Often data can be represented as a matrix, e.g., observations as rows and variables as columns, or as a doubly classified contingency table. Researchers may be interested in clustering the observations, the variables, or both. If the data is non-negative, then Non-negative Matrix Factorization (NMF) can be used to perform the clustering. By its nature, NMF-based clustering is focused on the lar...

In this paper we explore avenues for improving the reliability of dimensionality reduction methods such as Non-Negative Matrix Factorization (NMF) as interpretive exploratory data analysis tools. We first explore the difficulties of the optimization problem underlying NMF, showing for the first time that non-trivial NMF solutions always exist and that the optimization problem is actually convex...

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data. On one hand, although traditional Laplacian regularization can enhance the performance of NMF, it still suffers from the problem of its weak extra...

Matrix factorization based methods have widely been used in data representation. Among them, Non-negative Matrix Factorization (NMF) is a promising technique owing to its psychological and physiological interpretation of spontaneously occurring data. On one hand, although traditional Laplacian regularization can enhance the performance of NMF, it still suffers from the problem of its weak extra...

We propose a method based on Cholesky decomposition for Non-negative Matrix Factorization (NMF). NMF enables to learn local representation due to its non-negative constraint. However, when utilizing NMF as a representation leaning method, the issues due to the non-orthogonality of the learned representation has not been dealt with. Since NMF learns both feature vectors and data vectors in the f...

In this paper, we propose a novel non-negative matrix factorization (NMF) to the affinity matrix for document clustering, which enforces nonnegativity and orthogonality constraints simultaneously. With the help of orthogonality constraints, this NMF provides a solution to spectral clustering, which inherits the advantages of spectral clustering and presents a much more reasonable clustering int...

Searching and mining biomedical literature database, such as MEDLINE, is the main source of generating scientific hypothesis for biomedical researchers. Through grouping similar documents together, clustering techniques can facilitate user’s need of effectively finding interested documents. Since non-negative matrix factorization (NMF) can effectively capture the latent semantic space with non-...

Non-negative Matrix Factorization (NMF) can learn interpretable parts-based representations of natural data, and is widely applied in data mining and machine learning area. However, NMF does not always achieve good performances as the non-negative constraint leads learned features to be non-orthogonal and overlap in semantics. How to improve the semantic independence of latent features without ...

Non-Negative Matrix Factorization, NMF, attempts to find a number of archetypal response profiles, or parts, such that any sample profile in the dataset can be approximated by a close profile among these archetypes or a linear combination of these profiles. The non-negativity constraint is imposed while estimating archetypal profiles, due to the non-negative nature of the observed signal. Apart...

Three techniques called non-negative matrix factorization (NMF), local non-negative matrix factorization (LNMF), and discriminant non-negative matrix factorization (DNMF), have been recently developed for decomposing a data matrix into non-negative factors named basis images and decomposition coefficients. Although these techniques are closely related to each other since they impose certain com...