When analyzing patterns, our goals are (i) to find structure in the presence of noise, (ii) to decompose the observed structure into sub-components, and (iii) to use the components for pattern completion. Here, a novel loop architecture is introduced to perform these tasks in an unsupervised manner. The architecture combines sparse code shrinkage with non-negative matrix factorization and blend...

Inference of individual admixture coefficients, which is important for population genetic and association studies, is commonly performed using compute-intensive likelihood algorithms. With the availability of large population genomic data sets, fast versions of likelihood algorithms have attracted considerable attention. Reducing the computational burden of estimation algorithms remains, howeve...

Nonnegative matrix factorization (NMF) is the problem of decomposing a given nonnegative n×m matrix M into a product of a nonnegative n× d matrix W and a nonnegative d ×m matrix H . A longstanding open question, posed by Cohen and Rothblum in 1993, is whether a rational matrix M always has an NMF of minimal inner dimension d whose factors W and H are also rational. We answer this question negat...

We use a multiscale approach to reduce the time to produce the nonnegative matrix factorization (NMF) of a matrix A, that is, A ≈ WH. We also investigate QR factorization as a method for initializing W during the iterative process for producing the nonnegative matrix factorization of A. Finally, we use our approach to produce nonnegative matrix factorizations for classifying images and compare ...

Properties of a novel algorithm called non-negative matrix factorization (NMF), are studied. NMF can discover substructures and can provide estimations about the presence or the absence of those, being attractive for completion of missing information. We have studied the working and learning capabilities of NMF networks. Performance was improved by adding sparse code shrinkage (SCS) algorithm t...

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...

We study the problem of detecting and localizing objects in still, gray-scale images making use of the part-based representation provided by non-negative matrix factorizations. Non-negative matrix factorization represents an emerging example of subspace methods which is able to extract interpretable parts from a set of template image objects and then to additively use them for describing indivi...

Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...

In this paper, we apply a non-negative matrix factorization (NMF) technique to propose a method of estimating noise occurring in non-stationary environments. In the proposed method, the basis matrix of the target noise is first obtained via NMF training. The noise basis is then applied to estimate an activation matrix of the target noise from the noisy signal. The proposed method is finally app...