Cosine Similarity, Clearly Explained!!!

[@statquest]

To learn more about Lightning: lightning.ai/ Support StatQuest by buying my book The StatQuest Illustrated Guide to Machine Learning or a Study Guide or Merch!!! statquest.org/statquest-store/

[@marchanselthomas]

The explanation is so clean. I was clapping for him from my room. How can someone be so good at their job!

[@statquest]

Thank you! :)

[@nuridaw9586]

I clapped too, twice! :)

[@jwilliams8210]

You are EXCEPTIONALLY good at CLEARLY describing complex topics!!! Thank you!

[@statquest]

Thank you very much! :)

[@usamsersultanov689]

I think and hope that this video is a preamble for more comlex NLP topics such as Word Embeddings etc.. many thanks for all of your efforts!

[@statquest]

Yes it is! :)

[@xanderortega4359]

Cosine Similarity is used as an evaluation tool on word2vec

[@mattgenaro]

Such a simple, yet, a beautiful and powerful concept of similarity. Thanks, StatQuest!

[@statquest]

bam!

[@nossonweissman]

You literally make it so easy!! I can't help but smile 😊😊😊❤️❤️❤️ By far one of my favorite KZbin channels!

[@statquest]

Thank you so much! :)

[@insaiyancvk]

Wonderfully explained, Josh! You've earned a subscriber!

[@statquest]

Thank you!

[@jasonlough6640]

Dude these are so good. I have to watch them several times, and then I try write some code to reinforce the concept. Your vides are absolutely amazing.

[@statquest]

Thank you!

[@tysontakayushi8394]

I usually hate when people say that a video explains well, because usually this is not the case. But, haha, amazing job! Well done, really nice explained, it's a gamification, they way I understand!

[@statquest]

Thanks!

[@virenpai9395]

My Love for learning Data Science and Statistics has increased multi-folds because of you. Thank you Josh!!🙂

[@statquest]

bam! :)

[@kforay42]

Your videos are such a lifesaver! Could you do one on the difference between PCA and ICA?

[@statquest]

I'll keep that in mind.

[@torley]

QUADRUPLE BAM!!! Thanks for such fun yet pragmatic explainers.

[@statquest]

Thank you!

[@dukeduke1910]

This guy is seriously funny. I thought I was the only person who ever watched gymkata (like 50 times, especially the part in the town where everyone was crazy). This video def explains cosine sim clearly. Thk u!

[@statquest]

BAM! :)

[@olucasharp]

It all seems so easy when you speak about such complicated things! Huge talent! And so funny ⚡⚡⚡

[@statquest]

Thank you!

[@KarthikNaga329]

This is another great video, Josh! question: @3:51 you talk about having 3 Hellos and that still results in a 45 degree angle with Hello World. However, comparing Hello to Hello World seems to be a diff angle from comparing Hello to Hello World World. Is there an intuition as to why this is the case? That is adding as many Hellos to Hello keeps the angle the same, but adding more Worlds to Hello World seems to change the Cosine Similarity.

[@statquest]

Two answers: 1) Just plots the points on a 2-dimensional graph for the two pairs of phrases and you'll see that the angles are different. 2) The key difference is that "hello hello hello" only contains the word "hello". If we had included "world", then the angles would be different. Again, you can plot the points to see the differences.

[@bladongarland8635]

Hilarious, easy to understand, and entertaining. Bravo!

[@statquest]

Glad you enjoyed it!

[@user-yd8sr9ot9u]

wow thankyou!!! i don't know how to calculate it , but after watching this, i become mathmatician!!

[@statquest]

bam!

[@raphaelbonillo2192]

Você democratiza a matemática! Deveriam fazer assim nas escolas.

[@statquest]

Muito obrigado!

[@magicfox94]

Excellent explaination! I hope it is the first of a NLP series of videos!

[@statquest]

I hope to do word embeddings soon.

[@bjornnorenjobb]

Awesome video! I had no idea what Cosine Similarity was, but you explained super clearly

[@statquest]

Thanks!

[@suzhenkang]

pretty good .

[@AreyHawUstad]

Holy shit did I land on a gold mine. Love the explanation (minus the intro, sorry Josh). Thanks a bunch!

[@statquest]

Thanks!

[@FreeMc54]

you are insane at explaining clearly, btw you sing really well😂

[@statquest]

Thanks! 😃

[@spambaconeggspamspam]

Perfect! I'm trying to figure out how to best present my Single Cell Data in a UMAP and saw i cosine is the default distance metric in Seurat!

