StatQuest: Linear Discriminant Analysis (LDA) clearly explained.

[@statquest]

NOTE: The StatQuest LDA Study Guide is available! statquest.gumroad.com Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@realcirno1750]

woohoo

[@WIFI-nf4tg]

Can you please do something on canonical analysis ?

[@statquest]

@@WIFI-nf4tg I'll keep that in mind.

[@falaksingla6242]

Hi Josh, Love your content. Has helped me to learn a lot & grow. You are doing an awesome work. Please continue to do so. Wanted to support you but unfortunately your Paypal link seems to be dysfunctional. Please update it.

[@aayushtheapple]

website shows "Error establishing a database connection" !

[@yuniprastika7022]

the funny thing is, so many materials from this channel are for those university students (like me) but he keeps treating us like kindergarten children. Haha feels like i'll never be growing up, by watching your videos sir! QUADRO BAAM SIR, THIS WORLD HAS BEEN GONE TOO SERIOUS, THANK YOU FOR BRINGING BACK THE JOY

[@statquest]

Thank you very much! :)

[@daisy-fb5jc]

I am a kindergarden kid in this subject : (

[@andrejalabama1204]

@@daisy-fb5jc same here; i need someone to explain it like im a little kid

[@SinoLegionaire]

Remember: Us Adults are just big children

[@bokai5829]

Every time I heard the intro music. I know my assignment is due in 2 days.

[@statquest]

LOL! :)

[@bokai5829]

@@statquest Thank you very much!

[@KonesThe]

hahahah I'm on the same boat right now

[@HenriqueEC1]

Good to know I'm not alone.

[@PJokerLP]

10,5 hours till my machine learning exam. Thank you so much, I feel way better prepared than if I would have watched all of my class material.

[@beccalynch4407]

Just spent hours so confused, watching my lectures where the professor used only lin alg and not a single picture. Watched this video and understood it right away. Thank you so much for what you do!

[@statquest]

Glad it helped!

[@robinduan1985]

This is amazing! 15 mins video does way better than my lecturer in an 2 hours class

[@elise3455]

While these 15 min videos are excellent for gaining intuition, you still often need those 2-hour classes to get familiar with the mathematical rigor.

[@NoahElRhandour]

@@elise3455 no you dont. math follows super quick and easy when you understood what it is about

[@GaganSingh-zz9el]

@@NoahElRhandour yeah brother

[@Jacob-t1j]

@@elise3455 No you don't. Math become super easy once you understand what you doing

[@seifeldineslam]

This was honestly helpful, i am an aspiring behavioral geneticist (Aspiring because I am still an undergraduate of biotechnology) with really disrupted fundamentals of math especially statics. Your existence as a youtube channel is a treasure discovery to me !

[@statquest]

Thanks! :)

[@Muzik2hruRain]

You, sir, you are a life saver. Now in every complicated machine learning topics I look for your explanation, or at least wonder how you would have approached this. Thank you, really.

[@statquest]

Awesome! Thank you! :)

[@haydo8373]

Hey what is the intro track called? I couldn't find it on Spotify. . . :D

[@hiteshjoshi3061]

It's their own

[@hiteshjoshi3061]

Listen carefully it's the channel name in it and is cool 😂😂👌

[@PV10008]

I really like the systematic way you approach each topic and anticipate all the questions a student might have.

[@sridharyamijala4739]

Another excellent video just as great as the one on PCA. I read a Professor's view on most of the models and algorithms stuff in ML where he recommended understanding the concepts well so that we know where to apply and not worry too much about the actual computation at that stage. The thing that is great in your videos is that you explain the concept very well.

[@statquest]

Thank you very much! :)

[@rachelstarmer9835]

Awesome! Even I get it and love it! I'm going to share one of your stat-quest posts as an example of why simple explanations in everyday language is far superior to using academic jargon in complex ways to argue a point. Also, it's a great example of how to develop an argument. You've created something here that's useful beyond statistics! Three cheers for the liberal arts education!!!! Three cheers for Stat-Quest!!

[@kshitijkumar6610]

Are you somehow related to Joshua? :-P

[@georgeshibley9529]

@@rachelstarmer5073 ha

[@merida3975]

The song at the beginning made my day, even though I took wrong tutorial of Linear discriminant analysis in data science. Just awesome. Love it a lot. We need more and more funny teachers like you.

[@statquest]

Thanks!

[@RaghuMittal]

Great video! I initially couldn't understand LDA looking at the math equations elsewhere, but when I came across this video, I was able to understand LDA very well. Thanks for the effort.

