51–60 of 84 posts
Now apply them to the data used to identify the "Big Five" personality traits! This is an interesting application of factor analysis/matrix factorization: https://en.wikipedia.org/wiki/Big_Five_personality_traits
The article presents a note on the 6 well known matrix compositions. He states that all of them have cubic complexity, but practical algorithms with better exponents exist for all of them.
Could you link a practical algorithm with an exponent lower than 3? (I think of these things https://en.wikipedia.org/wiki/Computational_complexity_of_ma... as not being practical, but I'd love to be wrong. )
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This decomposition is not used much because it is not unique in any sense, it is not numerically stable, and it is fairly uninteresting: the matrix D can always be taken to consist of a diagonal of 1s of length rank(A) and the rest zeros. It is much more interesting once X and Y are constrained to something like unitary matrices (in which case we get SVD). This “rank decomposition” is a bit interesting algebraically…
It's not unique, but it can be implemented in a way that is stable. E.g. SVD does this (but is quite overkill for the requirements). It's highly relevant from an algebraic perspective, hence it's curious that it's not covered (at all) in the numeric literature.
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It's always been very ambiguous in practice. To avoid ambiguity I usually use `flop/s` but not everyone likes that :)
> To avoid ambiguity I usually use `flop/s` but not everyone likes that :) Flop/s makes no sense and is outright wrong. The whole point of flops is to express how many floating point operations are required by an algorithm. How many operations are performed per second is a property of the hardware you're using to run an implementation of the algorithm. You want to express computational complexity in terms of floating…
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
The math used in ML papers is very diverse. There is too much to learn. It is easier if you pick a problem and learn the math for it. Find a group that is already working on that problem and ask them for best way to learn the math for it.
Any suggestions on what to learn in Linear Algebra after Gilbert Strang’s 18.06SC? https://ocw.mit.edu/courses/18-06sc-linear-algebra-fall-2011... My goal is to learn the math behind machine learning.
If you want a beautiful abstract perspective on linear algebra to complement Strang's more down-to-earth, matrix- and linear equation-oriented lectures, pick up Axler's Linear Algebra Done Right .
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It's always been very ambiguous in practice. To avoid ambiguity I usually use `flop/s` but not everyone likes that :)
Speaking of SVD doctors, I heard many years ago (from Alan Edelman) that Gene Golub's license plate used to be "DR SVD". Later he switched to "PROF SVD". I couldn't confirm the DR SVD part, but the PROF SVD story appears to be real: https://www.mathworks.com/company/newsletters/articles/profe...
Spectral decomposition is pretty cool. Application 1 - spectral clustering - an alternative to k-means for nonlinear clusters. Get a Distance matrix of your data, spectral decomp, run k-means on your k top eigen vectors and that's your clusters. Application 2 - graph clustering - (run spectral clustering on adj matrix!) There's some tricks to getting it to work in practice like normalizing but it's a simple and power…
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It's always been very ambiguous in practice. To avoid ambiguity I usually use `flop/s` but not everyone likes that :)
> To avoid ambiguity I usually use `flop/s` but not everyone likes that :) Flop/s makes no sense and is outright wrong. The whole point of flops is to express how many floating point operations are required by an algorithm. How many operations are performed per second is a property of the hardware you're using to run an implementation of the algorithm. You want to express computational complexity in terms of floating…
Missing the LDLT decomposition.
Bunch–Kaufman is the "right" factorization for indefinite Hermitian/symmetric matrices but it's not as well know.