Research On The Convergence Performance Of A Generalized Momentum To Accelerate The Non-negative Latent Factor Model

In the era of big data,many industrial applications often deal with a large number of entities and their corresponding high-dimensional relationships.However,the number of entities involved in industrial applications is increasing explosively,the relationship between them cannot be completely observed.Therefore,high-dimensional and sparse(HiDS)matrix is widespreadly used to describe these relationships in practice.Despite the HiDS matrices are extremely sparse,they contain a wealth of valuable knowledge.Therefore,how to extract such valuable information becomes a tricky and crucial problem.Among them,the fast non-negative latent factor analysis(FNLFA)model is compatible with a generalized momentum method on the basis of the single latent factor-dependent non-negative multiplicative update(SLF-NMU)algorithm,and can extract the latent factor from the HiDS matrix faster than the non-negative latent factor analysis(NLFA)model.Unfortunally,we do not know how the generalized momentum method accelerates the SLF-NMU algorithm,which is extremely crucial for analyszing HiDS matrix.Notably,the main contents and innovations are presented as follows:(1)An analogy analysis is conducted between a single latent factor-dependent,non-negative,multiplicative and momentum-incorporated update(SLF-NM~2U)algorithm of FNLFA model and Newton's equations to prove that the momentum term is equivalent to the mass in Newton's equations.(2)In both discrete and continuous cases,the theory proves how the generalized momentum accelerates the NLFA model,and the corresponding acceleration conditions of the generalized momentum are obtained.(3)The experiment verifies the momentum acceleration condition in the discrete case and proves that the generalized momentum accelerates the convergence of the NLFA model.