Visual Explanation of Principal Component Analysis, Covariance, SVD

[@zacmac]

Great clarity. You clearly understand your stuff from a deep level so it's easy to teach.

[@patyyyou]

Nicely done. It hit the right level for someone who understands the linear algebra behind Eigenvectors and Eigenvalues but still needed to make the leap of connecting a dot or two in the application of PCA to a problem. Again, thank you!

[@tusharkush7]

This video needs a golden buzzer.

[@simonala7090]

Agreed!!!

[@MathematicsMadeSimple1]

Clear explanation. Thank you for shading more light especially on the application of eigenvalues and vectors.

[@sebgrootus]

Incredible video. Genuinely exactly what i needed.

[@riazali-vi8tu]

Well explained, you should do more videos

[@davestaggers2981]

Graphical interpretation of covariance is very intuitive and useful for me. Thank you.

[@roshinroy5129]

Awesome explanation!! Nobody did it better!

[@f0xn0v4]

I have always dreaded statistics, but this video made these concepts so simple while connecting it to Linear algebra. Thank you so much ❤

[@blackshadowofmysoul]

Best PCA Visual Explanation! Thank You!!!

[@apesnajnin]

Really, amazing lecture! It's make my conception clear regarding eigenvalue and eigenvector. Thanks a lot!

[@eturkoz]

Your explanations are awesome! Thank you!

[@anuraratnasiri5516]

Beautifully explained! Thank you so much!

[@Muuip]

Great concise presentation, much appreciated! 👍

[@Trubripes]

Thanks for concisely explaining that PCA is just SVD on the covariance matrix.

[@bottom297]

Extremely helpful. Thank you!

[@simonala7090]

Would love to request an in person version

[@TheSyntaxerror1]

Love this video, great work!

[@danielheckel2755]

Nice visual explanation of covariance!

[@softpeachhy8967]

1:37 shouldn’t the covariance be divided by (n-1)?

[@DanielDa2]

great explanation

[@basavg1]

Very Nice..pls keep posting

[@Pedritox0953]

Good explanation

[@sakkariyaibrahim2650]

Good lecture

[@Timbochop]

Good job, no wasted time

[@matato2932]

thank you for this amazing and simple explanation

[@Lapelu9]

I thought PCA was a hard concept. Your video is so great!

[@prof.laurenzwiskott]

Very nice video. I plan to use it for my teaching. What puzzles me a bit is that the PCs you give as an example are not orthogonal to each other.

[@nickweimer6126]

Great job explaining this

[@adriantorresnunez]

Best explanation I have heard from PCA. Thank you

[@vietdaoquoc7629]

thank you for this amazing video

[@Agastya007]

Plz do more videos

[@skewbinge6157]

thanks for this simple yet very clear explanation

[@123arskas]

Thank you. It was beautiful

[@VivekTR]

Hello Emma, Great job! Very nicely explained.

[@Darkev77]

I do understand that eigenvalues represent the factor by which the eigenvectors are scaled, but how do they signify “the importance of certain behaviors in a system”, what other information do eigenvalues tell us other than a scaling factor? Also, why do eigenvectors point towards the spread of data?

[@malstroemphi1096]

If you consider a raw matrix or just geometric examples eigenvalues are just a scaling factor indeed. And you cannot say much more. But here, we are talking with additional context: we know we are doing statistics and putting "data" into a covariance matrix, which means we can now add more interpretations. The eigen vector is not just some eigenvector of some matrix, it's the eigenvector of a *covariance matrix* in the context of statistics, we've put data into a matrix whose elements measure all the possible spread of data, which is why we can now say an eigenvector points towards the spread of data and its length (eigenvalue) relates to the importance of that spread.

[@1291jes]

This is excellent, Emma... I will subscribe to your videos!

[@zendanmoko5005]

Thank you! very nice video, well explained!

[@Agastya007]

I love the way u spelled "data" at [3:34]😁😁

[@Rami_Zaki-k2b]

PS: Video is targeted at people who already have a deep knowledge of what the video is trying to explain.

[@latanezimbardo7129]

1:28 I personally visualise covariance like this, I always thought i was wrong, I have never seen others doing this, how come??

