  We present a converged algorithm for Tikhonov regularized nonnegative matrix
factorization (NMF). We specially choose this regularization because it is
known that Tikhonov regularized least square (LS) is the more preferable form
in solving linear inverse problems than the conventional LS. Because an NMF
problem can be decomposed into LS subproblems, it can be expected that Tikhonov
regularized NMF will be the more appropriate approach in solving NMF problems.
The algorithm is derived using additive update rules which have been shown to
have convergence guarantee. We equip the algorithm with a mechanism to
automatically determine the regularization parameters based on the L-curve, a
well-known concept in the inverse problems community, but is rather unknown in
the NMF research. The introduction of this algorithm thus solves two inherent
problems in Tikhonov regularized NMF algorithm research, i.e., convergence
guarantee and regularization parameters determination.
