pretty dope. here I was laboring away in 223 dimensions. now I can put food on the table for my family with the time saved by removing 100 dimensions. thank u dr mike pound and computerphile
Why even have lectures? This fella explained why we "maximize the variance" so clearly in the first 5 minutes.. Lecturers should just make us watch this video in class... great stuff!
I gotta say I enjoy this video so much and kinda started to under stand what PCA is and what it is used for. Totally a new and different angle to look at this concept. Thank you again Dr. Mike.
I recommend doing a parallel analysis before extracting principal components. This will tell you how many PCs explain more variance than can be explained at random.
Thank you Dr. Pound, finally someone who can explain pca in easy words. Really helpful in my thesis - and by a strange accident I ended up writing both my thesis about pca. First time in my Bachelors I used it for data reduction, this time I use it to categorize data.
@@andrei642 I didn't know that at the time. I googled him and he turned out to be quite the expert. Regardless, He has a simple way of explaining things. not many others do.
Upon first hearing the phrase "principal component analysis", I thought it sounded very analogous to finding principal stress axes in a body under load. As Dr. Pound gave a more detailed explanation later, I realized that is exactly what it is - just expanded to take place in n-dimensional space instead of 3D space. May be a helpful way to visualize for any mechanical engineers out there.
So the idea behind it, is a finding a right angle to look at all data, where we can see clearly all data and distances between them. Looks more like support vector machine or SVM, where we increase dimensionality to fit the line on some other dimension.
Careful when scaling if you’re producing a model which will make predictions on unseen data - the mean that you will be subtracting and the standard deviation that you’re dividing by better be the same between the training set, the test set and the production sets!
I agree with most of what is being taught in this video . Using a new basis to maximize variance or minimize the projection error is why PCA is used . What I can't agree with however is the lecturer telling that PCA is used to cluster data . I don't think this is necessarily true . PCA clusters those features which are highly correlated together . It doesn't cluster the data points when they are represented using the new basis vectors . I hope I am not wrong
PCA clusters features by creating new axis, which can help to identify correlations for feature-engeneering. However you can still do actual clustering among the new axis and that wouldn't be affected by PCA at all, because data still has the exact same hyperdimensional relative positions, just the axis are shifted.
5:25 Why you have not constructed a center of data? Project points to both X and Y axis, calculate both averages and then draw perpendiculars where these averages will intersect which will be a center of dataset
The solution is not unique, since pca was already applied the new axis are non correlated, therefore applying pca could at best perform a rotation of axis, replacing ax by -ax.
I think you're minimizing the error when you're fitting a line (which will be the new axis) to existing data points from two previous dimensions. Thus, this error is (as it was mentioned in the video) the summed squared differences between each actual data point and the line that you're trying to fit.
Judging by his sketch, PCA tries to maximize variance along PC1 axis, while at the same time minimizing error along all the axes orthogonal to PC1, then does the same for PC2 and so on.
Recall his fists; the line of best fit would pierce these two data points and introduce the axis that can directionally pivot the data to reveal greater variance (spread) as observed by the space between his hands as he turned them along that newly introduced axis
Good stuff. Is the "weighted sum" the frobenius norm or related? I'm following a book and I'm trying to compare how it is teaching this to how it is explained in other forms of media like youtube videos.
And what is the benefit of doing PCA? Are we training our neural networker quicker or why would I do this? I still have to collect all the variables, so what is the point?
It is partly a coincidence, but not really. PCA1 gives you the axis that spreads out and separates your data the most (greatest variance). Because your data (from two dimensions) is now separated into one dimension, you can see if there are data points that correlate with eachother.
But how do we make use of principle components afterwards, despite the fact that we can’t interpret the components since they no longer represent the original variables? Without interpretability, can PC still be useful? What can PC still tell us?
they do represent the original variables, what you have to do is to go through the weights and try to make sense of what kind of hidden variable the PC is representing
Hey quick question for anyone out there. I'm failing to see if there's a difference between the principal component 1 and the linear regression. It seems to me they are the same thing. It is my understanding that Btw sorry bad english, not a native speaker.
Really not the same but clearly there is a link between both, one could transform pca optimization problem into a special regression using frobenus norm and basic algebra. Performing pca you look for non correlated axis, this is simply not the case for regression.
He's saying 'orthogonal', meaning the second principal component is going to be at a 90 degree angle to the first one. Orthogonal is used since it describes this relationship without ambiguity for higher than 2 dimensions as well. It simply means that the two axes are completely uncorrelated.
@@pranayyanarp4118 it's just his accent. The person who wrote the subtitles probably heard it the same way you did. He is for sure saying orthogonal though, it's the only thing that makes sense
Check out the full Data Analysis Learning Playlist: th-cam.com/play/PLzH6n4zXuckpfMu_4Ff8E7Z1behQks5ba.html
awesome, thank you!!
FINALLY!!! I watched like 20 videos before this to understand PCA ( intuition ) and no one could explain it like you. THANKS A LOT MAN.
