Principal Component Analysis (PCA)
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- เผยแพร่เมื่อ 1 มิ.ย. 2024
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A conceptual description of principal component analysis, including:
- variance and covariance
- eigenvectors and eigenvalues
- applications
As usual, very little formulas, lots and lots of pictures!
0:00 Introduction
0:46 Taking a picture
1:13 Dimensionality Reduction
2:02 Housing Data
5:09 Mean
7:46 Variance?
12:47 Covariance matrix
13:58 Linear Transformations
18:12 Eigenstuff
19:16 Eigenvalues
19:53 Eigenvectors
20:51 Principal Component Analysis (PCA)
26:05 Thank you! - วิทยาศาสตร์และเทคโนโลยี
Judging by how much you simplified the lesson without sacrificing the actual concept, I trust you have spent good time preparing for your lesson and animation. Thank you very much
I haven't seen any clearer explanation of PCA on the internet than this one. Many thanks!
I agree!
I second this - great channel!
agreeeeeeeeee
Completely Agree!
+1
I haven't seen a better explanation for PCA. Love it! And I always had trouble to conceptually understand covariance. I knew it was related to direction but always found it difficult to conceptualize. Thank you for your explanation.
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Excellent video. Very intuitive. Thanks
hi
I have confusion even after watching videos of 2+ hours...
26 minutes solved all doubts.
I like the way how you put all the concepts together.
Thanks.
lol this cracks me up
we may be aware of terms like mean, variance, covariance, linear-transforms, eigenvectors and eigenvalues, PCA. This video puts together all the relationships in an amazing way
You are the tutor we all need but don't deserve.
This is how you teach!! I wish my professors from university could do even 1% of this... I am paying thousands of dollars for something I get for free on youtube!! Very good job!!
I would literally clap for you if you gave this lecture in person. Thanks for this man. Keep doing what u do
This video is the eigenvector with the highest eigenvalue in the internet that describes PCA.
Appreciate all the time and effort on this work. You deserve the trophy.
this comment is underrated.
This is the clearest explanation of PCA I've ever seen. As a wannabe analytical chemist, this is pure gold because it gives you hints about the true meaning of PCA without excessively digging into statistics and pure mathematics which just blows your mind.
Congrats for the amazing explanation and the effort to make this video!
Quite literally the best video on PCA. You explained everything without skipping the math and the basics, amazing!
PCA, that I couldn’t really understand in five years (although I have been using in analysis without being clear), I am now crystal clear. There are so many articles and videos. Those are like a parroting. This lesson is the best.
This was AMAZING!!! You reconciled so many disparate concepts I had learned in college...I understand how it fits together now. Very down-to-earth explanation, and amazing animations!
That arguably might be the best tutorial I've ever watched on TH-cam. Thanks.
This is the best PCA explanation. If only I had this explanation 11 years ago...
This is without a doubt the best explanation on youtube.
Great explanation Luis! It took me a whole class and a conversation after with an instructor to get PCA, and still your video cleared up so much uncertainty/misconceptions I had on the subject.
far better PCA explanation on youtube, I saw a lot of videos, but only learned with this one.
i search all the pca tutorial on youtube, and this is the best one.
All these TH-cam videos are great. There is a 100% mapping between this and all the AI stuff with real brain observations and computational neuroscience. This author is brilliant!
This is the best PCA video ever seen, it's quite easy to follow and understand deeply.Thanks!
I am impresed with the level of information you were able to put together in a 20 minutes video. I mean you summarized a whole semester in such a way that a beginner could follow. Thats amazing
I have spent 3 days chasing eigenvectors and eigenvalues, and then I found you video. It puts it all together very nice, and mentally delivers it with ease - like a boss. I was very close to spending two weeks on Khan academy to understand what you delivered in 26 minutes. Thank you so much.
oh my god! this is unbelievable stuff. I wasted around a day on many lectures and books still can't able to grasp a shit about PCA. but this man explains it in such a beautiful way. You're a legend sir
wow! this was VERY worthwhile. thank you! so many lights switched on
well thats the best explanation i have ever seen, great job sir, thank you so much !
Only explanation which has core PCA explained in a very simple yet effective and useful manner.
His teaching skills are exemplary.
have never seen a better explanation of pca than this
Awesome explanation for PCA beats any in youtube tilll date
EXACTLY!!!!
Agree, even the one from 3Blue1Brown
Thank you for taking time to explain small detail
This is my first comment ever in youtube ,I was searching for PCA videos and was unable to figure out how exactly PCA works,but this video gave me complete clarity on the topic....Thanks Luis Serrano!!!
I am not sure why this video is not appearing in top search results under 'PCA'. Best video. Period.
