User sigmax - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T23:25:40Z http://mathoverflow.net/feeds/user/17301 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/77968/primes-are-to-irreducible-polynomials-as-prime-related-theorems-are-to Primes are to Irreducible Polynomials as Prime-related theorems are to ?? SigmaX 2011-10-12T22:28:37Z 2011-10-13T05:41:39Z <p>Irreducible polynomials are often introduced as the analog to prime numbers in polynomial rings. Prime numbers, of course, have a very rich theory, leading to the likes of the Riemann Zeta function and the Prime Number Theorem.</p> <p>Do any analogs and/or generalizations of primes, such as irreducible polynomials and prime elements, have similarly rich theorems/conjectures?</p> http://mathoverflow.net/questions/73371/what-is-the-mp-pseudoinverses-role-in-statistical-learning-and-self-organizing-m What is the MP pseudoinverse's role in statistical learning and Self-Organizing Maps? SigmaX 2011-08-22T00:10:35Z 2011-08-22T12:13:34Z <p>During a discussion in our lab last month, a professor mentioned to me that the behavior of Self-Organizing Maps can be described in terms of repeated applications of the Moore-Penrose psuedoinverse, in a vaguely similar way to how single-layer neural networks with Hebbian learning can be described by Principle Component Analysis.</p> <p>An engineering student friend of mine confirmed that the MP inverse is used for dimensionality reduction, but I can't find any material on this online. Can someone point me to an article, paper, or book on the subject?</p>