How Linear Algebra Powers Machine Learning (ML)

5:59 I think you mean when cos(theta) = 1 , not -1 for the first of those.

How on earth do you all do these lectures while writing on glass In backwards.. its blowing my mind

05:59 – Great explanation! To recap: when two vectors point in the exact same direction angle theta is 0, so cos(theta) = 1. This represents maximum similarity.

Thank you, Ms. Lee, for such an excellent presentation. I think my neurons are on fire... By using either method to measure similarity, does this give clues to dimensionality reduction? I understand the concept of matrix reduction, but it seems that matrix vectorization (factorization -term?) could be approached in many directions and that deciding on a way to partition data is part of the problem (especially when moving to multi-dimensional tensors). Also, since a opinion is a representation of an individual user's opinions, what are the problems/possibilities of using inference to develop a more global dataset, or using inference/extrapolation from other people's opinions (individual matrices/tensors)? Polling 10^8 different opinions would be inefficient and redundant, so how could data be assigned a "value" (i.e. a critic's opinion vs a casual viewer)? Can a property of "truthiness" (sorry for the Colbert reference) be used?

Thanks for posting continuously educational videos despite not so much views. This is the best channel for educational content. Keep going!

5:57 ERROR. CORRECTION NEEDED. She probably meant 1. NOT -1

Great explanation, but just a heads up: the first example should be *cos θ = 1*.

COS similarity -1 repeated :( First one should be read as COS similarity +1

I'm learning, and asking a question: 6:42 we cover cosine similarity of -1 for the second time. Is it safe to assume the first iteration should have been positive 1?

@ 6:51, shouldn't the 2 vectors that are heading the same direction be cosine positive 1? Cosine 1: are two vectors are pointing in the exact same direction (they are parallel). Cosine -1: are vectors that point in exactly opposite directions. Cosine 0: Two vectors are orthogonal (perpendicular), meaning they have no directional similarity.

Hello, thank you, a small mistake here, cos 0 = 1 not -1

Back in 2007, I had implemented these methods (from scratch, using Delphi/Pascal) to build a neural network for predicting the next day’s closing price of a stock, based on the previous year’s closing prices, in combination with the corresponding prices of other stocks.

Everyone at IBM is left-handed apparently.

you guys should drop these great content faster, i'm tired of waiting.

Amazing presentation! Super informative and explained well

What role does linear algebra play in diffusion models? Is it simply a loop where random noise is created, then a similarity to what is asked for is computed using the tools of linear algebra, then the data is permuted to get closer to what the user asked for and the loop continues until some agreed upon close enough value?

6:06 - I suddenly began to rethink my entire existence... 6:41 - ... drew me back to life

You made a very complex topic in a way that was clear and easy to understand. Thanks for the amazing job!

5:53 when the cosine similarity is equal to 1 (not negative 1), the two vectors point in the same direction.

Thank you for this course. I understand better the relationship between Linear algebra and Machine Learning. ❤🙏