover the statistics for functional data in particular the analysis in functional principal components; you have no idea how to model by functional linear model ... You like clear and detailed explanations. Click on this link amikour.wordpress.com/nos-formations/
@ahmad3823
@ahmad3823 2 ай бұрын
Amazing
@ritvikmath
@ritvikmath 2 ай бұрын
Thank you! Cheers!
@quark37
@quark37 Жыл бұрын
Fun video. Thank-you. And thanks for all the pre-req videos. Question: I've seen other videos that describe PCA vectors as orthogonal, but using eigenvectors they would not necessarily be orthogonal, right? What is the correct way to think about the orthogonality of PCA vectors? Thanks. * I think I answered my own question. The eigenvectors in question are of the covariance matrix of the related variables. This matrix is symmetrical so the eigenvectors will be orthogonal. Correct?
@dr.kingschultz
@dr.kingschultz 2 жыл бұрын
Do you have a video about instrumental variables? Because in general seems to be just regular manipulation, but in a more complex way. Also, do you have videos applying this concepts? Could be using R or Python. That would be very nice.
@diegolazareno8020
@diegolazareno8020 4 жыл бұрын
Never stop making these videos!!! One of Logistic Regression would be nice
@ritvikmath
@ritvikmath 4 жыл бұрын
Hey I appreciate the kind words! I do have a vid on logistic regression here: kzbin.info/www/bejne/b6vaaGmGiZinsNU
@mainakmukherjee3444
@mainakmukherjee3444 10 ай бұрын
We find the equation of the variance of the vector, on which we are going to project the data, and then tried maximizing it, because, the vector, for which the variance will be highest (max eigen value), is gonna retain most of the information of the data, after dimensionality reduction.
@yurongluo447
@yurongluo447 3 ай бұрын
Your video is helpful for us. Can you create one video to explain Independent Component Analysis in detail? Thanks.
@suvikarhu4627
@suvikarhu4627 2 жыл бұрын
@ritvikmath 5:02 I don't understand where is this formula of projection (proj(xi)=ut xi u) coming from. The projection video does not say that. What the projection video exactly says is that the proj(xi) = (xi dot u)*u. No transpose there! Where did you get that transpose from? And the dot product is missing ? Another question, at 5:50 why do you take only the magnitude of the vector?
@mwave3388
@mwave3388 Жыл бұрын
I'm preparing for a job interview. Thanks, the best PCA video I found.
@nirjasmuhammed
@nirjasmuhammed 3 жыл бұрын
thank u sir
@thirumurthym7980
@thirumurthym7980 3 жыл бұрын
@ 4.54 - you are referring about projection video - on how you arrive projections formula. There is no such mention of U transpose in that projections video.
@AG-dt7we
@AG-dt7we 3 ай бұрын
Thanks for such amazing videos. Have 1 question: In the projection video you derived projection as X. V / ||V|| * u here you took started with u1T Xi u. What is the difference? Will be helpful if you can point me to some resources !
@RealLifeKyurem
@RealLifeKyurem 3 жыл бұрын
Since principal component analysis is used to reduce the dimensions, thus lessen the curse of dimensionality, can you calculate the maximum amount of dimensions you need for a given dataset to find patterns?
@thirumurthym7980
@thirumurthym7980 3 жыл бұрын
nice video. Very useful to me. You are also mentioning about link to couple of external resources @13.18 , could you please share?. thanks.
@XXZSaikou
@XXZSaikou 2 ай бұрын
nicely explained! but I noticed you didn't mention the need to standardize the original data for PCA. Is standardization a little trick to make things faster or is it needed in the underlying math?
@poornanagasai262
@poornanagasai262 Жыл бұрын
It's really a great explanation and one question I got is from the video of vector projection it is clear that the vector onto which we wanna project has the value is (u.x)u where (u.x) is the magnitude and u being the unit vector. Here comes my question in this present video(math behind pca) you used (u^T .x)u as the vector magnitude of the vector which is projected on to. What is the difference in using u and u^t(u transpose)? Can you please answer me?
@knp4356
@knp4356 4 жыл бұрын
Hey Ritvik, It would be great if you can generate some problems for viewers to solve. Watching is great but if you can supplement with actual problems then it would drive the points into viewers head. You can then further post solutions on your medium site. Hopefully at least 4-5 problems per each video. I've watched many videos on DS subjects but something in your teaching method is making it simpler to understand. Thanks.
@ritvikmath
@ritvikmath 4 жыл бұрын
I honestly really appreciate that you're trying to help me be more effective at what I do. I think it's a great idea and I'll look into it. Thanks :)
@kisholoymukherjee
@kisholoymukherjee Жыл бұрын
Hi ritvik, thanks for the video. Can you please tell me how the vector projection formula is being used to calculate the projection of xi on u here? The formulae in the two videos seem to be quite different. Would really appreciate if you could help understand the underlying math
@ArpitAnand-yd7tr
@ArpitAnand-yd7tr 11 ай бұрын
That's just a dot product between the potential u1 and Xi. It gives the magnitude of the projection in the direction of the unit vector u
@Markks100
@Markks100 11 ай бұрын
I don't understand why the projected form of Xi on U1 is U1^TXiU. From your lecture on vector projections, P=(X.U)U, so why the change?
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