Most comprehensive explanation, thank you so much. Tomorrow, I have interview for big tech company and now after watching whole video, I feel confident to answer questions on PCA. \m/
Thank you! I hope your interview went great!
This excellent, Luis. My only thought to improve the video would be to pull the thread through using your original example of housing data. Good job, and thank you!
I am NOT watching his video because I wanted to learn math or Machine learning. I am already pretty good at math and machine learning. I am watching these Luis Serrano videos to learn how to effectively teach this stuff to young people. Those who might think that they can't do machine learning or math. I sent his book to my son, a business/communication major in university, he is now studying machine learning with the help of Luis Serrano's machine learning book. Thanks
Bravo!!!! The best explanation on the net on PCA.
HIT THE LIKE BUTTON IF YOU LOVE THIS VIDEO!!!
You did it! You nailed it!! You killed it!!!
Just when I was about to give up on this topic after watching a series on PCA, I ran into yours and BOOM!!! IT WAS THE BEST THING I DID!!!!
I am going to watch it again because you gave me an ideal explanation of the topic.
You started off with related background knowledge necessary for perfect understanding.
THANKS A LOT!
Recognizing your name from your Udacity lectures, I was thrilled to have stumbled upon your youtube channel today - really gentle, concise, intuitive explanation of a complex topic. Nice shout out to 3blue1brown - watching this reminded me of his videos and style (though his visualizations are insane :] ). One question: from the end of your video, it seems to me that eigenvalues can be thought of as measures of feature importance, but in your housing example, multiple similar features (size, #rooms, etc) become a new single representative feature. How do we know what the features are that we are left with after PCA in much higher dimensional examples? Say we reduce a 100 dimensional data set to 10 dimensions, how do we know what those 10 dimensions represent? Thanks again - looking forward to diving into your channel.
footfalcon thank you for the kind message! (And sorry for the late reply). The new features are combinations of previous ones, but in general they may not mean much. However, since you know what combinations they are, you can look for example at the biggest coefficients in the linear combination, and see if you find trends. For example, if the top feature has big coefficients for several features that are size related (in a house) and small coefficients for other features that are not related to size, you can associate that feature with size in general. But it’s more of an observation than a mathematical way to do it.
One of the most lucid presentations on PCA I've ever seen. Nice work!
Well Luis, that's the best and most intuitive PCA tutorial I've seen so far.
Bravo!
This is great tutorial.
Can you make a similar video about - Markov Chain Monte Carlo, since its too complicated to understand why are we doing what we do?
f
Same here, really would love a video on this topic
up
I second that
The skeptic in me wants to say I understood most clearly from this lecture because I had a solid subconscious understanding from watching probably a hundred of these over the years
The other part of me tells the skeptic to shut up and appreciate the magnificence of this presentation. This is a great example of data storytelling from my view.
Thanks! Very good explanation of how projections, eigenvectors and eigenvalues all come together in PCA analysis!
This is so far the best video on PCA.
The first 20 mins is like sharpening your axe and last 6 mins- cut the tree.
Probably the best explanation of PCA. Mean, variance, covariance, correlation such a smooth explanation, great.
Finally someone telling me why. why do we use eigenvectors of covariance matrix to calculate the Principle components. Thank you so much!
Luis, ONE OF THE BEST PCA EXPLAINED ON TH-cam ARENA OF MACHINE LEARNING. I read many blogs, almost all the PCA tutorials on youtube but I was unclear about the PCA concept, was thinking what is this PCA.. but when I started viewing your PCA explanation , within 20 seconds PCA lighten up in my mind, which started from the taking picture example.
The way you explained this confusing concept, It's totally insane, You are an exponentially amazing tutor. many thanks for sharing this stuff.
you are simply amazing :) Thank you so much Luis.
I am a teacher. And I tell you this. You are the best!!! The absolute best over all!
I watched many videos on PCA over the last year and by far this is the best. Thank you.
I spent so many hours looking at other videos and content online and could not make sense of it. This video really helped me a lot. Especially in understanding the role of eigenvectors and eigenvalues. Thank you so much!
Dear Sir, you are the best at explaining PCA!. I thank you very much.
I hated eigenvectors and eigenvalues for 20 years because I thought they were useless.
Now, I have an appreciation for these concepts because of your video.
Thank you!
The most informative but graspable explanation of PCA I have encountered online ever. Thanks so much!
By far the best conceptual and visual explanation online. Great work. Thanks!
One of the best descriptions of PCA I've seen. Bravo!
Just amazing. I have an exam and I have gone through so much material already but nothing could have summed PCA better than you did. Thank you!
You are a great teacher, teaching is an art and this guy is an artist. Million Thanks Sir.
