We describe an algorithm that performs regularized non-negative matrix factorization (NMF) to find independent components in non-negative data. Previous techniques proposed for this purpose require the data to be grounded, with support that goes down to 0 along each dimension. In our work, this requirement is eliminated. Based on it, we present a technique to find a low-dimensional decompositio...

Non-negative matrix factorization (NMF) is a powerful feature extraction method for finding parts-based, linear representations of non-negative data . Inherently, it is unsupervised learning algorithm. That is to say, the classical NMF algorithm does not respect the class-specific information. This paper presents an improvement of the classical NMF approach by imposing Fisher constraints. This ...

Non-Negative Matrix Factorization (NMF) implies that a given nonnegative matrix is represented by a product of two non-negative matrices. In this paper, a factorization condition (consistent condition) on basis matrix is proposed firstly. For a given consistent basis matrix, although there exist infinite solutions (factorizations) generally, the sparse solution is unique with probability one, w...

Non-negative Matrix Factorization (NMF) is a traditional unsupervised machine learning technique for decomposing a matrix into a set of bases and coefficients under the non-negative constraint. NMF with sparse constraints is also known for extracting reasonable components from noisy data. However, NMF tends to give undesired results in the case of highly sparse data, because the information inc...

Generally, data mining in larger datasets consists of certain limitations in identifying the relevant datasets for the given queries. The limitations include: lack of interaction in the required objective space, inability to handle the data sets or discrete variables in datasets, especially in the presence of missing variables and inability to classify the records as per the given query, and fi...

In this chapter, I briefly introduce a multivariate analysis technique called non-negative matrix factorization (NMF), which has attracted a lot of attention in the field of audio signal processing in recent years. I will mention some basic properties of NMF, effects induced by the non-negative constraints, how to derive an iterative algorithm for NMF, and some attempts that have been made to a...

In this paper, I will give a brief introduction to a data analysis technique called non-negative matrix factorization (NMF), which has attracted a lot of attention in the field of audio signal processing in recent years. I will mention some basic properties of NMF, effects induced by the non-negative constraints, how to derive an iterative algorithm for NMF, and some attempts that have been mad...