Related papers: Supervised Class-pairwise NMF for Data Representat…

Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing…

Matrix factorization is a popular framework for modeling low-rank data matrices. Motivated by manifold learning problems, this paper proposes a quadratic matrix factorization (QMF) framework to learn the curved manifold on which the dataset…

Nonnegative matrix factorization can be used to automatically detect topics within a corpus in an unsupervised fashion. The technique amounts to an approximation of a nonnegative matrix as the product of two nonnegative matrices of lower…

Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes…

Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be…

This paper describes algorithms for nonnegative matrix factorization (NMF) with the beta-divergence (beta-NMF). The beta-divergence is a family of cost functions parametrized by a single shape parameter beta that takes the Euclidean…

Nonnegative matrix factorization (NMF) was popularized as a tool for data mining by Lee and Seung in 1999. NMF attempts to approximate a matrix with nonnegative entries by a product of two low-rank matrices, also with nonnegative entries.…

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…

Matrix factorization has been recently utilized for the task of multi-modal hashing for cross-modality visual search, where basis functions are learned to map data from different modalities to the same Hamming embedding. In this paper, we…

Nonnegative Matrix Factorization(NMF) is a common used technique in machine learning to extract features out of data such as text documents and images thanks to its natural clustering properties. In particular, it is popular in image…

In recent years, semi-supervised multi-view nonnegative matrix factorization (MVNMF) algorithms have achieved promising performances for multi-view clustering. While most of semi-supervised MVNMFs have failed to effectively consider…

Existing nonnegative matrix factorization methods focus on learning global structure of the data to construct basis and coefficient matrices, which ignores the local structure that commonly exists among data. In this paper, we propose a new…

Non-negative matrix factorization (NMF) is a new knowledge discovery method that is used for text mining, signal processing, bioinformatics, and consumer analysis. However, its basic property as a learning machine is not yet clarified, as…

Matrix factorization is a widely used approach for top-N recommendation and collaborative filtering. When implemented on implicit feedback data (such as clicks), a common heuristic is to upweight the observed interactions. This strategy has…

This paper provides a theoretical explanation on the clustering aspect of nonnegative matrix factorization (NMF). We prove that even without imposing orthogonality nor sparsity constraint on the basis and/or coefficient matrix, NMF still…

In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…

Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…

In this paper, we propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D…

The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…