1. A topic modeling system, comprising: at least one calculating unit; and at least one computer readable medium in communication with the at least one calculating unit and having instructions and a first equation stored therein, the first equation having terms including a term-document matrix D, a term-topic matrix U, a topic-document matrix V, a regularization of vectors of the term-topic matrix U and a regularization of vectors of the topic-document matrix V, the term-document matrix D having N columns, N>1, each column of the term-document matrix D representing a respective document and having M (M>1) members in which each member represents a respective term of the respective document, the term-topic matrix U and the topic-document matrix V are related such that the term-document matrix D is approximated by a matrix multiplication of the term-topic matrix U and the topic-document matrix V, when executed by the at least one calculating unit, cause the at least one calculating unit to perform acts comprising: for a number of iterations, minimizing the first equation while holding the topic-document matrix V fixed; updating the term-topic matrix U based at least on values of the topic-document matrix V calculated in a most recent minimization of the first equation; minimizing the first equation while holding the term-topic matrix U fixed; and updating the topic-document matrix V based at least on values of the term-topic matrix U calculated in a most recent minimization of the first equation.
10. The topic modeling system as recited in claim 1 , wherein the minimizing the first equation while holding the topic-document matrix V fixed includes the regularization of column vectors of the term-topic matrix U, and the minimizing the first equation while holding the term-topic matrix U fixed includes the regularization of column vectors of the topic-document matrix V.