N. Kutz, "Randomized nonnegative matrix factorization," Pattern Recognition Letters, vol. 104, pp. 1 - 7, 2018.Erichson NB, Mendible A, Wihlborn S, Kutz JN (2018). "Randomized Nonnegative Matrix Factorization." Pattern Recognition Letters....
where the first inequality uses that both yTBy and yTDBy are nonnegative. By taking the maximum with respect to all vectors of norm 1 one obtains ‖B−DB‖2 on the left-hand side, which shows that it is bounded by ‖B‖2. Now, the claimed result follows from Corollary 1 using the...
1.1Main Contributions There are two main contributions in this paper: (1) the generalization of the randomized singular value decomposition (SVD) algorithm for learning matrices from matrix-vector products to Hilbert–Schmidt (HS) operators and (2) a theoretical learning rate for discovering Green’s...
Fast Parallel Randomized Algorithm for Nonnegative Matrix Factorization with KL Divergence for Large Sparse DatasetsMathematics - Optimization and Controldoi:10.18178/IJMLC.2016.6.2.583Duy Khuong NguyenTu Bao HoarXiv
Nonnegative Tensor Factorization (NTF) is a particular case of such methods, mostly addressed for processing nonnegative multi-way arrays, such as hyperspectral observations or a set of images. One of the most efficient algorithms for NTF is the Hierarchical Alternating Least Squares (HALS) ...
Linear programming (LP) is used in many machine learning applications, such as `1-regularized SVMs, basis pursuit, nonnegative matrix factorization, etc. Interior Point Methods (IPMs) are one of the most popular methods to solve LPs both in theory and in practice. Their underlying complexity ...
Orthogonal nonnegative matrix factorization (ONMF) is widely used in blind image separation problem, document classification, and human face recognition. The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method. When...
For the localization problem of receiver failure in reverberant environments, a matrix completion algorithm that relies on the low-rank characteristic is developed for the Hankel matrices of received signals [18]. The non-negative matrix factorization (NMF) algorithm is utilized to calculate the low-...