Machine Learning | Singular Value Decomposition (with mathematical equations and examples)

[@RanjiRaj18]

For notes👉 github.com/ranjiGT/ML-latex-amendments

[@DrAndyShick]

It is astonishing the number of rules for SVD that are supposedly generally accepted, but if you watch any two videos on it, the procedure will be very different regarding what to do, what you're allowed to do, etc

[@marklunch]

That method of calculating the determinant using the trace/original determinant/minors is genius! Why have I been going through all that algebra before? Completely error prone the old way.

[@shashankbangera7753]

Wow, what a beautiful explanation Ranji Sir. I comprehended every step you did Thank you so much for putting enormous efforts into making flawless videos. I got huge respect for you!

[@shubhamkumar3198]

Wonderful explanation I won't find any video on svd decomposition better than this Thank you so much

[@premrajanprasad7755]

While calculating v matrix when you took eigen value of 10 and using Cramer's rule the eigen vector should be 2,-1,0

[@anjanimittal3411]

YESSSS

[@adddddi781]

yes

[@rubix438]

Though this topic is quite complex, but you explained it really well. I was able to understand the topic on the very first go. Thank you so much!

[@RanjiRaj18]

Glad it was helpful!

[@ujjwalahuja2831]

Saved me from failing in exams.. thanks .. OP teaching .. U r THE BEST./

[@premrajanprasad7755]

Otherwise , I was trying to understand this svd and I have completely understood by your teaching thankyou sir make this type of videos it helps us a lot

[@frankribery3362]

I was watching MIT lectures and I dint know some random kid here in India taught this better

[@tula__]

Yeah he compiled it in a better than GS.

[@piyushkumar-wg8cv]

At 11:00 , I think we are doing normalisation not the orthogonalsation, please correct me if I am wrong.

[@DevanshShukla11]

Amazingly taught ! Easier to understand the problem and solve SVD!

[@RanjiRaj18]

Glad you liked it!

[@rvandrangi]

Very good explanation. The SVD is made so simple particularly in characteristic equation the coefficient of lambda is the sum of the minors of diagonal elements is not covered in many UG text books. I liked the video quality particularly the white board and lighting without any glare on the board.

[@RealUniquee]

finally got mathematical explanation that was easy to understand

[@h_3401]

I am math teacher and for this video i too increase my concepts amazing and great thank u

[@RanjiRaj18]

Most welcome 😊

[@sivashankar3889]

when we divided with X becomes -2 and -X2 becomes -1 sir here X2=1 why X1=-2 why X1 =2 please tell me ma'am

[@sivashankar3889]

when we divided with X becomes -2 and -X2 becomes -1 sir here X2=1 why X1=-2 why X1 =2 please tell me ma'am

[@vatsal_gamit]

You are a blessing!! Thank you for this video :)

[@varunsen2802]

That was one very good SVD Explanation. Thank You so much for the effort.

[@Annasupari]

This is the video by which i understood SVD after watching n confusing videos.

[@sugata83]

nicely described..even people like me who knows nothing can easily understand..thanks a lot for sharing your knowledge.

[@RanjiRaj18]

Thank you for your feedback 🙂

[@dineshv231]

Clear and concise explanation, loved it!

[@RanjiRaj18]

Glad it was helpful!

[@prernajat1712]

Sir why you not using the 12 eigen value to calculate eigen vectors.

[@constructivecritic8069]

second column of V is transpose of [-2 1 0]...there is a negative sign missed in calculation ....in your calculation it is coming to be transpose of [ 2 1 0]....but I got the idea...thanks

[@terrylee6904]

Yes, I got the same as you, it should be [-2 1 0 ]

[@groudon3524]

you are living up to your name

[@simranlahrani]

Does order of lambda 1,2,3 affects the matrix?

[@siddhantdeokar]

@@groudon3524 is that a Digimon in ur Prof pic?

[@groudon3524]

@@siddhantdeokar no that's Groudon a Pokemon

[@jyothinkjayan6508]

10:40 how can u substitute like that

[@venkateshkodgire4288]

yeah exactly

[@rexmagat4051]

number 1.. explanation

[@ftt5721]

This is the best SVD problem-solving video...

[@jessewolf6806]

At 8:33 u say A(At)= U. Earlier u derived A(At) = U (Sigma) (Sigma t) (Ut). What happened?