[@stephenaloia6695]

Thank you, Ma'am!

[@TechLord79]

Very well done!

[@szilike_10]

Believe it or not, I've been wondering a lot about the concept of covariance because every video seems to miss the reason behind the idea. But I think I kind of figured it out today before watching this video and I drew the same exact thing that is in the thumbnail. So I guess was thinking correctly : ))

[@jordigomeztorreguitart]

Great explication. Thank you.

[@abdulrahmanmohamed8800]

A very good explanation.

[@vitokonte]

Very nice explanation!

[@Matt-bq9fi]

Great explanation!

[@user-or7ji5hv8y]

Wow, that was quite good explanation.

[@liviyabags]

I LOVE YOU !!!!! whattay explanation... thank you so much

[@skshahid5565]

Why do you stop making videos?

[@m.y.s4260]

awesome explanation! thx!

[@tusharpandey6584]

awesome explanation! make more vids pls

[@haroldsu]

Thank you for this great lecture.

[@arjunbemarkar7414]

How do u find eigenvalues and eigenvectors from the covariance matrix?

[@Eta_Carinae__]

Same as usual, right? Find lambda using det(Sigma - lambda * I) = 0, so just take lambda away from the main diagonal of the Cov. Matrix, take the determinant of that and you'd be left with some polynomial of lambda which you then solve for, each solution being a unique eigenvalue.

[@saDikus1]

Great video! Can anyone tell how she decided that PC1 is spine length and PC2 is Body mass? Should we guess (hypothesize) this in real world scenarios?

[@crispinfoli9448]

Great video, thank you!

[@콘충이]

Awesome!

[@subinnair3835]

Dear mam, How did you obtain the matrix at 5:30 ?

[@emfreedman3905]

Find the Covariance Matrix of these variables, like at 2:15, and find its eigen decomposition (find its two dominant eigenvectors). The matrix at 5:30 is the two dominant eigenvectors. Each column is an eigenvector.

[@subinnair3835]

Emma Freedman thank u ! The video's explanation was great and covered all the fundamentals required to fully understand PCA !! 😃

[@DoFlamingo_1P]

AWESOMEEE 🤘🤘🤘

[@EdeYOlorDSZs]

poggers explination thankyou

[@SpeakerSparkTalks]

nicely explained

[@nbr2737]

beautiful, thanks a lot!

[@raghav5520]

Well explained

[@AEARArg]

Congratulations Emma, your work is excellent!

[@siliencea9362]

thank you so much!! :)

[@mahmoudreda1083]

thanks A LOT

[@spyhunter0066]

Around the minute of 1.36, you said "we divide by n for covariance", but we divide by n-1, instead. Please, do check on that. Thanks for the video. Maybe, I sohuld say estimated covariance has the n-1 division.

[@astiksachan8135]

5:12 was very good

[@thryce82]

nice job was always kinda confused by this.

[@KimJennie-fl3sg]

I just love the voice🙄😸

[@ivandda00]

ty

[@checkout8352]

Tnks

[@Shrek-pooh]

“Eigen vectors perform same transformations as matrices”: What does this even mean? Project the behaviour of the system and Also signify the relative dominance of certain behaviours within the system. What does this even mean?

[@tractatusviii7465]

investigate hedge/hogs

[@getmotivated3619]

You are awesome... u make a mediocre out of a knownothing.

[@astiksachan8135]

4:35

[@ABC-hi3fy]

No one explains why they use covariance matrix. Why not use actual data and find its igen vector/igen values. I have been watching hundreds of videos books. No one explains that. It just doesn't make sense to me to use covariance matrix. Covariance is very useless parameter. It doesn't tell you much at all.

[@malstroemphi1096]

No it does especially using PCA. But you are right, you need actual data. Say the data are 3D points of some 3d objects, if you use this technique (build a cov matrix using the 3D points and do the PCA of it) then you will find a vector aligned with overall direction of the shape: for instance you will find the main axis of a 3d cylinder. This is quite a useful information.

[@2894031]

babe var(x,x) makes no sense. either you say var(x) or cov(x,x)