Wow..One of the best explanation about PCA..The best part is that you explained clearly the purpose of PCA in simple way!!!Billion thanks.
Thank you!! Out of all the videos I watched on TH-cam this one helped me understand the most about what PCA is, how it works, and when to use it.
I have had struggled visualizing co-variance and PCA, you have done it so marvelously, literally out of words for the gratitude after seeing this video, now I have understood PCA by heart. Kudos!
You have a very intuitive way of teaching things that's hard to infer when reading or watching lectures from other teachers.
Best video i have even seen about PCA. Thank you so much sir.
I went over at-least 30+ videos + materials , articles from 2 weeks , At last you made it so clear . You are wonderful teacher 🙏
This is the best explanation of PCA, individual components broken down, emphasis on visualization instead of just the method and then all the components put together for the big picture. I cant thank you enough for the fantastic teaching style that clicks with me.
This is one of the best tutorials which I have ever seen. Being a teacher, I appreciate the way how difficult concepts are explained in a simple way. It is must-to-read video for all students who want to understand PCA.
Amazing. Perhaps the best PCA explanation video in the internet.
This video is amazing! Many students in college are taught how to compute the eigenvector and eigenvalue but the college seldom explained its geometrical meaning, but you did this which helped me a lot! Thank you!
Thank you! This is the most comprehensible and complete video about PCA I've found!
Thank you for making this video!! PCA and linear algebra have never been so easy and understandable to beginners, but you’ve made things clear and logical!
If only i could know this in my graduation days, Linear Algebra would have been my favorite subject. I was blindly solving lambda as per the books and finding the value of x,y....
Shit!! ! ! ! ! !
It's like a "whole grad summarised in a video !"
Keep it up Luis!
Thank You So much !
The covariance explanation just struck me unguarded, it blew my mind. Thank you
Never have I understood PCA in such a simplified and intuitive way. You're a magician! ❤️
Luis, I have seen so many videos for PCA but this one is the best that I came across. Really appreciate your work and thank you for making the video. It's really awesome.
You are a gifted lecturer. You know how to motivate the theory and provide that understanding of WHY we're taking all the computational steps. That is rare!
I needed to understand how pca is used to calculate the normals of a point cloud and by far this is the best explanation I've seen. Thank you!
Best ever explanation on PCA. You put so much effort into this. Thanks!!
One of best explanation after going through lot of PCA videos. Now it will make sense to drill down further.
Thanks!
Best PCA explanation I have ever seen. Thank you so much Luis.
Fantastic, absolutely the best simple, straight to the point presentation of the PCA . Thank you
There are so many videos on the internet but none explained to this detailed and fundamental level as you did! Thank you sir!
Very comprehensively explained,cleared a lot of concepts.Bravo!
Luis, thank you so much for sharing your knowledge. I've seen countless videos on data science and this PCA explanation is one of (if not the) best ones out there! This is the first of your videos that I've seen, but I'm excited to find others now. Again, thank you!
Thank you so much for this amazing explanation Luis!! This is the best and most intuitive explanation of PCA I've found on the internet! I was literally struggling to understand this concept for weeks! :')
This is by far the best PCA video i have come across. Thank You!!
By far the best basic explanation of PCA on the internet! Thank you so much, I did not think I could ever understand this without being an expert mathematician.
Thank you very much! I hardly comment on TH-cam but when you see real skills, you have to acknowledge. I have watched several other videos on PCA but didn't really get what was going on. This video is so simple and clear for anyone with elementary knowledge in geometry and statistics to understand. Thank you very much !
Simply awesome. PCA conceptually cannot be explained better than this.
I cannot state how intuitive this video is! Even a layman can now understand this! Loved it, subscribed and looking for more!!
the best explanation on the Earth..! Thanks Luis.! Shrikant from India
This is one the simplest and most precise explanation of PCA. Thanks !!
I am in the process of studying for my machine learning exam and had a hard time grasping this concept for some reason. Thank you so much for making such a clear and easy to follow explanation.
One of the best explanations ever, PCA or no PCA!
Luis is hands down the best instructor in the ML field!
Best explanation available on TH-cam for PCA!! Amazing work Luis :)
This is the best video on PCA I have come across. Its so well explained
This is the best explanation for PCA. I have tried with so many videos, but this saves me. Thank you
By far the very best PCA explanation! Very clear and understandable for everyone!
Best explanation of PCA till now i saw many videos on pca i always look at time when they will finish because they are not clear but your video im not bother about time because it is simple n clear, i will watch all your videos.Thanks alot Luis
This is the best explanation of PCA in the whole TH-cam!Thanks so much!!
The best and neatest explanation of PCA.. bravo, and you’ve earned a lifelong fan and follower!!