[@mahdimantash313]

I really can't thank you enough for that...you did in 16 mins what I couldn't do in 4 hours. keep on the good work!! and thank you again !!!

[@statquest]

Thanks!

[@phoenixflames6019]

10/10 intro song 10/10 explanation using PCA, I can reduce these two ratings to just one: 10/10 is enough to rate the whole video using LDA, the KZbin chapters feature maximizes the separation between these 2 major components (intro and explanation) of the video

[@statquest]

BAM!!! :)

[@lifeislarge]

Never thought anyone could explain things this easily. I appreciate the effort. Thank You

[@statquest]

Thank you! :)

[@neelkhare6934]

Wow , that is one of the best explanations of LDA it helped me get an intuitive idea about LDA and what it actually does in classification Thank You!

[@statquest]

Hooray! Thank you! :)

[@neelkhare6934]

Can you make a video on quadratic discriminant Analysis

[@statquest]

@@Sachin-vr4ms Which part? Can you specify minutes and seconds in the video?

[@statquest]

@@Sachin-vr4ms I'm sorry that it is confusing, but let me try to explain: At 9:46, imagine rotating the black line a bunch of times, a few degrees at a time, and using the equation shown at 8:55 to calculate a value at each step. The rotation that gives us the largest value (i.e. there is a relatively large distance between the means and a relatively small amount of scatter in both clusters) is the rotation that we select. If we have 3 categories, then we rotate an "x/y-axis" a bunch of times, a few degrees each time, and calculate the distances from the means to the central point and the scatter for each category and then calculate the ratio of the squared means and the scatter. Again, the rotation with the largest value is the one that we will use. Does that help?

[@statquest]

@@Sachin-vr4ms I'm glad it was helpful, and I'll try to include more "how to do this in R and python" videos.

[@neillunavat]

I am so glad this channel has grown to around 316k subscribers. Very well explained. The best of bests.

[@statquest]

Wow, thank you!

[@Azureandfabricmastery]

Hi Josh, Helpful to understand the differences between PCA and LDA and how LDA actually works internally. You're indeed making life easier with visual demonstrations for students like me :) God bless and Thank you!

[@statquest]

Glad it was helpful!

[@leeamraa]

among the best best 15 minutes you can spend on youtube! thank you.

[@statquest]

Wow, thanks!

[@adejumobiidris2892]

Thank you so much for helping me provide a faster solution for the confusion that has taken control of my head for 72h.

[@statquest]

Happy to help!

[@laurading7012]

I just graduated from high school, but your videos helped me understand many research papers. Thank you very much!!!!!

[@statquest]

BAM and congratulations!!! :)

[@138shreyshekhar2]

@@statquest DOUBLE BAM !!

[@nishisaxena4831]

much better than my university lecture that I listened to twice but couldn't understand ... this was awesome, thanks!

[@statquest]

Hooray! I'm glad the video was helpful. :)

[@rohil1993]

This explains the beauty of LDA so well! Thank you so much!

[@statquest]

Awesome! Thank you very much! :)

[@sassmos008]

wow... my professor has been trying to teach me the concepts for weeks. and now I finally understand. Thank you so much. I will refer this to my mates.

[@peterantley]

You are my hero. I am a senior hoping to get into data science and your videos are great and very helpful. Keep up the good work.

[@chemicalbiomedengine]

always excited when i look for a topic and its available on statquest

[@statquest]

Awesome! :)

[@scottsun9413]

Really great videos, saved me from my data science classes. I'm applying for graduate program at UNC, hope I can have the opportunity to meet the content creators sometime in the future.

[@statquest]

Best of luck!

[@balexander28]

All of your StatQuest videos are awesome! Thanks for using your time to help others! Much appreciated!

[@alis5893]

Josh. you are an amazing teacher. i have learned so much from you , a big thank you from the bottom ofmy heart. god bless you

[@statquest]

My pleasure!

[@elizabeths3989]

You are about to be the reason I pass my qualifying exam in bioinformatics 🙏🙏

[@statquest]

Good luck!!! BAM! :)

[@saiakhil1997]

I really liked how you compared the processes of PCA and LDA analysis. I got to know a different way to view LDA due to this video

[@statquest]

Bam!

[@alexhoneycutt8352]

This helped me understand LDA before my midterm! I could not wrap my head around how the functions worked and what they did, but I got an "ah-hah!" moment at 6:49 and I totally understand it now. Thank you for explaining this!

[@statquest]

Hooray! Good luck with your midterm. :)

[@hlatse98]

Brilliant video! Very helpful. Thank you.

[@Illinoise888]

Thanks for the video! I have an exam next week and even though its open book, I still didn't feel comfortable going into it. This video definitely helped!