It is data reduction if you only plot PC1 and PC2 as a 2 dimensional graph.
Which is very common.
Thank you Dr. Mike. I showed this to my neighbors and they told me it totally changed their life. My village also greatly appreciated PCA.
Did you show it to your parents as well? Do they still love you?
Did PCA transformed your village?
Holy shit this pca explanation was just what i needed all this time
Same for me
Yep, it boggles the mind how formalism can completely obscure intuition. I guess the formal stuff works for the academic types
pretty dope. here I was laboring away in 223 dimensions. now I can put food on the table for my family with the time saved by removing 100 dimensions. thank u dr mike pound and computerphile
Dr Mike provided the best explanation of PCA to non-experts which I have ever seen. I very enjoyable and insightful video overall.
Yea. Everything he explains feels that way
Why even have lectures? This fella explained why we "maximize the variance" so clearly in the first 5 minutes.. Lecturers should just make us watch this video in class... great stuff!
He's such a great presenter. Thank you for such wonderful videos.
I finally get it!! It's people like you that keep me motivated for my work !
Best PCA explanation I found so far, and I searched for days. Thanks man!
I gotta say I enjoy this video so much and kinda started to under stand what PCA is and what it is used for. Totally a new and different angle to look at this concept. Thank you again Dr. Mike.
I recommend doing a parallel analysis before extracting principal components. This will tell you how many PCs explain more variance than can be explained at random.
Thank you Dr. Pound, finally someone who can explain pca in easy words. Really helpful in my thesis - and by a strange accident I ended up writing both my thesis about pca. First time in my Bachelors I used it for data reduction, this time I use it to categorize data.
Dude, you're better at explaining this than our uni professor :""D
please keep doing what you're doing.
Thank you.
Well Omar, he is too a University Professor...
@@andrei642 I didn't know that at the time. I googled him and he turned out to be quite the expert. Regardless, He has a simple way of explaining things. not many others do.
this is brilliantly explained. one can only simplify if one truly understands it. thanks
Thank you for this brilliant video. In a less then a half an hour I developed intuition that it would take me a month to do from a book.
Upon first hearing the phrase "principal component analysis", I thought it sounded very analogous to finding principal stress axes in a body under load. As Dr. Pound gave a more detailed explanation later, I realized that is exactly what it is - just expanded to take place in n-dimensional space instead of 3D space. May be a helpful way to visualize for any mechanical engineers out there.
I really struggled to grasp the concept of PCA before, but thanks to your video it is now clear to me. Thank you
best explanation for PCA I could find, thank you!
I am just happy to see him using R for this example
This video was EXACTLY what I needed right now. Thank you so much!!!
What a simple way to explain PCA! Thank you so much for the video.
FInally I learnt what is PCA is and what is does, thank you very much.
Dr. Mike your explanations are brilliant.
Fricking loved that it was applied in R!
Dr. Mike, you are a genius.
Best explanation I've come upon as of yet. Thanks!
summary:
(1) draw line to maximize spread
(2) minimize square error accumulation
(3)project data to axis which maximize dataset variance
hence, “axial reprojection”
@@PLAYERSLAYER_22 thanks
the best explanation I have seen so far. thank you so much!
Thank you for explaining this! Very good quality of the video
Great video. The understanding is very relevant to a lot of feature selection etc in data sciences
I'm late to the party but this playlist is gold. Thanks guys :)
It is very pleasant to listen to you. Thanks!
So the idea behind it, is a finding a right angle to look at all data, where we can see clearly all data and distances between them. Looks more like support vector machine or SVM, where we increase dimensionality to fit the line on some other dimension.
Probably the best explaination
Careful when scaling if you’re producing a model which will make predictions on unseen data - the mean that you will be subtracting and the standard deviation that you’re dividing by better be the same between the training set, the test set and the production sets!
I agree with most of what is being taught in this video . Using a new basis to maximize variance or minimize the projection error is why PCA is used . What I can't agree with however is the lecturer telling that PCA is used to cluster data . I don't think this is necessarily true . PCA clusters those features which are highly correlated together . It doesn't cluster the data points when they are represented using the new basis vectors . I hope I am not wrong
PCA clusters features by creating new axis, which can help to identify correlations for feature-engeneering.
However you can still do actual clustering among the new axis and that wouldn't be affected by PCA at all, because data still has the exact same hyperdimensional relative positions, just the axis are shifted.
I seriously watch these videos for fun
Dutch angle is highly appropriate in this topic) Well done, cameraman :)
Beautiful explanation with the minimization of error
As I shall mention in my blog, There is a Method to Dr Mike's Madness. Brilliant!
Great explanation. THANK YOU!
A very nice explanation! Thanks!
Congratulations again for a great video. Thank you!
ridiculously understandable explained! thank you very much!
Outstanding explanation. Thank you, thank you, thank you!
Best explanation came upon so far!!
Very nice explanation. I almost never subscribe but you got me. Thank you.
Thanks Dr. Mike, really helpful!
