Abstract: For the multiplicative updating rule in solving the non-negative matrix factorization, there were some shortcomings of high computational complexity an
d low iterative efficiency. We proposed a stochastic variance parameter adjusted gradient method. Combining the variance reduction strategy with the multiplicative updating rule, a parameter was adopted to adjust the stochastic gradient estimator, and the gradient descent direction was corrected to balance its deviation and variance, so as to reach the optimal solution quickly and accurately. Experiments were carried out on the real data sets, and the results verify the feasibility and effectiveness of the proposed algorithm.

Key words: non-negative matrix factorization, stochastic gradient descent, parameter adjusted gradient, variance reduction, multiplicative update