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...

It is today accepted that matrix factorization models allow a high quality of rating prediction in recommender systems. However, a major drawback of matrix factorization is its static nature that results in a progressive declining of the accuracy of the predictions after each factorization. This is due to the fact that the new obtained ratings are not taken into account until a new factorizatio...

In kernel machines, such as kernel principal component analysis (KPCA), Gaussian Processes (GPs), and Support Vector Machines (SVMs), the computational complexity of finding a solution is O(n), where n is the number of training instances. To reduce this expensive computational complexity, we propose using Kronecker factorization, which approximates a positive definite kernel matrix by the Krone...

Abstract. Gas- and particle-phase molecular markers provide highly specific information about the sources atmospheric processes that contribute to air pollution. In urban areas, major of pollution are changing as regulation selectively mitigates some climate change impacts surrounding environment. this study, a comprehensive thermal desorption aerosol gas chromatograph (cTAG) was used measure v...

This paper presents a block Schur algorithm to obtain a factorization of a symmetric block Toeplitz matrix. It is inspired by the various block Schur algorithms that have appeared in the literature but which have not considered the innuence of performance tradeoos on implementation choices. We develop a version based on block hyperbolic Householder reeectors by adapting the representation schem...