PCA : the math - step-by-step with a simple example
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- Опубліковано 19 чер 2024
- You can buy the corresponding PDF of this video at:
www.tilestats.com/
In this second video about PCA, we will have a look at its math (the eigendecomposition). We will compute the PCA based on the eigenvectors of the covariance matrix.
You're probably the only one on the Internet who explained PCA mathematically! Thank you so much!
After I watch this video, I feel like everyone else make PCA complicated, deliberately. Thank you for making it easy!
This video is totally underated. If my uni's lecture is even half good as yours, I won't spend so much time.
Trust me after having spent hours on google and youtube, this is the best thing that i found on PCA, hats off to you and thanks a lot!!
Wish you all the best for your channel.
Thank you!
I so agree. I don't understand why PCA is presented in such an overly complicated fashion by almost everybody. This video is so simple because it covers every step of the process and gives clear and easy explanations without unnecessary details and confusing language. THANK YOU.
True, great explanation 👏
totally underrated video I've been searching for a simple yet informative explanation of PCA and you are the best you should be the top on on the search . thank you
This is one of the best videos explained the PCA concept mathematically.
Best lecture on PCA calculations so far!
Thank you
Your video gave me 100% understanding of PCA, before that, I know nothing about PCA. Thank you!
you're a life saver! I've been trying to understand this for daysssss and this is the only video that nailed it! Thank you so muchhh
Best PCA video I have seen at this platform. Well done - Greetings from Germany
I would like to sincerely thank you for this video. Almost all YT maths videos only focus on the high level concepts. Finding a linear, step by step explication of the process is rare. Please do make more of these videos. Others I would love to see are: a step by step of one of the GLM's (logistic?), a SBS of gaussian process, and maybe a step by step of factor analysis. Thanks again
Thank you! I think my videos about logic regression will interest you. You find all my videos at
www.tilestats.com
It is a great video. The corresponding PDF file of this video is also great .Thank you very much.
Thank you so much. Your videos are the best and this particular video is beyond amazing.
best explanation of PCA so far!!! thank you so much
best tutorial ever on PCA I have ever found!
Best explanation for PCA. Thank you. Wish you the best ❤❤
You are the best TileStats. I love you a lot man!
Thanks for this nice video, best explaination of PCA. Others just explain without showing the calculation.
Excellent explanation of a very complex topic.
Please do try to explain the SVD procedure if you can.
Thanks 👍
Amazing! Best teacher for PCA
I simply loved your teaching way. AWESOME video!
Thank you!
Good job man!!! Thank you so much
Perfect presentation! Thanks!
Tomorrow will be my quiz I had not even attend the lecture but after watching your tutorial I am ready for quiz so Thanks 🙏
appreciate the video, helped a lot
you are the best teacher i ever known
God bless you sir what an amazing explanation I'm really touched and thank you for this video
man, it's so helpful, thank you so much!!!
thank you so much for this great video
absolutely brilliant!
This is an excellent explanation. Thanks a lot.
Thank you!
great video, thanks!
Your videos are very helpful . Thanks
Thank you!
Very informative! Thank you!
Thanks!
Perfect
Thanks
great, thanks for this video
This was amazing, so clear
Thank you!
This is so good, Thank you!
Thank you!
Very well explained ... indeed !! Keep up the good work ..!!
Many thanks for conceiving and producing this excellent series on PCA. I look forward to viewing your videos on other topics !!
Zz
Zz
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One of the best videos about pca that I have seen. but where is svd ?:))
Very helpful, thank you!
Thank you!
Thank you very much
Your videos are a godsend, extremely helpful and clear. Thanks a lot. Is there any chance you will cover Correspondence Analysis any time soon? That would nicely complement the series of videos on data dimensionality reduction techniques. Just wondering....
Thank you! That method is not on my list but maybe in the future. However, there will soon be a video on principal component regression.
Able to understand mathematics of PCA with your videos ...Many Thanks ... if you reading this comment do watch explanation on GLM , probably best explaination available on youtube
the best 🙏🏼
bro, great job, love the way you explain things. You might see this comment copied and pasted across few of your other videos, I am just doing this for the algorithm.
Thank you!
That is so helpful.
That's great!
Amazing Explanation!
Thank you!
Sir can you please upload a similar mathematical video on oblige rotation of Principal components? It will be very helpful.
Thanks
Love from China😘
thank you so much
Thank you!
Thanks for that video what name of book that you depend upon?
I mainly used internet to learn ML.
Amazing Video, very well explained. A question: Anybody knows a way to sum the eigenvectors (weights) to 1. To exactly how much of of orginal valeus contribute to the component?
Thank you! To transform the weights so that they sum to one, simply divide each weight by the sum of the weights (given that the weights are positive). However, I usually like to think of the weights as correlation coefficients as I explain in the fourth video about PCA.
@@tilestats I have find out that if we power all the weights by 2 it will end up summing to 1 ! regardless the signal. Thanks for the contribution ! Appreciate it
Yes, but note that the weights are usually expressed as loadings (see PCA 4 video) by most statistical software tools. The square of these loadings do not then sum up to one.
