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On explicit Wiener-Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix.

ABSTRACT: As it is known, the existence of the Wiener-Hopf factorization for a given matrix is a well-studied problem. Severe difficulties arise, however, when one needs to compute the factors approximately and obtain the partial indices. This problem is very important in various engineering applications and, therefore, remains to be subject of intensive investigations. In the present paper, we approximate a given matrix function and then explicitly factorize the approximation regardless of whether it has stable partial indices. For this reason, a technique developed in the Janashia-Lagvilava matrix spectral factorization method is applied. Numerical simulations illustrate our ideas in simple situations that demonstrate the potential of the method.

SUBMITTER: Ephremidze L

PROVIDER: S-EPMC7428035 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature

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On explicit Wiener-Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix.

Ephremidze L L Spitkovsky I I

Proceedings. Mathematical, physical, and engineering sciences 20200624 2238

As it is known, the existence of the Wiener-Hopf factorization for a given matrix is a well-studied problem. Severe difficulties arise, however, when one needs to compute the factors approximately and obtain the partial indices. This problem is very important in various engineering applications and, therefore, remains to be subject of intensive investigations. In the present paper, we approximate a given matrix function and then explicitly factorize the approximation regardless of whether it has ...[more]

PMID: 32831589

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Project description:BackgroundMatrix factorization is a well established pattern discovery tool that has seen numerous applications in biomedical data analytics, such as gene expression co-clustering, patient stratification, and gene-disease association mining. Matrix factorization learns a latent data model that takes a data matrix and transforms it into a latent feature space enabling generalization, noise removal and feature discovery. However, factorization algorithms are numerically intensive, and hence there is a pressing challenge to scale current algorithms to work with large datasets. Our focus in this paper is matrix tri-factorization, a popular method that is not limited by the assumption of standard matrix factorization about data residing in one latent space. Matrix tri-factorization solves this by inferring a separate latent space for each dimension in a data matrix, and a latent mapping of interactions between the inferred spaces, making the approach particularly suitable for biomedical data mining.ResultsWe developed a block-wise approach for latent factor learning in matrix tri-factorization. The approach partitions a data matrix into disjoint submatrices that are treated independently and fed into a parallel factorization system. An appealing property of the proposed approach is its mathematical equivalence with serial matrix tri-factorization. In a study on large biomedical datasets we show that our approach scales well on multi-processor and multi-GPU architectures. On a four-GPU system we demonstrate that our approach can be more than 100-times faster than its single-processor counterpart.ConclusionsA general approach for scaling non-negative matrix tri-factorization is proposed. The approach is especially useful parallel matrix factorization implemented in a multi-GPU environment. We expect the new approach will be useful in emerging procedures for latent factor analysis, notably for data integration, where many large data matrices need to be collectively factorized.

Dataset Information

On explicit Wiener-Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix.

Publications

On explicit Wiener-Hopf factorization of 2 × 2 matrices in a vicinity of a given matrix.

Similar Datasets

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