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

Four algorithms to solve symmetric multi-type non-negative matrix tri-factorization problem