Non-negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “Iterative weighted non-smooth non-negative matrix factorization” (IWNS-NMF). A new cost fun...

The non-negative matrix factorization (NMF) algorithm is a classical matrix factorization and dimension reduction method in machine learning and data mining. However, in real problems, we always have to run the algorithm for several times and use the best matrix factorization result as the final output because of the random initialization of the matrix factorization. In this paper, we proposed ...

Non-negative Matrix Factorization (NMF) is a part-based image representation method which adds a non-negativity constraint to matrix factorization. NMF is compatible with the intuitive notion of combining parts to form a whole face. In this paper, we propose a framework of face recognition by adding NMF constraint and classifier constraints to matrix factorization to get both intuitive features...

Non-negative matrix factorization (NMF) has proven to be a useful decomposition technique for multivariate data, where the non-negativity constraint is necessary to have a meaningful physical interpretation. NMF reduces the dimensionality of non-negative data by decomposing it into two smaller non-negative factors with physical interpretation for class discovery. The NMF algorithm, however, ass...

In order to solve the problem of algorithm convergence in projective non-negative matrix factorization (P-NMF), a method, called convergent projective non-negative matrix factorization (CP-NMF), is proposed. In CP-NMF, an objective function of Frobenius norm is defined. The Taylor series expansion and the Newton iteration formula of solving root are used. An iterative algorithm for basis matrix...

Non-negative matrix factorization (NMF, Nature 401 (1999) 788-791) is a method to derive non-negative basis functions for sets of data that are inherently non-negative, such as color spectra. We applied NMF to Munsell color spectra and investigated the color names associated with the non-negative basis functions. NMF yields basis functions compatible with established color naming categories.

Non-negative matrix factorization (NMF) is a recently developed method for finding parts-based representation of non-negative data such as face images. Although it has successfully been applied in several applications, directly using NMF for face recognition often leads to low performance. Moreover, when performing on large databases, NMF needs considerable computational costs. In this paper, w...

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...

Abstract—What matrix factorization methods do is reduce the dimensionality of data without losing any important information. In this work, we present Non-negative Matrix Factorization (NMF) method, focusing on its advantages concerning other factorization. We discuss main optimization algorithms, used to solve NMF problem, and their convergence. The paper also contains a comparative study betwe...

Non-negative matrix factorization (NMF) is a recently popularized technique for learning partsbased, linear representations of non-negative data. The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption, and hence not suitable if the data are grossly corrupted. To improve the robustness of NMF, a novel algorithm named robust nonnegative matrix factorization (RNMF) i...