Great video. I also enjoyed the throwback stripey dot-matrix printer paper :)
Genius explanation
Excellent video
Great Video. I guess I would never forget PCA
You saved me! Excellent video!!!
Extra points for using R! Very much approved! Lovely! (:
Thank you for the explanation.
Thank you for this video.
I wonder how mike learned so much if computerphile could give me the book from where we can extend the horizon??
"A new principal component is gonna come out orthogonal to the ones before, until you run out of dimensions and you can't do it anymore."
- poetry
5:25 Why you have not constructed a center of data? Project points to both X and Y axis, calculate both averages and then draw perpendiculars where these averages will intersect which will be a center of dataset
This is great content. It genuinely makes me want to pick RStudio and try to learn data analysis.
thank you this made life easier .......i love your accent
What if you take these new axis (PC1, PC2, PC3...) and do a PCA again? Will they spread even more, or will they give the same exact result?
You'd get the exact same result, as with the constraints given in PCA, the solution is unique.
The solution is not unique, since pca was already applied the new axis are non correlated, therefore applying pca could at best perform a rotation of axis, replacing ax by -ax.
Great video Peter Parker
Great explanation
brilliant, thanks!
amaziiiing
Brilliant, thanks!
Well that escalated quickly!
SVD when? Mike might also consider mentioning SVD approximation for convolutions, neural networks, etc.
If you are using PCA, in all likelihood you were applying SVD at some point (maybe without realizing it).
If I remember multivariate statistics correctly, the name "factor analysis" comes to mind. Indeed, I like PCA better.
How do you get column names of that 133 features that make up PCA1 for submitting that as a data frame for Kmeans?
Thanks for this
Why does minimizing the error means maximizing the variance?
I think you're minimizing the error when you're fitting a line (which will be the new axis) to existing data points from two previous dimensions. Thus, this error is (as it was mentioned in the video) the summed squared differences between each actual data point and the line that you're trying to fit.
Judging by his sketch, PCA tries to maximize variance along PC1 axis, while at the same time minimizing error along all the axes orthogonal to PC1, then does the same for PC2 and so on.
Recall his fists; the line of best fit would pierce these two data points and introduce the axis that can directionally pivot the data to reveal greater variance (spread) as observed by the space between his hands as he turned them along that newly introduced axis
i fall in love:D
Good stuff. Is the "weighted sum" the frobenius norm or related? I'm following a book and I'm trying to compare how it is teaching this to how it is explained in other forms of media like youtube videos.
That maximizes the variance=r2? Bc it seems like p1 was tvhere to minimize the variiance between the linne and the points no?
Cool 😎
And what is the benefit of doing PCA? Are we training our neural networker quicker or why would I do this? I still have to collect all the variables, so what is the point?
Could not find the dataset. Could you please give a dropbox or drive link.
5:34 why when we rotate the axis data also split out as 2 clusters?
It is partly a coincidence, but not really. PCA1 gives you the axis that spreads out and separates your data the most (greatest variance). Because your data (from two dimensions) is now separated into one dimension, you can see if there are data points that correlate with eachother.
What about Exploratory Factor Analysis?
Why minimum distance of data points from the principal axis ensure the maximum length of the axis? Can someone explain or maybe I got something wrong?
But how do we make use of principle components afterwards, despite the fact that we can’t interpret the components since they no longer represent the original variables? Without interpretability, can PC still be useful? What can PC still tell us?
they do represent the original variables, what you have to do is to go through the weights and try to make sense of what kind of hidden variable the PC is representing
Hey quick question for anyone out there. I'm failing to see if there's a difference between the principal component 1 and the linear regression. It seems to me they are the same thing. It is my understanding that
Btw sorry bad english, not a native speaker.
Really not the same but clearly there is a link between both, one could transform pca optimization problem into a special regression using frobenus norm and basic algebra.
Performing pca you look for non correlated axis, this is simply not the case for regression.
What.does ' foggin all ' mean?...at 8.47 time in video
He's saying 'orthogonal', meaning the second principal component is going to be at a 90 degree angle to the first one. Orthogonal is used since it describes this relationship without ambiguity for higher than 2 dimensions as well. It simply means that the two axes are completely uncorrelated.
@@jfagerstrom u mean he is pronouncing orthogonal as' foggin all" ?... It's in subtitles also
@@pranayyanarp4118 it's just his accent. The person who wrote the subtitles probably heard it the same way you did. He is for sure saying orthogonal though, it's the only thing that makes sense
@@jfagerstrom thanx man
don't watch the video if you know nothing about pca , come back after you know what is it from StatQuest or other channels
11:58
@ 9:45 starts r
Dr. Mike can you teach me privately please. . .
"sponsorship from by Google" - was this piece of English generated by Google's AI?
Dude, please use data.table::fread() instead of read.csv() for larger data
I agree, dude.
Dude
dude
“Orffogonal”
auto-generated subs pleaseeee!!!!!
It was nice but could have been better and longer if maths were included..