We use a multiscale approach to reduce the time to produce the nonnegative matrix factorization (NMF) of a matrix A, that is, A ≈ WH. We also investigate QR factorization as a method for initializing W during the iterative process for producing the nonnegative matrix factorization of A. Finally, we use our approach to produce nonnegative matrix factorizations for classifying images and compare ...

We propose an extension of nonnegative matrix factorization (NMF) to multilayer network model for dynamic myocardial PET image analysis. NMF has been previously applied to the analysis and shown to successfully extract three cardiac components and time-activity curve from the image sequences. Here we apply triple nonnegative-matrix factorization to the dynamic PET images of dog and show details...

In non-negative matrix factorization, it is difficult to find the optimal non-negative factor matrix in each iterative update. However, with the help of transformation matrix, it is able to derive the optimal non-negative factor matrix for the transformed cost function. Transformation matrix based nonnegative matrix factorization method is proposed and analyzed. It shows that this new method, w...

Even though Nonnegative Matrix Factorization (NMF) in its original form performs rank reduction and signal compaction implicitly, it does not explicitly consider storage or transmission constraints. We propose a Frobenius-norm Quantized Nonnegative Matrix Factorization algorithm that is 1) almost as precise as traditional NMF for decomposition ranks of interest (with in 1-4dB), 2) admits to pra...

Nonnegative matrix factorization (NMF) aims at factoring a data matrix into low-rank latent factor matrices with nonnegativity constraints on (one or both of) the factors. Specifically, given a data matrix X ∈ RM×N and a target rank R, NMF seeks a factorization model X ≈WH>, W ∈ RM×R, H ∈ RN×R, to ‘explain’ the data matrix X, where W ≥ 0 and/or H ≥ 0 and R ≤ min{M,N}. At first glance, NMF is no...

In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Most NMF methods assume that each factorizing matrix appears only once in the approximation, thus the approximation is linear in the factorizing matrices. We present a new class of approximative NMF methods, called Quadratic Nonnegative Matrix Factorization (QNMF), wh...