PCA 5: finding eigenvalues and eigenvectors

Full lecture: bit.ly/PCA-alg
To find the eigenvectors, we first solve the determinant equation for the eigenvalues. We then solve for each eigenvector by plugging the corresponding eigenvalue into the linear system. Remember that eigenvectors must have unit length.

[@evawilhelmsson3469]

I'm so happy and proud. Just solved my first PC by hand, with help from this video. Thanks!!

[@pavelkonovalov8931]

Thank you you very much! Your video helped me to get the idea behind the PCA and also, the philosophy behind the calculus

[@tiarcandrawardaya7610]

Thank you very much. I've been looking for that euclidean length as a divisor just like for ever.

[@liwang248]

Hi Victor,
This is the best PCA explaining video I can find online. Could you also provide a link of the Powerpoint used in your video?
Thank you very much!
Li Wang

[@rahelrapazzini7229]

Thank you so much for this very clear and step by step explanation! Saved me a lot of time and helped me prepare for my exam!

[@Nissearne12]

Thanks. very helpful.
I have seen "Power Method" also but that seems to solve only the first (dominant, strongest) eigenvector. Is there any method to get out several eigenvector (in order from dominant and down) by use Power Method ?
Best Regards
Olle Welin

[@moganraj2833]

really thanks prof, its very useful to my work.thank u very much.

[@rishijoshi1977]

Thank you so much for such a great explanation. I was losing my mind over this.

[@cookie920211]

Thanks very much. Your video is very inspiring!!!

[@jiashenglai5509]

This is simply excellent.

[@yeah6732]

Great tutorial! But why the slop of two eigenvectors are expected to be the same?!

[@ogunyemisegun4909]

I don't seem to understand the final step, what did u use to divide to get those final PC

[@manuarteteco6153]

thanks, this was really helpful!

[@zamanmakan2729]

Is using Lagrange multiplier an alternative or another step?

[@mmuuuuhh]

Doing SVD (by calling the routin in Matlab^^) is only a quick alternative algorithm for doing those calculations you presented for finding the Eigenvectors, isn't it?

[@vlavrenko]

mmuuuuhh Yes.

[@jaredsalinasgonzalez9899]

Amazing video !!!

[@MehmetAltuntasmehmetcc]

Dude you totally rock!

[@affectionlifeaffliction]

what is the Euclidean distance? I did not get how he solved the final eigenvector when e1 =1 and e2= 1

[@JoaoVitorBRgomes]

Euclidian distance can be the distance of a point from the origin (giving the size of the vector) or can be the distance between 2 points. In this case it is the size of the vector. He wants to put it all in the 0-1 scale so he divides by its size

[@saurabh75prakash]

Excellent tutorial on PCA and Eigen values/vectors. How a dxd matrix have d Eigen values/vectors?

[@JoaoVitorBRgomes]

It is because the number of eigenvectors is going to be the same as the number of columns your matrix has

[@aman6487]

What if we get two independent eigenvectors for one eigenvalue

[@abidahmed4182]

how did you find the euclidean distance

[@scares009]

You would take the coordinates of the vector, square them, and add them together, then take the square root. That gives you its distance from the origin, the actual length you would get by measuring the vector with a ruler. :)

[@chan-holee7031]

is the first symmetric matrix covariance matrix(Of raw data)??

[@JoaoVitorBRgomes]

Yes he uses the covar matrix to find the eigenvalues and eigenvectors

[@FarhanAli-zj3rb]

Thank you

[@arulpraveen]

but the points (2.2, 1) dosn't fit in the second equation and so cannot be considered as a solution. in that case what do we do ??

[@AhmadTalkss]

at 4:00 how did u go from 2.2, 1 to 0.91, 0.41

[@JoaoVitorBRgomes]

he divide by the euclidian distance

[@JoaoVitorBRgomes]

d = sqrt(2.2^2 + 1^2) = 2,41660 ; then divide 2.2/2,41... = 0.91

[@dominicdannies7482]

can somebody explain 3:03 ?

[@MarceloRuan]

I didn't get too.

[@dmitriidatsenko]

0.8*0.8 = 0.64

[@aiinabox1260]

fantastic job....One Stop Shopp