[@statquest]

Good luck and let me know how it goes. :)

[@jahanvi9429]

the song in the introduction is always awesome. thanks lol! and very useful video

[@statquest]

Thanks!

[@hanaibrahim1563]

Amazing. Thank you for this excellent video. Explained everything super clearly to me in a super concise manner without all the academic jargon getting in the way.

[@statquest]

Glad it was helpful!

[@oklu_]

thank you for your kind, slow, and detailed explanation😭

[@statquest]

You’re welcome 😊!

[@rmiliming]

very clearly explained. the video is very enjoyable to watch too! Statquest has all that is needed to learn machine learning algos and stats well

[@statquest]

Thank you!

[@SeqBioMusic]

Awesome! It'll be good to give some differences of PCA and LDA. For example, PCA is studying the X. LDA is studying the X->Y.

[@DaveGogerly]

I love your stuff, you have the knack to explain things better than most!

[@statquest]

Thank you!

[@meng-laiyin2198]

@@statquest Thank you so much for this video. I tried to understand LDA by reading lots of materials (books, papers, etc.), but none of them can explain things as clear as you do. Really appreciate it!

[@statquest]

@@meng-laiyin2198 Thanks! :)

[@datoubi]

i recommended all your videos to my fellow students in the data analysis course

[@statquest]

Thank you very much! :)

[@jialingzhang1341]

Thanks for this brilliant video! One thing I think is worth mentioning or emphasizing is LDA is supervised and PCA is unsupervised.

[@statquest]

Noted

[@Dr.CandanEsin]

Too much time and effort spent, but they worth it. Best explanation I watched after six weeks of search. Cordially thank you.

[@statquest]

Thanks! :)

[@rodrigolivianu9531]

Great video! Just wanted to point out that LDA is a classifier, which involves a few more steps than the procedure described here, such as assumption that the data is gaussian. The procedure here described is only the feature extraction/dimensionality reduction phase of the LDA. G

[@statquest]

You are correct! I made this video before I was aware that people had adapted LDA for classification. Technically we are describing "Fisher's Linear Discriminant". That said, using LDA for classification is robust to violations to the gaussian assumptions. For more details, see: sebastianraschka.com/Articles/2014_python_lda.html

[@rodrigolivianu9531]

StatQuest with Josh Starmer That said, I must admit I am having a really hard time understanding how the fisherian and baysian approach lead to the same conclusion even with completely different routes. If you have any source on that it would be of enormous help for my sanity haha

[@aneeshmenon12]

woww........toooo goodddddddddddd.....dear Starmer...nothing to say..you are incredible...I am eagerly waiting for your next video...

[@arungandhi5612]

you are very cool bro. I aced my work at my research institute because of youuuuuuuu

[@statquest]

That's awesome!!! So glad to hear the videos are helpful. :)

[@ChaminduWeerasinghe]

Best explanation iv ever seen on ML. This is the first time iv watch ML youtube video without rewind :| .. Keep Up bro..

[@statquest]

Wow, thanks!

[@wtfJonKnowNothing]

I'm more aligned to hear and love the song than the lecture these days :)

[@statquest]

:)

[@amrit20061994]

"But what if we used data from 10k genes?" "Suddenly, being able to create 2 axes that maximize the separation of three categories is 'super cool'." Well played, StatQuest, well played!

[@statquest]

Thanks!

[@worldofbrahmatej2023]

Excellent! You are a better teacher than many overrated professors out there :)

[@statquest]

Thank you! :)

[@daisy-fb5jc]

I wish I can throw this video to my professor, and teach her how to give understandable lectures. Just a wish.

[@statquest]

:)

[@seant7907]

subscribed just because the way you described this topic is so simple and understandable. nice job!

[@statquest]

Thank you very much! :)

[@whasuklee]

Came for my midterm tomorrow, stayed for the intro track.

[@onurdemir353]

You are awesome.Eventually,I was able to reach understanding point of machine learning staffs thanks to you.

[@statquest]

Awesome! :)

[@LifeofTF]

Loved the explanation. Your channel has been a truly invaluable source for studying ML. I was wondering whether you could make a video on the differences/similarities along with use cases for KNN/LDA/PCA.

[@statquest]

I'll keep that in mind.

[@Anmolmovies]

Absolutely brilliant. Kudo's to you for making seem it so simple. Thanks!

