|M.Sc Student||Hadad Alon|
|Subject||Nonnegative Matrix Factorizations|
|Department||Department of Applied Mathematics||Supervisor||Professor Emeritus Abraham Berman|
The nonnegative matrix factorization (NMF) problem is : Given an nonnegative matrix A, find an nonnegative matrix U and an nonnegative matrix V such that r is small and UV approximates A.
NMF has recently been shown to be a very useful technique in approximating high dimensional data, where the data are comprised of nonnegative component.
Because of the nonnegativity constraint, NMF has the advantage that the matrices U and V have special meaning. In the thesis, this special meaning is explained and demonstrated in the context of text mining.
There are several algorithms for NMF, in the thesis we compare the main algorithm of Lee and seug with another algorithm of Patrick Hoyer and described the advantage of each method.
We also discuss the nonnegative rank problem : given an A, the problem is to find the smallest integer k, such that there are tow nonnegative matrices U of order and V of order such that , and the completely positive rank problem : given a square nonnegative matrix A of order n find, if possible, the smallest integer k, such that where B is a nonnegative matrix