11–19 of 19 posts
This 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.
Earlier 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).
Foundations of Data Science by Avrim Blum, John Hopcroft and Ravindran Kannan: https://www.cs.cornell.edu/jeh/book2016June9.pdf
This 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.
Is this a more formal treatment for algorithm that Simon Funk gave? http://sifter.org/~simon/journal/20061211.html
Also related is the 'alternating least squares' algorithm.
Earlier quoted context omitted.
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.
Related but different: Foundations of Data Science by Avrim Blum, John Hopcroft and Ravindran Kannan: https://www.cs.cornell.edu/jeh/book2016June9.pdf
Earlier 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?
Do they make use of the fact that smooth signals are sparse in DCT domain? Sure. But this has been true long before compressed sensing was a thing.
AFAIK the specific techniques of compressed sensing have not made their way into industry at all.
Not that they couldn't be applied, I'm fond of "Spatial Sparsity-Induced Prediction for Images and Video: A Simple Way to Reject Structured Interference".
(And, in my view it seems that compressed sensing almost completely diverted academic attention away from techniques that would be useful for signal compression in industry; maybe with a couple more orders of magnitude improvement in computing power the common techniques in that space will become more useful for compression.)
Related but different: Foundations of Data Science by Avrim Blum, John Hopcroft and Ravindran Kannan: https://www.cs.cornell.edu/jeh/book2016June9.pdf
Do you know what the prereqs are for high dimensional geometry? Any additional resources? From the looks of it, the subject seems to require the knowledge of some measure theory and functional analysis. Advanced undergrad/grad level math subjects. Threshold for entry here seems very steep (at least for high-dim geo).
This 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.