Semiring is an algebraic structure with which some problems that are nonlinear in classical algebra, can be solved in a linear manner. By matrix factorization, decomposing input matrix into two (or more) matrices, various problems in data mining and machine learning can be solved. We present how the problems of finding properties of term-document matrices and forecasting electricity production of renewable resources can be solved by matrix factorization over semirings. We describe algorithm Cancer, one the algorithms for matrix factorization over different semirings and compare how each of them affects the results.
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