Comments on: Latent Semantic Indexing, SVD, and Zipf’s Law
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/
Cleve Moler is the author of the first MATLAB, one of the founders of MathWorks, and is currently Chief Mathematician at the company. He writes here about MATLAB, scientific computing and interesting mathematics.Sun, 06 Aug 2017 19:43:46 +0000hourly1https://wordpress.org/?v=4.7By: Tom Holden
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/#comment-6250
Sun, 06 Aug 2017 19:43:46 +0000http://blogs.mathworks.com/cleve/?p=2624#comment-6250I missed that somehow, sorry. But as something that is acceptably fast in MATLAB right now, double double surely wins. (Test my class to see!) And it’s not quite true that the exponent bits of the second double are ignored. Numbers that are 1+something_small are relatively common in numerical computing, and with double double, the exponent bits of the second double are used to insure that something_small is stored as accurately as it would be without the “1+”. In the kind of problems I work with, the need for big exponent ranges can always be simply fixed by working in logs (being careful with e.g. log(sum(exp(…))) of course).
]]>By: Cleve Moler
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/#comment-6249
Sat, 05 Aug 2017 18:41:43 +0000http://blogs.mathworks.com/cleve/?p=2624#comment-6249I did mention double double in my quad precision post, in the paragraph titled “Beyond Double”. One big advantage that quad precision has over double double is the much larger exponent range.
]]>By: Tom Holden
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/#comment-6248
Sat, 05 Aug 2017 16:37:57 +0000http://blogs.mathworks.com/cleve/?p=2624#comment-6248Hi Cleve,
In regards to your article on quadruple precision, on which the comments are now closed, a much better approach is to represent an extended precision number as an unevaluated sum of two or more double precision numbers. This permits the use of existing fast code for double precision math, including vectorisation. A fairly comprehensive implementation (though somewhat sparsely documented!) is available here: https://github.com/tholden/DoubleDouble
Hope this is of some interest.
Best regards,
Tom
]]>By: Cleve Moler
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/#comment-6247
Tue, 01 Aug 2017 18:34:55 +0000http://blogs.mathworks.com/cleve/?p=2624#comment-6247Thanks, Mike.
]]>By: Michael Berry
https://blogs.mathworks.com/cleve/2017/07/31/latent-semantic-indexing-svd-and-zipfs-law/#comment-6246
Tue, 01 Aug 2017 15:02:36 +0000http://blogs.mathworks.com/cleve/?p=2624#comment-6246Well done Cleve! Great illustration of Matlab for document parsing and SVD-based modeling of text.
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