[@alphabetadministrator]

Hello Josh. As always, thank you for your super intuitive videos. I won't survive college without you. I do have an unanswered conundrum about this video, however. For Linear Discriminant Analysis, shouldn't there be at least as many predictors as the number of clusters? Here's why. Say p=1 and I have 2 clusters. In this case, there is nothing I can do to further optimize the class separations. The points as they are on the line already maximizes the Fisher Criterion(between-class scatter/in-class scatter). While I do not have the second predictor axis to begin with, even if I were to apply a linear transformation on the line to find a new line to re-project the data on, it will only make the means closer together. Extending this reasoning to the 2D case where you used gene x and gene y as predictors and 3 classes, if the 3 classes exist on a 2D plane, there is nothing we can do to further optimize the separation of the means of the 3 classes because re-projecting the points on a new tilted 2D plane will most likely reduce the distances between the means. Now, if each scatter lied perfectly vertically such that as Gene Y goes up the classes are separated distinctly, then we could re-project the points on a new line(that would be parallel to the invisible vertical class separation line) to further minimize each class's scatter, but this kind of case is very rare. Given my reasoning, my intuition is that an implicit assumption for LDA is that there needs to be at least as many predictors as the number of classes to separate. Is my intuition valid?

[@statquest]

I believe your question might be answered in this video on PCA tips: kzbin.info/www/bejne/pYPZmKRva5uskMk

[@RaviShankar-jm1qw]

Simply superb! Awesome Josh!!!!

[@statquest]

Thank you very much! :)

[@hamzaghandi4807]

Besides this wonderful explanation, Your music is very good !

[@statquest]

Many thanks!

[@paulhamacher773]

This channel is pure gold!

[@statquest]

Thank you! :)

[@gptty]

I get it! You sir is the best lecturer in statistics

[@statquest]

Thanks!

[@saharafox2360]

That helped me a lot! Thank you sooo much! Now I'm ready for my exam tomorrow :)

[@statquest]

Best of luck!

[@nuttapatchaovanapricha]

Very useful and intuitive, also sick intro music right there as usual! xD

[@statquest]

I think this might be my favorite intro.

[@muskanjhunjhunwalla8505]

It was a very helpful video. I get to understand it in the first attempt only. Thanks a lot for this video sir.

[@statquest]

Hooray!!! I'm glad the video was so helpful! :)

[@sanketbadhe3572]

I just watched all your videos for intro track :P ......awesome tracks and nicely explained videos

[@statquest]

Awesome! :)

[@cnbmonster1042]

Amazing! I subscribed after watching your video only twice!

[@statquest]

Wow, thanks!

[@nintishia]

Once again, a fantastic job. Thanks, StatQuest.

[@statquest]

Thanks again!

[@wei-tingko7871]

I really like your channel, the explanation of concepts was clear and precise!!

[@statquest]

Thank you!

[@karannchew2534]

Like PCA, LDA "compress" the data into lower dimensions. But unlike PCA, it do so while keeping/maximising the classificability (separability) of the data according to the given classification, as much as possible. Data must already be classified to use LDA. Find the line (the new lower dimension) such that the difference between the means of two classes of data are maximised. At the same time, the variance among the data of the same class is minimised.

[@statquest]

:)

[@weixu553]

great video, you make all the academic terms very understandable, cheers from China

[@gaboceron100]

Very illustrative, thanks for the video!

[@statquest]

Thanks!

[@Pmarmagne]

Another clearly explained video by StatQuest!

[@statquest]

BAM! :)

[@sureshmakwana8709]

The best explanation on whole internet 💯

[@statquest]

Thank you! :)

[@duchuyho7027]

Great video Joshua ! Looking forward to learning more from you ! Cheers from Japan !

[@tomaszberent801]

The video shows how LDA reduces dimensions and we can clearly see a newly constructed axis (like with PCA) which - in LDA analysis - maximizes the separation. That was very clear!. How does this line relates to a line that actually separates the two categories on an original XY plain you refer to on 2:48 minute of your video?. After all it is this line (do we call it a discriminant function?) which is usually used to show the separation?. The latter is intuitively understood as a separation border, the former explains how we reduced dimension. What is the link between the two?

[@statquest]

That's a good question. There are a few options for coming up with a threshold that allows you to classify new observations into one of the categories in your training dataset. The simplest is to transform the new observation using the transformation that the training dataset created, and then measure the euclidean distance between the new observations and the center of each classification. The classification that is closest to the new observation is used to classify the new observation.

[@ThangPham-dx9ic]

Super interesting video! Your videos are much better than those boring equations on the books BTW, may I ask you a question? What you mean in "LDA for 3 categories" is number of LDs = number of categories - 1, right?

[@statquest]

Yes.

[@xujerry7891]

Hi, Joshua. Thank you for your videos, it’s really helpful. I have a question: so when you have a LDA to categorize n categories, does it mean that you need (n-1) axis to separate the points? In that case, how can I visualize them?

