Matrix factorization is one of the crucial algorithms of the Recommendation system. It implies that the relationship between user and contents can be explained by hidden latent variables. However, it is not intuitive to understand the meaning of these hidden latent variables. Therefore, this study suggests a way to learn the meaning from supplementary data such as comments and use in matrix fac...

An online nonnegative matrix factorization (NMF) algorithm based on recursive least squares (RLS) is described in a matrix form, and a simplified algorithm for a low-complexity calculation is developed for frame-by-frame online audio source separation system. First, the online NMF algorithm based on the RLS method is described as solving the NMF problem recursively. Next, a simplified algorithm...

I review the known approaches to two-body nonleptonic B meson decays, including factorization assumption, modified factorization assumption, QCD factorization, and perturbative QCD factorization. Important phenomenological aspects of these approaches are emphasized.

Quadrant Interlocking Factorization (QIF), an alternative to LU factorization, is suitable for factorizing invertible matrix A such that det(A) , 0. The QIF, with its application in parallel computing, the most efficient factorization technique yet underutilized. two forms of QIF among others, which are not only similar algorithm but also computation, WZ and WH differs applications properties. ...

Tensor factorization arises in many machinelearning applications, such knowledge basemodeling and parameter estimation in latentvariable models. However, numerical meth-ods for tensor factorization have not reachedthe level of maturity of matrix factorizationmethods. In this paper, we propose a newmethod for CP tensor factorization that usesrandom projections to ...

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 ...

QCD factorization for exclusive non-leptonic B-meson decays: General arguments and the case of heavy–light final states Abstract We provide a rigorous basis for factorization for a large class of non-leptonic two-body B-meson decays in the heavy-quark limit. The resulting factorization formula incorporates elements of the naive factorization approach and the hard-scattering approach , but allow...

Let O be an order of an algebraic number field. It was shown by Ge that given a factorization of an O-ideal a into a product of O-ideals it is possible to compute in polynomial time an overorder O′ of O and a gcdfree refinement of the input factorization; i.e., a factorization of aO′ into a power product of O′-ideals such that the bases of that power product are all invertible and pairwise copr...

The unfolding of a concurrent system represents in a compact manner all possible runs of this system. Unfoldings are used in many applications, ranging from model-checking (offline) to failure diagnosis (on-line). Their factorization properties form the basis of modular/distributed algorithms to achieve these tasks. The trellis structure proposed here is an alternate and more compact representa...