[@aditipandey7936]

same doubt

[@venkateshkodgire4288]

10;56 how we substitute like this both lambda 1 and 2 in same matrix

[@sanjoyroy5970]

why you put lamba 2 first and then put lamda 1 in the case of substracting from diagonal elements of U

[@jayanthperneti9213]

sir, u didn't calculated U entirely. You need to write U in terms of eigen vectors of AA'.

[@priyam86f]

if we are given a 2x2 matrix, how do we arrive at VT after getting V? How to use the cramer's rule in such case?

[@ajith.studyingmtech.atbits1512]

I have one doubt, while substituting values of lambda for U, upper one was lambda one and lower one was substituted as lambda 2. But in case of V, each lambda values were substituted for the matrix. Since U have 1 and -1 it did not throw error. what if the values are dissimilar say 2 and -1. Can we substitute in one go? Otherwise great explanation and techniques. Love your other videos and all the best. Ajith.

[@champstark8974]

did you get the answer of this? am also confused about that part

[@lalitkumardhanjani1636]

SAME DOUBT

[@sivashankar3889]

Same doubt

[@kunwarssahi6283]

Sir what would be the singular matrix if both the eigen values comes different???

[@AmitKumar-ul9fy]

well explained but one doubt why you have not considered lambda-2 for U calculation, only one lambda was considered for U and can you try to prove that it is correct decomposition

[@ninglunmang]

Very Good Lecture!! Thank you so much!! May God bless U more!!

[@RanjiRaj18]

Thank you so much

[@saumyashah6622]

sir in start, you said AtA = V Z Zt Vt and later you said AtA = V . Why?? Here, t = Transpose, Z = Sigma

[@rezonator2442]

Actually here sir forgot to tell that Z Zt is also a diagonal matrix so V (Z Zt) Vt is eigen value decomposition of AtA so here V is treated as eigen vector of AtA. So if you want to evaluate V then you can use normal eigen value problem by considering matrix as AtA.

[@adityabapat3024]

simply amazing sir thanks a lot

[@614_dharmeshcharde8]

Thank you very much sir Your way of teaching is so simple I completely understood the topic 😊

[@priyam86f]

Hi sir, thanks for such a well defined smooth explaination. Just a doubt, do we follow the same process if a 2X2 matrix is given in the question?

[@jyotiahuja3142]

Is it possible to find singular value decomposition of a singular Matrix

[@abpokeunite3463]

thanks a lot sir you have saved my day

[@RanjiRaj18]

Happy to help

[@abpokeunite3463]

@@RanjiRaj18 after three years also you replied be sir its great to see such dedication thanks a lot sir

[@thechhavibansal]

what do u mean by singular values?? please tell.. thanks for the video

[@vivekt9445]

singular values are all the diagonal entries in that sigma diagonal matrix.

[@swapnilgupta7627]

first you have to take any one value of lemda and solve and then other value ,but you have taken both at once this is wrong

[@suhailsaifi5065]

he has calculated eigenvectors for each value of lambda, then arranged it column-wise, he skipped one step, but the result is correct,

[@sivashankar3889]

X÷-16=-X2÷-8=X3=0 sir when we divided with X becomes -2 and -X2 becomes -1 sir here X2=1 why X1=-2 why X1 =2 sir please sir tell me

[@garimasharma6575]

why does the sigma matrix value have values sqrt(12) and sqrt(10) instead of 12 and 10?

[@mohammedrehman4109]

Ranji, you are Geni of SVD.

[@vaagishandhin9350]

thank you Raj perfect explanation

[@RanjiRaj18]

Thanks and welcome

[@sathviksrikanth7362]

thanks a lot sir!

[@rajamk4278]

Really understandable

[@subarnamath]

Sir, There are many mistakes in your calculations throughout the video , please, calculate properly 🙏🙏

[@PriyankaSingh-ou5pb]

Yes I agree too.coz when lambda2 =10, then the corresponding eigen vectors are [-1/2,1,0]

[@manicj6907]

if var(x)=15var (y)=6 and var (x+y)=35 then what is tha value of cov (x,z)

[@charanreddy7923]

why are you doing square root to the eigenvalues in sigma matrix?