[@statquest]

BAM! :)

[@ibrahimogunbiyi4296]

I came here as I need to learn something in NLP. Thank you, I understood it clearly.

[@statquest]

BAM! :)

[@RichardGreco]

Great video. Very interesting. I hope to see you apply this to more examples.

[@statquest]

We'll see it used in CatBoost for sure.

[@abdulrafay2420]

What a great way of explaination !! Love it ❤

[@statquest]

Thanks!

[@infraia]

Excellent explanation!

[@statquest]

Thanks!

[@theedspage]

Hello! Hello! Hello! Thank you for introducing me to this topic! Subscribed.

[@statquest]

Awesome! Thank you!

[@Ghulinzer]

Great video! I've seen though in many articles out there that people consider cosine similarity the same as Pearson's correlation since they produce the same outcome when E(X) = E(Y) = 0 and the means of X and Y = 0. This is not true since both measure different things. Cosine similarly measures the cosine of the angle between two vectors in a multi-dimensional space and returns a similarity score as explained in the video, while Pearson's correlation measure the linear relationship between 2 variables.

[@statquest]

Correct!

[@user-yu7ie2em5b]

You really are the best !

[@RaynerGS]

I love you!!!! Salute from Brazil.

[@statquest]

Muito obrigado! :)

[@davidmurphy563]

Could you cover discrete cosine/fourier transforms pretty please?* I've love to know how to break signals up into their component frequencies. If you haven't already!

[@statquest]

I'll keep that in mind.

[@Iiochilios1756]

Have you seen 3blue1brown video on this topic? Not sure if it about descreet FT.

[@exoticcoder5365]

I must watch Gymkata ! Thanks for the recommendation ! And excellent explanation of the topic !

[@statquest]

bam! :)

[@ericvaish]

How am I able to understand this topic? Wasn't this supposed to be difficult? 😭 Seriously Great Explanation Josh.

[@statquest]

Thank you!

[@user-kp8lw1nz7m]

you are the King Josh 👏👏👏👏 wonderful job!!!

[@statquest]

Thank you! 😃

[@MOROCCANFREEMIND]

The quality of your explanation is more than triple bam!!😂

[@statquest]

Thanks!

[@anuj5576]

Super simplistic explanation! Thanks for your effort.

[@statquest]

Thanks!

[@willw4096]

Great video! My notes: 3:52 4:23

[@statquest]

bam!

[@chrisguiney]

This video also does a good job highlighting how cosine and dot products are the same. Unless I'm mistaken, that equation can be written dot(a, b) / (magnitude(a) * magnitude(b)), where magnitude(x) = sqrt(dot(x, x))

[@statquest]

yep

[@suaridebbarma1255]

this video was absolutely a BAM!!

[@statquest]

Thanks!

[@DrKnowsMore]

Like most things, it is relatively straightforward when you remove the jargon

[@statquest]

bam! :)

[@azzahamed2063]

This is an AMAZING explanation !!

[@statquest]

Thank you!

[@limebro8833]

This video saved me, I cannot thank you enough.

[@statquest]

Bam! :)

[@AU-hs6zw]

You deliver the moment I need it. Thanks

[@statquest]

BAM! :)

[@abrahammahanaim3859]

Hey josh thanks for the video nice explanation.

[@statquest]

You bet!

[@muhammadazeemmohsin5666]

what's an amazing explanation. Thanks for the video.

[@statquest]

Thanks!

[@AmineBELALIA]

this video needs more views it is awesome

[@statquest]

Thank you! :)

[@fazelamirvahedi9911]

Thank you for making all of these informative, simple and precise videos. I wondered what happens if two phrases deliver the same meaning but have different orders of words, for instance: A) I like Gymkata. B) I really like Gymkata. In this case doesn't the extra adverb "really" in the second sentence disturb the phrase matrix? And one more question, if the three phrases have the same length and two of them have the same meaning but have used different words, like: A) I like Gymkata. B) I love Gymkata. C) I like volleyball. In this case, would the cosine similarity between A and B be more than A and C?

[@statquest]

In this video, we're simply counting the number of words that are the same in different phrases, however, you can use other metrics to calculate the cosine similarity, and that is often the case. For example, we could calculate "word embeddings" for each word in each phrase and calculate the cosine similarity using the word embedding values and that would allow phrases with similar meanings to have larger similarities. To learn more about word embeddings, see: kzbin.info/www/bejne/rJq9o4Kkf8ifj5I

[@bachdx2812]

thanks a lot. this kind of videos are super helpful for me !!!