[@chieftainsupreme9387]

You're an excellent teacher. Thank you so much.

[@statquest]

Thank you! :)

[@eniisy]

This lesson is just so beautiful dude!!!!

[@statquest]

Thank you!

[@tomaszberent801]

Josh, BRILLIANT!!!! Some quations tough. 1) In what sense LDA generates the same separation as linear regresssion (however understood) as often claimed? Doesn't LDA use its own "optimazation" criterion, somewhat different from e.g. OLS? 2) Can we do ROC having identified a "separation line" between two categories using LDA? I am a bit confused here. As far as logistic regression is concerned, it is all clear: we can do ROC as different cutoffs are available to us after we estimate the curve. But with LDA, it looks to me that the "optimization" criterion defines (kind of) one cutoff point and we should not mess with it anyore, i.e. should not use other cutoffs for the line eatimated.. If I am correct, why are there so many research papers which estimate the z-scores (using LDA) and subsequently change the cutoff point to calculate specificity and sensitivity (or any other classification or misclassification metric), or ROC/AUC itself. Hopefully my inquiry is clear. Still I wish I was so clear as you are on those funny videos.

[@statquest]

LDA is totally different from Linear Regression. Way, way different. If you have questions about OLS, watch my videos: kzbin.info/www/bejne/hpKpgZWYa5t3rrM As for ROC - for LDA, if you are using Bayes' Theorem for Classification, then you can change the threshold you use for the posterior distribution. If you are not using Bayes' Theorem, and instead using K-means clustering on top of LDA, you can alter the values for "k".

[@livetolearn477]

Really great explanation. Thanks.

[@vishwanathg8083]

Thankyou , Explanation of LDA & PCA is very clear....

[@happylearning-gp]

Excellent Tutorial, Thank you very much

[@statquest]

Glad you liked it!

[@mrunalwaghmare]

love ur vids they are simple to understand

[@statquest]

Glad you like them!

[@mastermike890]

This is an AWESOME vid. Thanks for making this idea so simple

[@mohammadadnan8248]

Tomorrow is my exam, that might be helpful Thanks a lot from India

[@jennysspiceoflife8581]

Thank you for the illustration, it's very clear!

[@statquest]

Glad it was helpful!

[@EbraM96]

That musical intro is much fun :D

[@JalerSekarMaji]

Wow! At first "wt.f is Statquest" then At the end of video, STATQUEST! and I checked on the description. Its a great website ! Thanks

[@sakhawat3003]

Hey man! That was a nice clear cut explanation . I have been doing machine learning using LDA but I never knew what this LDA actually does . I only had a vague idea . By the way , you wrote "seperatibility" instead of "separability " at 5:26 ....

[@statquest]

That's embarrassing. One day when StatQuest is making the big bucks I will hire an editor and my poor spelling will no be source of great shame.

[@michaelgeorgoulopoulos8678]

Fav statQuest intro!

[@statquest]

I think this is my favorite as well. It's a classic!

[@mrdoerp]

this videos are incredible, i would pay for it if i had money

[@statquest]

Sometimes it's the thought that counts! I'm glad you enjoy the videos. :)

[@amanzholdaribay9871]

Thanks as every time! The best explanations of complicated things!

[@statquest]

Thanks!

[@namanjha4964]

Thank You very very very much, You bring joy to me

[@statquest]

Thank you!

[@MartinUToob]

When's the StatQuest album coming out? (Here come the Grammies!) 🎸👑 Actually, the only reason I watch your videos is for the music. 😍🎶🎵

[@greina6945]

Very nice explanation. The only issue I have is that the first and second axes for both PCA and LDA are not Gene 1 and Gene 2. They are instead some linear combination of Gene 1 and Gene 2. So in a 10,000 gene space, you will get some combination of some of the 10,000 genes that clearly separate the two groups. For example, LD1 could be one third of Gene 12 plus one third of gene 45 plus one sixth of gene 456 plus one sixth of gene 1,234.

[@BillHaug]

I would agree that "awesome song..." is an appropriate label.

[@statquest]

bam!

[@BillHaug]

@@statquest I would even say double bam... btw... "we're going to do a lot of maths step by step" = triple bam

[@statquest]

@@BillHaug Awesome!!! I love that you're a connoisseur of StatQuest themes!!!

[@ramarajugadiraju6886]

Very nice video . Admiring your passion and contribution !

[@statquest]

Thank you! :)

[@gauranggarg549]

Cant understand a topic and then u find a statquest video on it TRIPLE BAMM!!

[@statquest]

:)