Non-negative matrix factorization (NMF) is a natural model of admixture and is widely used in science and engineering. A plethora of algorithms have been developed to tackle NMF, but due to the non-convex nature of the problem, there is little guarantee on how well these methods work. Recently a surge of research have focused on a very restricted class of NMFs, called separable NMF, where prova...

We apply the vectorized Non-negative Matrix Factorization (NMF) method to post-processing of direct imaging data for exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a non-orthogonal and non-negative basis of components using given reference images, then models a target with the components. The constructed model is then rescaled with a factor t...

Abstract Non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to mining machine learning community, due its advantages such as simple form, good interpretability less storage space. In this paper, we give detailed survey on existing NMF methods, including comprehensive analysis of their design principles, characteristics d...

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...

Non-negative matrix factorization (NMF) is one of the most popular decomposition techniques for multivariate data. NMF is a core method for many machine-learning related computational problems, such as data compression, feature extraction, word embedding, recommender systems etc. In practice, however, its application is challenging for large datasets. The efficiency of NMF is constrained by lon...

Data Clustering has been an active area of research in many different application areas, with existing clustering algorithms mostly focusing on partitioning one modality or representation of the data. In this study, we delineate and demonstrate a new, enhanced data clustering approach whose innovation is its exploitation of multiple data modalities. We propose BI-NMF, a bi-modal clustering appr...

The features of human lip motion from video clips are extracted by three unsupervised learning algorithms, i.e., Principal Component Analysis (PCA), Independent Component Analysis (ICA), and Non-negative Matrix Factorization (NMF). Since the human perception of facial motion goes through two different pathways, i.e., the lateral fusifom gyrus for the invariant aspects and the superior temporal ...

5 Abstract—Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factorsW andH, for the 6 given input matrix A, such thatA WH. NMF is a useful tool for many applications in different domains such as topic modeling in text 7 mining, background separation in video analysis, and community detection in social networks. Despite its popularity in the data min...

Non-negative matrix factorization (NMF) is a relatively new approach to analyze gene expression data that models data by additive combinations of non-negative basis vectors (metagenes). The non-negativity constraint makes sense biologically as genes may either be expressed or not, but never show negative expression. We applied NMF to five different microarray data sets. We estimated the appropr...

Nonnegative matrix factorization (NMF) is a popular dimension reduction technique that produces interpretable decomposition of the data into parts. However, this decompostion is not generally identifiable (even up to permutation and scaling). While other studies have provide criteria under which NMF is identifiable, we present the first (to our knowledge) characterization of the non-identifiabi...