[@statquest]

Thanks! :)

[@lifeisbeautifu1]

Thank you!

[@statquest]

Thanks!

[@millennialm1money500]

Great video 🎉

[@statquest]

Thank you 😁!

[@sciab3674]

thanks a lot. easy to understand

[@statquest]

Thanks!

[@chris-graham]

"in contrast, this last sentence is from someone who does not like troll 2" - I was expecting a BOOOO after that lol

[@statquest]

Ha! That would have been great.

[@jonathanramos6690]

Amazing!!

[@statquest]

Thanks!

[@debatradas1597]

Thank you so much

[@statquest]

You're most welcome!

[@murilopalomosebilla2999]

Hello!! Nice video!

[@statquest]

Thank you!

[@kavita8925]

Your Explanation is great

[@statquest]

Thanks!

[@edmiltonpeixeira3221]

Parabéns pelo conteúdo. Excelente explicação, como não encontrei em nenhum outro vídeo

[@statquest]

Muito obrigado! :)

[@ymperformance]

Great video and great explanation! Thanks.

[@statquest]

Glad it was helpful!

[@gsp_admirador]

nice easy explanation

[@statquest]

Thanks!

[@banibratamanna5446]

the generalized equation of cosine similarity comes from the dot product of 2 vectors in multidimension.....by the way big fan of yours❤

[@statquest]

scaled to be between -1 and 1. :)

[@pouryajafarzadeh5610]

Cosine similarity is a good method for comparing the embedding vectors, especially for face recognition.

[@statquest]

Nice!

[@dataanalyticswithmichael8931]

superb ! Thank you for the explanation

[@statquest]

Thanks!

[@madhubabukencha5037]

Man you are not human, you are my god 😀

[@statquest]

:)

[@mystmuffin3600]

Cool! (in StatQuest voice)

[@statquest]

bam! :)

[@samrasoli]

useful, thanks

[@statquest]

Thanks!

[@smegala3815]

Very useful 👍

[@statquest]

Thank you! :)

[@miltonborges7356]

Amazing

[@statquest]

Thanks!

[@CristianoGarcia10]

Excellent and clear video! I wonder why NLP applications use more often cosine distance rather than other metrics, such as euclidean distance. Is there a clear reason for that? Thanks in advance

[@statquest]

I'm not certain, but one factor might be how easy it is to compute (people often omit the denominator making the calculation even easier) and it might be nice that the cosine similarity is always between 0 and 1 and doesn't need to be normalized.

[@cartulinito]

Great video as we are used to.

[@statquest]

Thank you! :)

[@Levy957]

you are amazing

[@statquest]

Thanks!

[@Francescoct]

Great video! Have you made one for the Word Embeddings?

[@statquest]

Coming soon!

[@Shehab-Codes]

Thank you so much I had no idea what cosine similarity is and you illustrated it easily, appreciate it Btw how cosine similarity can result in -ve number

[@statquest]

The cosine similarity can be calculated for any 2 sets of numbers, and that can result in a negative value.

[@luizcarlosazevedo9558]

Hey, great video as always!! Is the cosine similarity good for regression problems in which the targets are pretty close to zero? Im trying to implement some accuracy metrics for a transformer model

[@statquest]

Hmm... I bet it would work (if you had a row of predictions and a row of known values).

[@AxDhan]

I'm a native spanish speaker, and it surprised me when it started speaking spanish, it will reach more people, but they will miss your motivating silly songs xD

[@statquest]

Thanks! Yeah - I'm not sure what to do about the silly songs. :)

[@lonok84]

Wow, I used this to make a bot from whatsapp, to put client on flow/menu based on the first message from client

[@statquest]

bam!

[@yuan8947]

Always thank you for the great and easy-understanding video! And I have a question about the totally different word. If there are 2 sentences like very good/super nice, since very, good, super, nice are totally different, the cosine similarity will be 1. However, they are actually the same meaning! I want to ask what else preprocessing should we do toward such situation? Thank you so much!

[@statquest]

I think you might need more context (longer phrases) to get a better cosine similarity. I just used 2 words because I could draw them, but in practice, you use more.

[@itSinger]

tysm

[@statquest]

Thanks!

