The separability assumption (Donoho & Stodden, 2003; Arora et al., 2012a) turns non-negative matrix factorization (NMF) into a tractable problem. Recently, a new class of provably-correct NMF algorithms have emerged under this assumption. In this paper, we reformulate the separable NMF problem as that of finding the extreme rays of the conical hull of a finite set of vectors. From this geometri...

Recent research in machine learning has focused on breaking audio spectrograms into separate sources of sound using latent variable decompositions. These methods require that the number of sources be specified in advance, which is not always possible. To address this problem, we develop Gamma Process Nonnegative Matrix Factorization (GaP-NMF), a Bayesian nonparametric approach to decomposing sp...

Non-negative matrix factorization (NMF) condenses high-dimensional data into lower-dimensional models subject to the requirement that data can only be added, never subtracted. However, the NMF problem does not have a unique solution, creating a need for additional constraints (regularization constraints) to promote informative solutions. Regularized NMF problems are more complicated than conven...

In this article, the hyperspectral unmixing problem is solved with the nonnegative matrix factorization (NMF) algorithm. The regularized criterion is minimized with a hierarchical alternating least squares (HALS) scheme. Under the HALS framework, four constraints are introduced to improve the unmixing accuracy, including the sum-to-unity constraint, the constraints for minimum spectral dispersi...

Hyperspectral unmixing is an important technique for analyzing remote sensing images which aims to obtain a collection of endmembers and their corresponding abundances. In recent years, non-negative matrix factorization (NMF) has received extensive attention due its good adaptability mixed data with different degrees. The majority existing NMF-based methods are developed by incorporating additi...

Nonnegative matrix factorization (NMF) has been successfully applied in several data mining tasks. Recently, there is an increasing interest the acceleration of NMF, due to its high cost on large matrices. On other hand, privacy issue NMF over federated worthy attention, since prevalently image and text analysis which may involve leveraging (e.g, medical record) across parties (e.g., hospitals)...

Human action recognition is important in improving human life in various aspects. However, the outliers and noise in data often bother the clustering tasks. Therefore, there is a great need for the robust data clustering techniques. Nonnegative matrix factorization (NMF) and Nonnegative Matrix Tri-Factorization (NMTF) methods have been widely researched these years and applied to many data clus...

In this paper, we investigate the performance of classifierbased non-negative matrix factorization (NMF) methods for detecting overlapping acoustic events. We provide evidence that the performance of classifier-based NMF systems deteriorates significantly in overlapped scenarios in case mixed observations are unavailable during training. To this end, we propose a K-means based method for artifi...

In this paper, an incremental algorithm which is derived from Nonnegative Matrix Factorization (NMF) is proposed for background modeling in surveillance type of video sequences. The adopted algorithm, which is called as Incremental NMF (INMF), is capable of modeling dynamic content of the surveillance video and controlling contribution of the subsequent observations to the existing representati...

Non-negative matrix factorization (NMF) is becoming a popular tool for decomposition of data in the field of signal and image processing like Independent Component Analysis (ICA). In this study we are relaxing the requirement of non-negative data for NMF making the update equations simple and thus making it Matrix Factorization (MF) and implementing it on simulated Functional Magnetic Resonance...