Factorization Methods

Author(s):  
Fioralba Cakoni ◽  
David Colton
2021 ◽  
Vol 15 (8) ◽  
pp. 841-853
Author(s):  
Yuan Liu ◽  
Zhining Wen ◽  
Menglong Li

Background:: The utilization of genetic data to investigate biological problems has recently become a vital approach. However, it is undeniable that the heterogeneity of original samples at the biological level is usually ignored when utilizing genetic data. Different cell-constitutions of a sample could differentiate the expression profile, and set considerable biases for downstream research. Matrix factorization (MF) which originated as a set of mathematical methods, has contributed massively to deconvoluting genetic profiles in silico, especially at the expression level. Objective: With the development of artificial intelligence algorithms and machine learning, the number of computational methods for solving heterogeneous problems is also rapidly abundant. However, a structural view from the angle of using MF to deconvolute genetic data is quite limited. This study was conducted to review the usages of MF methods on heterogeneous problems of genetic data on expression level. Methods: MF methods involved in deconvolution were reviewed according to their individual strengths. The demonstration is presented separately into three sections: application scenarios, method categories and summarization for tools. Specifically, application scenarios defined deconvoluting problem with applying scenarios. Method categories summarized MF algorithms contributed to different scenarios. Summarization for tools listed functions and developed web-servers over the latest decade. Additionally, challenges and opportunities of relative fields are discussed. Results and Conclusion: Based on the investigation, this study aims to present a relatively global picture to assist researchers to achieve a quicker access of deconvoluting genetic data in silico, further to help researchers in selecting suitable MF methods based on the different scenarios.


Author(s):  
ASHOKA JAYAWARDENA ◽  
PAUL KWAN

In this paper, we focus on the design of oversampled filter banks and the resulting framelets. The framelets obtained exhibit improved shift invariant properties over decimated wavelet transform. Shift invariance has applications in many areas, particularly denoising, coding and compression. Our contribution here is on filter bank completion. In addition, we propose novel factorization methods to design wavelet filters from given scaling filters.


2006 ◽  
Vol 74 (2) ◽  
pp. 762-766 ◽  
Author(s):  
V. A. Babeshko ◽  
O. M. Babeshko ◽  
O. V. Evdokimova

2018 ◽  
Vol 35 (11) ◽  
pp. 1940-1947 ◽  
Author(s):  
Johannes Leuschner ◽  
Maximilian Schmidt ◽  
Pascal Fernsel ◽  
Delf Lachmund ◽  
Tobias Boskamp ◽  
...  

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