[@XEQUTE]

You're kinda like Phil from Mordern Family but for Data Science/ Statistics

[@statquest]

:)

[@cheesus8594]

Great explanation but I can’t believe how pissed I got when u kept repeating hello!!!!! And world!!! Omg

[@statquest]

noted

[@cheesus8594]

@@statquest thanks statquest🙏

[@s0meus3r]

I got it BAMM !!🎉

[@statquest]

BAM!

[@MrJ17J]

Super interesting ! Do you have examples of how those are implemented in practice ?

[@statquest]

I talk about that at the start of the video, but it's also used by CatBoost to compare the predicted values for a bunch of samples to their actual values.

[@SystemDesign-pro]

if you say DOUBLE BAM one more time, I'm goona FLMAO

[@statquest]

:)

[@aquagardening5803]

BAM!!!

[@statquest]

:)

[@nidhi_singh9494]

Hey...so cosine is only depends on angle not on lengths... When the case of three Hello were shown, how it can be distinguished between them as similarity is same for both sentence

[@statquest]

What time point, minutes and seconds, are you asking about?

[@fathan3306]

BAMMM!

[@statquest]

:)

[@jainanshu2000]

Great video ! One question - how is this diffrent from the regular string comparison we use various programming languages?

[@statquest]

I'm not sure I understand your question. My understanding of string comparison in programming languages is that it just compares the bits to make sure they are equal and the result is a boolean True/False type thing.

[@001kebede]

how can we relate this with correlation between two continuous random variables?

[@statquest]

See: stats.stackexchange.com/questions/235673/is-there-any-relationship-among-cosine-similarity-pearson-correlation-and-z-sc#:~:text=TL%3BDR%20Cosine%20similarity%20is,a%20norm%20of%20%E2%88%9An.&text=To%20convert%20a%20z%2Dscore,function%20for%20a%20Gaussian%20distribution.

[@raven-888]

Love you

[@tophat593]

Love you too

[@statquest]

:)

[@skiraf]

"Troll 2" should be considered 1 word. It refers to only one idea, the troll sequel movie which is different than the first troll movie.

[@statquest]

Sounds good to me!

[@arvindmathur5556]

Somewhere it says Cosine Similarity is a number between -1 and +1 but in other places it is said to be between 0 & 1. What is the truth?

[@statquest]

The cosine similarity can be between -1 and 1. If all the input data are positive (like they are in a bunch of the examples in this video, since we are just using count data, and count data is positive) then you'll be restricted to values between 0 and 1, but the data don't always have to be positive.

[@Mrnafuturo]

Does cosine similarity equation ends up being a vector normalization of the projection of one vector over the other one?

[@statquest]

I believe that is correct.

[@ZOBAER496]

Can you please tell about some applications of cosine similarity like where is it used in which type of problems?

[@statquest]

I talk about that at the start of the video, but you can also use it whenever you want to compare two rows of data. For example, CatBoost uses it compare predicted values for a bunch of data to their actual values.

[@sushi666]

Can you please do Spherical K Means with Cosine Similarity as the distance metric?

[@statquest]

I'll keep that in mind.

[@hansu7474]

What is the applications of cosine similarity?

[@statquest]

Umm... Did you watch the video? It's the first thing I talk about.

[@rajashreechakraborty747]

Can u please help me with this? This is my data: A: cosine: 0.58, z-score: 372 B: cosine: 0.63 , z-score: 370 How can I find the p-value/significance of the 0.5 change in the cosine similarities?

[@statquest]

We didn't cover p-values in the video.

[@PromitiDasgupta-mz7uc]

can i use cosine similarity for building a similarity matrix between two different brain regions?

[@statquest]

Probably.

[@Olddays100s]

but if the phrases are Hello World and World Hello. The cosine would still be 1. how to differentiate between them using cosine similarities? do algorithms introduce another dimension?

[@statquest]

Algorithms use other methods to keep track of word order. For example, transformers use positional encoding. To learn more, see: kzbin.info/www/bejne/sKm0qoeBbdaor7s

[@eddiesec]

I still don't understand how that works for embeddings though. Each embedding dimension should represent loosely a grammatical property of the words, than how can one word that is farther than another in a single dimension (as in your Hello Hello Hello example) be considered identical?

[@statquest]

I'll do a video on embeddings soon.

[@c.nbhaskar4718]

what is the formula if we have more than 2 sentences ??

[@statquest]

I believe you just calculate it for all combinations of the sentences.