A nonlinear orthogonal non-negative matrix factorization approach to subspace clustering

A Nonlinear Orthogonal Non-Negative Matrix Factorization Approach to Subspace Clustering

A recent theoretical analysis shows the equivalence between non-negative matrix factorization (NMF) and spectral clustering based approach to subspace clustering. As NMF and many of its variants are essentially linear, we introduce a nonlinear NMF with explicit orthogonality and derive general kernelbased orthogonal multiplicative update rules to solve the subspace clustering problem. In nonlin...

A new approach for building recommender system using non negative matrix factorization method

Nonnegative Matrix Factorization is a new approach to reduce data dimensions. In this method, by applying the nonnegativity of the matrix data, the matrix is ​​decomposed into components that are more interrelated and divide the data into sections where the data in these sections have a specific relationship. In this paper, we use the nonnegative matrix factorization to decompose the user ratin...

A Purely Geometric Approach to Non-Negative Matrix Factorization

We analyze the geometry behind the problem of non-negative matrix factorization (NMF) and devise yet another NMF algorithm. In contrast to the vast majority of algorithms discussed in the literature, our approach does not involve any form of constrained gradient descent or alternating least squares procedures but is of purely geometric nature. In other words, it does not require advanced mathem...

Non-negative matrix factorization

Non-negative Matrix Factorization Approach to Blind Image Deconvolution

A novel approach to single frame multichannel blind image deconvolution is formulated recently as non-negative matrix factorization (NMF) problem with sparseness constraint imposed on the unknown mixing vector. Unlike most of the blind image deconvolution algorithms, the NMF approach requires no a priori knowledge about the blurring kernel and original image. The experimental performance evalua...