Algorithms for Nonnegative Tensor Factorization
نویسنده
چکیده
Nonnegative Matrix Factorization (NMF) is an efficient technique to approximate a large matrix containing only nonnegative elements as a product of two nonnegative matrices of significantly smaller size. The guaranteed nonnegativity of the factors is a distinctive property that other widely used matrix factorization methods do not have. Matrices can also be seen as second-order tensors. For some problems, it is necessary to process tensors of third or higher order. For this purpose, NMF can be generalized to Nonnegative Tensor Factorization (NTF). NMF and NTF are used in various application areas, for example in document classification and multi-way data analysis. The aim of this report is to give an overview over some algorithms to compute Nonnegative Tensor Factorizations, including two multiplicative algorithm based on the Alphadivergence and the Beta-divergence, respectively, two Hierarchical Alternating Least Squares algorithms and a Block Principal Pivoting algorithm utilizing matricization.
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