[@phanikirans4728]

To make it orthogonal as for an orthogonal matrix, the determinant should be either +1 or -1. The first calculated U matrix has a determinant of -2 and hence can't be orthogonal (which it must be as per the requirements, so should V matrix)...but after applying the cramer's rule ,t determinant becomes -1...condition for orthogonality satisfied...

[@mthetree]

A^T*A= V *∑^T * ∑*V^T at the beginning and them A^T * A= V in the example why and how ?

[@RanjiRaj18]

The first expression is to demonstrate how the decomposition is done (beginning) and the second gives the Eigenvectors that's why it is written as only V

[@bhargavasavi]

A^T * A= V and A * A^T= U , this is confusing....It basically V is the eigen vector of A^T * A....Similarly U is the eigen vector of A * A^T. So we calculate V,U which are the eigen vectors of A ^T* A and A * A^T

[@gauranshisingh7210]

A typical equation of relation between eigenvalues and eigen vectors is Ax=λx, x in this case is V. Its a small mathematical substitution ( remember V is orthogonal)

[@rishabh27ful]

How to find Σ if no common values in both U and V's eigen values?

[@mr.s.srinivasaraosrinivasa7860]

Always eigen values are common ... because symmetric matrices are same eigen values

[@anshika5914]

Thank you sir

[@Prajwal_KV]

Thanks a lot sir.

[@Toxic-th4si]

How to calculate "U"?

[@Royal_job_Info]

Thank you bro 🎉

[@RanjiRaj18]

Welcome 😊

[@yashodakotana8859]

Thank you so much sir this is very helpful to me

[@RanjiRaj18]

Most welcome

[@prettyice15]

Thank you, I'am very helpful 😁

[@mohammadsamiuddin2176]

Hidden gem

[@rohitpradhan9375]

loved this....thanks for making it look so simple...one request please make a video on moore-penrose pseudoinverse as soon as possible

[@syedowaisahmed4347]

great

[@pratikbhangale3538]

Nice video

[@puruskr9831]

Dear my friends,there are many calculation mistakes.Ignore it and don't waste time better to focus on process explained well😊

[@AkshitGupta29]

Thanks for an amazing video! I have one doubt that is the order in which we write v1,v2,v3 matters? If so, how do we check them?

[@srisangeeth4131]

excellent teaching bro

[@baburajkv4166]

Very good explanation sir

[@arnabbanik6403]

You just divided the columns of U with the norm of the column instead of Gram-Schmidt orthogonalization

[@rivali9660]

V=A^t.A how 3x3 Matrix will come

[@CC.cinematics]

the way you calculated U doesnt maje any sense

[@abhahimani5188]

Best

[@danalex2991]

how is at.a = v ?? you wrote just before that at .a = v . sigmat . sigma . vt !

[@itv5610]

Your V isn't symmetric which means something went wrong.

[@rrrajat04]

For V, lambda 1 ,2 and 3 were 0,12 and 10 when you calculated but you used lambda 1,2,3 as 12, 10 , 0.......did i missed anything?

[@mohiuddinshojib2647]

I thin,k he just rename the all lambdas. After getting the lamdas value it does not matter which is lamda 1 ,2 or 3. You just plug in the lamdas' values that's it

[@aabid123]

method complicated hai ye wala.

[@sushankbais4702]

7: 34 is starting time 🙃😂

[@mohammadasifshirzad9367]

Yes ok

[@eddy8112]

A=[3, - 4; 4, 3] help me to solve this Eigen vector becomes zero.

[@Sujataj331]

Too much lengthy 😅😅

[@Sulemanjansari]

v3 should be (1,-2,-5)

[@natureboyranjith]

Can u solve 1 1 1 0 0 1

[@Ewwww167]

Eigen vectors values direct ga veysav andhi ayya Chappam antey Step to step clarity explaination undali Nuv endhoo direct ga cheppeysav

[@nikitakhale9172]

Sab kuch badhiya lekin 1 aise kon bnata h 😫 koi 7 smjh le 1 ko

[@Ilovenqfutures]

SSStttrong

[@somikexplorer]

So many errors in calculations

[@intergalacticbajrangdal9106]

abe U to nikaala hi nhi

[@techtalentblueprints]

thank you sir

[@fullseries2155]

Thank you sir

[@RanjiRaj18]

Welcome