Abstract Non-negative matrix factorization (NMF) is a powerful tool for data science researchers, and it has been successfully applied to mining machine learning community, due its advantages such as simple form, good interpretability less storage space. In this paper, we give detailed survey on existing NMF methods, including comprehensive analysis of their design principles, characteristics d...

introduction non-invasive fluorescent reflectance imaging (fri) is used for accessing physiological and molecular processes in biological media. the aim of this article is to separate the overlapping emission spectra of quantum dots within tissue-equivalent phantom using svd, jacobi svd, and nmf methods in the fri mode. materials and methods in this article, a tissue-like phantom and an optical...

Simplex Volume Maximization (SiVM) exploits distance geometry for e ciently factorizing gigantic matrices. It was proven successful in game, social media, and plant mining. Here, we review the distance geometry approach and argue that it generally suggests to factorize gigantic matrices using search-based instead of optimization techniques. 1 Interpretable Matrix Factorization Many modern data ...

Recommender system has been more and more popular and widely used in many applications recently. The increasing information available, not only in quantities but also in types, leads to a big challenge for recommender system that how to leverage these rich information to get a better performance. Most traditional approaches try to design a specific model for each scenario, which demands great e...

Matrix factorization (MF) is a prevailing collaborative filtering method for building recommender systems. It requires users to upload their personal preferences to the recommender for performing MF, which raises serious privacy concerns. This paper proposes a differentially private MF mechanism that can prevent an untrusted recommender from learning any users’ ratings or profiles. Our design d...

The problem of efficiently applying a kernel-induced feature space factorization to a largescale data sets is addressed in this thesis. Kernel matrix factorization methods have showed good performances solving machine learning and data analysis problems. However, the present growth of the amount of information available implies the problems can not be solved with conventional methods, due their...

A large portion of Linear algebra (scientific computing) is devoted to accelerate computationally intensive operations through the deeper understanding on the structure of the matrix. While it is not extremely hard to obtain an analytical solutions for the problems of interest, often a large-size matrix or repetetive nature of the computations prohibit us from getting the actual solution in num...

Even though Nonnegative Matrix Factorization (NMF) in its original form performs rank reduction and signal compaction implicitly, it does not explicitly consider storage or transmission constraints. We propose a Frobenius-norm Quantized Nonnegative Matrix Factorization algorithm that is 1) almost as precise as traditional NMF for decomposition ranks of interest (with in 1-4dB), 2) admits to pra...

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and present generalization error bounds based on analyzing the Rademacher complexity of low-norm factorizations.