Hi, thanks for the very informative tutorial, can you please explain at 11:00 how you obtained the pc scores by multiplying the eigenvector matrix with centred data?
Have a look at this video, starting at about 9 min, to see how to do matrix multiplication:
ua-cam.com/video/QtAZsWseIKk/v-deo.html
Okay, got it ! thank you so much🙏
for the example that starts @18:00 , first you have vector [-2/ 3] , then you multiply by the covariance matrix to get vector: [8 / 12] (to transform the vector), and then you multiply again [8/12] by the covariance matrix to get the direction of the eigenvector. However, in the second example you dont transform the vector and just multiply the initial one [4/1] by the covariance matrix. So my question is: why it is necessary to transform the vector in the first case? Thank youu!!!
I just show one iteration in the second example but the more iterations you do (multiply the new vector with the covariance matrix), the closer you will get to the eigenvector.
I see that you centered the data. Is only centering required for "standardization" or scaling is also normally done such that the mean =0; standard deviation=1? this will then change the covariance matrix since variance of individual dimensions will equal 1.
It is not a requirement, mathematically, to standardize your data (mu = 0, SD = 1), but it is highly recommended, especially if you have variables with a large difference in the variance. I discuss that in the next video about PCA:
ua-cam.com/video/dh8aTKXPKlU/v-deo.html
Can you please tell me where are the precious video related eigenvalues nd eigenvectors?
If you go to
www.tilestats.com
You find all my videos in a logical order.
Great but not sure how you got normalized values of eigen vectors. Can you please direct me towards that video or step you skipped? Thanks. Also, what are the eigen vectors that you get for eigen value 0.32? My simplified value of y is -0.72 x I dont know why you got 0.81.
ua-cam.com/video/9CT0jnem4vM/v-deo.html
Starts at around 8 min.
@@tilestats Got it and I forgot to take the sqrt of the denominator :/ thank you again
@@tilestats Thanks for this very informative video. I have one question - For lambda = 0.32, I am getting y = -0.73 when x =1, the normalized vector with unit length of 1 is [0.81, -0.59] instead of [-0.81, 0.59]. Please verify and advise
If you set x= 1, you get [0.81, -0.59], but if you set y=1, you will get [-0.81, 0.59]. If you set x to 1, or y to 1, is arbitrary because both vectors are eigenvectors to the covariance matrix (they just point in the opposite direction). Both vectors will give the same variance of PC2.
@@tilestats Many thanks for the explanation. Much appreciated!
please explain about kernel PCA
hi, instead of center(ing) the data, is it also viable to standardise the data?
Sure, have a look at the next video:
ua-cam.com/video/dh8aTKXPKlU/v-deo.html
@@tilestats Thanks, I just watched it! Hoping you could help me with following as well: if I am applying the eigenvectors to another set of new data (with same variables as the original data) (i.e., not the original data i ran PCA on), I assume I should also standardise the new data before applying the eigenvector (weighting) on the new data?
minute 6.17, how did you get the value 3.84? Should it not be 35.2?
4.4 x 8 - 5.6 x 5.6 = 3.84
Thanks~! I want to but this channel stock~!, it will be bigger one.
Thank you :)
why for the standarlization of data did not need to divide standard deviation
Here I only center the data, but you can also standardize as I do in this video
ua-cam.com/video/dh8aTKXPKlU/v-deo.html
why did you take n-1 while calculating the covariance matrix
Because that is how you calculate the variance. Have a look at this video if you like to know more:
ua-cam.com/video/pLH1QA4F9uE/v-deo.html
Please why others don't center the data first before using it to form the covariance matrix
You do not need to center the data to compute a covariance matrix. You will get the same matrix with uncentered data because the spread of the data does not depend on the mean. The reason why I center the data in this video is because that is the first step in PCA.
Tile stats best
9:17 how to do normalization?
Have a look at around 8 min in this video:
ua-cam.com/video/9CT0jnem4vM/v-deo.html
@@tilestats OKAY THANK YOU
U cud hv explained how to calculate eigen values as part of this itself ...to make us watch other videos causes loosung of interest...sry uts not a one stop shop. Y dont u make it comprehensive
Because I try to keep the videos below 20 min and then I cannot include all details that I have covered in previous videos. This video is just one, out of many, in my course:
ua-cam.com/play/PLLTSM0eKjC2fZqeVFWBBBr8KSqnBIPMQD.html
@@tilestats wow 👏 thanx
I executed the steps in python .. I notice that the Matrix of Eigen Vectors returned by the sklearn ..
pc = PCA(n_components = 2)
pc.components_ is as follows:
[ [-0.58906316, -0.80808699],
[-0.80808699, 0.58906316] ]
Whereas the one that you have calculated is:
[ [ -0.80808699 , 0.58906316],
[ 0.58906316 , 0.80808699 ] ]
It would help if you could help me understand this difference . What am I missing ??
It seems like your function rotate the data counter clockwise, which explains the difference. It does not matter for the results. You may try to switch order of the input variables to see of that change the output.
Great video, thanks !
Thank you!