Lecture Notes on Randomized Linear Algebra (2013)
1–10 of 19 posts
Re: Lecture Notes on Randomized Linear Algebra (2013)
#2This stuff is incredibly useful when dealing with large matrices. The idea is that an n-by-n matrix often doesn't contain n^2 pieces of independent information, but can be written a product of matrices of size at most n-by-r (for r It should be noted that this overview dates from 2013 and that a lot of new results have appeared since then. The author gives some good references in the abstract.
Re: Lecture Notes on Randomized Linear Algebra (2013)
#3This is a very good and timely compilation of all the important topics!
I ask this earnest question because I have a deep interest in randomized linear algebra, random projections, 'sketching'/sampling, compressive sensing, etc.:
Do any of you use it in industry applications? If so, at a high level, how do you use it?
I know I'm asking a "I have a hammer and that is a nail"-type question, but I am interested in seeing "deployable" applications of these topics. I don't have any to report, other than academic ones.
Re: Lecture Notes on Randomized Linear Algebra (2013)
#4This is a very good and timely compilation of all the important topics! I ask this earnest question because I have a deep interest in randomized linear algebra, random projections, 'sketching'/sampling, compressive sensing, etc.: Do any of you use it in industry applications? If so, at a high level, how do you use it? I know I'm asking a "I have a hammer and that is a nail"-type question, but I am interested in seein…
Compressive Sensing is widely used in imaging.
https://en.wikipedia.org/wiki/Compressed_sensing#Application...
Re: Lecture Notes on Randomized Linear Algebra (2013)
#5This is a very good and timely compilation of all the important topics! I ask this earnest question because I have a deep interest in randomized linear algebra, random projections, 'sketching'/sampling, compressive sensing, etc.: Do any of you use it in industry applications? If so, at a high level, how do you use it? I know I'm asking a "I have a hammer and that is a nail"-type question, but I am interested in seein…
Compressive Sensing is widely used in imaging. https://en.wikipedia.org/wiki/Compressed_sensing#Application...
Not a great example. Compressive imaging is (was?) a hot research area but hasn't made the transition to industry. I can think of only a single commercial product that relies on compressive sensing.
Re: Lecture Notes on Randomized Linear Algebra (2013)
#6Earlier quoted context omitted.
Compressive Sensing is widely used in imaging. https://en.wikipedia.org/wiki/Compressed_sensing#Application...
Not a great example. Compressive imaging is (was?) a hot research area but hasn't made the transition to industry. I can think of only a single commercial product that relies on compressive sensing.
Don't most lossy codecs make use of compressed sensing?
Re: Lecture Notes on Randomized Linear Algebra (2013)
#7This is a very good and timely compilation of all the important topics! I ask this earnest question because I have a deep interest in randomized linear algebra, random projections, 'sketching'/sampling, compressive sensing, etc.: Do any of you use it in industry applications? If so, at a high level, how do you use it? I know I'm asking a "I have a hammer and that is a nail"-type question, but I am interested in seein…
Compressive Sensing is widely used in imaging. https://en.wikipedia.org/wiki/Compressed_sensing#Application...
I'm reasonably well plugged into that community. All the applications there are 'academic' applications. There are efforts to build hardware based on this- startups, etc. However, the translation is still slow and nowhere near as fast as what we saw with deep learning (just comparing apples and apples with apples defined as step-change jumps in research).
Re: Lecture Notes on Randomized Linear Algebra (2013)
#8Earlier quoted context omitted.
Compressive Sensing is widely used in imaging. https://en.wikipedia.org/wiki/Compressed_sensing#Application...
I'm reasonably well plugged into that community. All the applications there are 'academic' applications. There are efforts to build hardware based on this- startups, etc. However, the translation is still slow and nowhere near as fast as what we saw with deep learning (just comparing apples and apples with apples defined as step-change jumps in research).
How many startups are operating in the CS imaging area? I only know of InView. Rambus likes to sell their lensless sensor as "compressive", but it doesn't really fit.
Re: Lecture Notes on Randomized Linear Algebra (2013)
#9Earlier quoted context omitted.
Not a great example. Compressive imaging is (was?) a hot research area but hasn't made the transition to industry. I can think of only a single commercial product that relies on compressive sensing.
Don't most lossy codecs make use of compressed sensing?
It's tricky. You need to define what "compressed sensing" is. Of course, for 10 years, anything with a hint of sparsity has had the "compressed sensing" buzzword added, even though these ideas are decades old.
Many lossy codecs utilize the fact that the signals of interest (audio, video, images, whatever) are sparse when viewed in some transform domain- Fourier or wavelet. We apply the transformation and retain only the largest coefficents- these get quantized and transmitted, and then we use the inverse transformation to reconstruct our signal. The 'loss' comes from the thresholding/quantization procedure. It's certainly sparsity driven, but I wouldn't call it "compressed sensing".
"Compressed sensing" should mean "stable reconstruction of my signal using data that is acquired at an optimal rate". The "optimal rate" is roughly proportional to the sparsity of the signal.
Check out the first section of [1].
Re: Lecture Notes on Randomized Linear Algebra (2013)
#10This stuff is incredibly useful when dealing with large matrices. The idea is that an n-by-n matrix often doesn't contain n^2 pieces of independent information, but can be written a product of matrices of size at most n-by-r (for r It should be noted that this overview dates from 2013 and that a lot of new results have appeared since then. The author gives some good references in the abstract.
Sparse x low-rank: if you collected every cell in the matrix, you paid too much for your sensor :-)
Emmanuel Candes' lectures on compressed sensing changed my life.