A Comprehensive Evaluation of Large-scale Parallel Matrix Factorization Algorithms
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Published: 2018
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Published: 2018
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DOWNLOAD EBOOKAuthor: Andrzej Cichocki
Publisher: John Wiley & Sons
Published: 2009-07-10
Total Pages: 500
ISBN-13: 9780470747285
DOWNLOAD EBOOKThis book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.
Author: Krister Dackland
Publisher:
Published: 1992
Total Pages: 26
ISBN-13:
DOWNLOAD EBOOKAuthor: Venkata Sesha Pavana Srinadh Bhojanapalli
Publisher:
Published: 2015
Total Pages: 422
ISBN-13:
DOWNLOAD EBOOKLow rank matrix factorization is an important step in many high dimensional machine learning algorithms. Traditional algorithms for factorization do not scale well with the growing data sizes and there is a need for faster/scalable algorithms. In this dissertation we explore the following two major themes to design scalable factorization algorithms for the problems: matrix completion, low rank approximation (PCA) and semi-definite optimization. (a) Sampling: We develop the optimal way to sample entries of any matrix while preserving its spectral properties. Using this sparse sketch (set of sampled entries) instead of the entire matrix, gives rise to scalable algorithms with good approximation guarantees. (b) Bi-linear factorization structure: We design algorithms that operate explicitly on the factor space instead on the matrix. While bi-linear structure of the factorization, in general, leads to a non-convex optimization problem, we show that under appropriate conditions they indeed recover the solution for the above problems. Both these techniques (individually or in combination) lead to algorithms with lower computational complexity and memory usage. Finally we extend these ideas of sampling and explicit factorization to design algorithms for higher order tensors.
Author: Hiroyuki Takizawa
Publisher: Springer Nature
Published: 2023-04-07
Total Pages: 526
ISBN-13: 3031299272
DOWNLOAD EBOOKThis book constitutes the proceedings of the 23rd International Conference on Parallel and Distributed Computing, Applications, and Technologies, PDCAT 2022, which took place in Sendai, Japan, during December 7-9, 2022. The 24 full papers and 16 short papers included in this volume were carefully reviewed and selected from 95 submissions. The papers are categorized into the following topical sub-headings: Heterogeneous System (1; HPC & AI; Embedded systems & Communication; Blockchain; Deep Learning; Quantum Computing & Programming Language; Best Papers; Heterogeneous System (2); Equivalence Checking & Model checking; Interconnect; Optimization (1); Optimization (2); Privacy; and Workflow.
Author: Daphnia Milagros Linares-Pantigoso
Publisher:
Published: 2001
Total Pages: 244
ISBN-13:
DOWNLOAD EBOOKAuthor: Thomas Frederick Coleman
Publisher: SIAM
Published: 1990-01-01
Total Pages: 278
ISBN-13: 9780898712681
DOWNLOAD EBOOKPapers from a workshop held at Cornell University, Oct. 1989, and sponsored by Cornell's Mathematical Sciences Institute. Annotation copyright Book News, Inc. Portland, Or.
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Published: 1995
Total Pages: 702
ISBN-13:
DOWNLOAD EBOOKAuthor: Ivan Lirkov
Publisher: Springer Science & Business Media
Published: 2006-02-14
Total Pages: 701
ISBN-13: 3540319948
DOWNLOAD EBOOKThis book constitutes the thoroughly refereed post-proceedings of the 5th International Conference on Large-Scale Scientific Computations, LSSC 2005, held in Sozopol, Bulgaria in June 2005. The 75 revised full papers presented together with five invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections.
Author: Jill P. Mesirov
Publisher: SIAM
Published: 1991-01-01
Total Pages: 360
ISBN-13: 9780898712797
DOWNLOAD EBOOKThis text on very large scale computation in the 21st century covers such topics as: challenges in the natural sciences and physics; chemistry; fluid dynamics; astrophysics; biology; challenges in engineering; challenges in algorithm design; and challenges in system design.