  In this paper, we consider the symmetric multi-type non-negative matrix
tri-factorization problem (SNMTF), which attempts to factorize several
symmetric non-negative matrices simultaneously. This can be considered as a
generalization of the classical non-negative matrix tri-factorization problem
and includes a non-convex objective function which is a multivariate sixth
degree polynomial and a has convex feasibility set. It has a special importance
in data science, since it serves as a mathematical model for the fusion of
different data sources in data clustering.
  We develop four methods to solve the SNMTF. They are based on four
theoretical approaches known from the literature: the fixed point method (FPM),
the block-coordinate descent with projected gradient (BCD), the gradient method
with exact line search (GM-ELS) and the adaptive moment estimation method
(ADAM). For each of these methods we offer a software implementation: for the
former two methods we use Matlab and for the latter Python with the TensorFlow
library.
  We test these methods on three data-sets: the synthetic data-set we
generated, while the others represent real-life similarities between different
objects.
  Extensive numerical results show that with sufficient computing time all four
methods perform satisfactorily and ADAM most often yields the best mean square
error ($\mathrm{MSE}$). However, if the computation time is limited, FPM gives
the best $\mathrm{MSE}$ because it shows the fastest convergence at the
beginning.
  All data-sets and codes are publicly available on our GitLab profile.
