A Matrix Factorization and Its Application to Large-Scale Linear Programming

Recommender systems aim to personalize the experience of user by suggesting items to the user based on the preferences of a user. The preferences are learned from the user’s interaction history or through explicit ratings that the user has given to the items. The system could be part of a retail website, an online bookstore, a movie rental service or an online education portal and so on. In this paper, I will focus on matrix factorization algorithms as applied to recommender systems and discuss the singular value decomposition, gradient descent-based matrix factorization and parallelizing matrix factorization for large scale applications.

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Molecular Inverse Comorbidity between Alzheimer’s disease and Lung Cancer: new insights from Matrix Factorization

10.1101/643890 ◽

2019 ◽

Author(s):

Alessandro Greco ◽

Jon Sanchez Valle ◽

Vera Pancaldi ◽

Anaïs Baudot ◽

Emmanuel Barillot ◽

...

Keyword(s):

Lung Cancer ◽

Alzheimer’S Disease ◽

Alzheimer's Disease ◽

Matrix Factorization ◽

Large Scale ◽

Molecular Mechanisms ◽

Biological Data ◽

Biological Data Analysis ◽

Specific Factors ◽

Molecular Bases

AbstractMatrix Factorization (MF) is an established paradigm for large-scale biological data analysis with tremendous potential in computational biology.We here challenge MF in depicting the molecular bases of epidemiologically described Disease-Disease (DD) relationships. As use case, we focus on the inverse comorbidity association between Alzheimer’s disease (AD) and lung cancer (LC), described as a lower than expected probability of developing LC in AD patients. To the day, the molecular mechanisms underlying DD relationships remain poorly explained and their better characterization might offer unprecedented clinical opportunities.To this goal, we extend our previously designed MF-based framework for the molecular characterization of DD relationships. Considering AD-LC inverse comorbidity as a case study, we highlight multiple molecular mechanisms, among which the previously identified immune system and mitochondrial metabolism. We then discriminate mechanisms specific to LC from those shared with other cancers through a pancancer analysis. Additionally, new candidate molecular players, such as Estrogen Receptor (ER), CDH1 and HDAC, are pinpointed as factors that might underlie the inverse relationship, opening the way to new investigations. Finally, some lung cancer subtype-specific factors are also detected, suggesting the existence of heterogeneity across patients also in the context of inverse comorbidity.

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A non-convex optimization framework for large-scale low-rank matrix factorization

10.36227/techrxiv.12199026 ◽

2020 ◽

Author(s):

Sajad Fathi Hafshejani ◽

Saeed Vahidian ◽

Zahra Moaberfard ◽

Reza Alikhani ◽

Bill Lin

Keyword(s):

Matrix Factorization ◽

Large Scale ◽

Significant Loss ◽

Low Rank ◽

Function Evaluation ◽

Dimensional Manifold ◽

Step Size ◽

Rank Matrix ◽

Real World Datasets ◽

Low Rank Matrix

Low-rank matrix factorization problems such as non negative matrix factorization (NMF) can be categorized as a clustering or dimension reduction technique. The latter denotes techniques designed to find representations of some high dimensional dataset in a lower dimensional manifold without a significant loss of information. If such a representation exists, the features ought to contain the most relevant features of the dataset. Many linear dimensionality reduction techniques can be formulated as a matrix factorization. In this paper, we combine the conjugate gradient (CG) method with the Barzilai and Borwein (BB) gradient method, and propose a BB scaling CG method for NMF problems. The new method does not require to compute and store matrices associated with Hessian of the objective functions. Moreover, adopting a suitable BB step size along with a proper nonmonotone strategy which comes by the size convex parameter $\eta_k$, results in a new algorithm that can significantly improve the CPU time, efficiency, the number of function evaluation. Convergence result is established and numerical comparisons of methods on both synthetic and real-world datasets show that the proposed method is efficient in comparison with existing methods and demonstrate the superiority of our algorithms.

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