## Multiplicative update for NMF is bad (Under construction)See my boss's work “Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization”, 2011. Without acceleration, MU is slow. With acceleration, A-MU is still, less competitive than A-HALS. But people still use MU for NMF. This is super unhealthy. ## Why people still use MU?## Why MU is badThe concept fo step size contraction
Why gradient descent (without being forced to satisfy the non-negativity constraint) plus projection is better
Theoretical convergence proof of projected gradient descent (with convergence rate) \ see Bolte().
## How about Kullback–Leibler divergence ?See Felipe Yanez and Francis Bach, “Primal-Dual Algorithms for Non-negative Matrix Factorization with the Kullback-Leibler Divergence” |