The Non-negative Matrix Factorization (NMF) is a popular technique for intelligent systems, which can be widely used to decompose nonnegative matrix into two factor matrices: basis and coefficient one, respectively. main objective of NMF ensure that the operation results matrices are as close original possible. Meanwhile, stability generalization ability algorithm should ensured. Therefore, per...

Stochastic Gradient Descent (SGD) is a popular online algorithm for large-scale matrix factorization. However, SGD can often be di cult to use for practitioners, because its performance is very sensitive to the choice of the learning rate parameter. In this paper, we present non-negative passiveaggressive (NN-PA), a family of online algorithms for non-negative matrix factorization (NMF). Our al...

In this paper, we consider an arbitrary binary polynomial sequence {A_n} and then give a lower triangular matrix representation of this sequence. As main result, we obtain a factorization of the innite generalized Pascal matrix in terms of this new matrix, using a Riordan group approach. Further some interesting results and applications are derived.

Multiplicative update algorithms have encountered a great success to solve optimization problems with nonnegativity constraints, such as the famous non-negative matrix factorization and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov’s stability theory prov...

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...

we used qcd factorization for the hadronic matrix elements to show that the existing data, in particular the branching ratios br ( ?j/?k) and br ( ?j/??), can be accounted for this approach. we analyzed the decay within the framework of qcd factorization. we have complete calculation of the relevant hard-scattering kernels for twist-2 and twist-3. we calculated this decays in a special scale ( ...

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...