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New Protocols for Secure Linear Algebra: Pivoting-Free Elimination and Fast Block-Recursive Matrix Decomposition
secure linear algebra multiparty computation
2018/8/2
Cramer and Damgård were the first to propose a constant-rounds protocol for securely solving a linear system of unknown rank over a finite field in multiparty computation (MPC). For mm linear equ...
A Matrix Decomposition Method for Optimal Normal Basis Multiplication
Finite fields matrix decomposition method
2015/12/24
We introduce a matrix decomposition method and prove that multiplication in GF(2^k) with a Type 1 optimal normal basis for can be performed using k^2-1 XOR gates irrespective of the choice of the irre...
A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis
Canonical correlation analysis DNA copy number Integrative genomic analysis L1 Matrix decomposition Principal component analysis Sparse principal component analysis SVD.
2015/8/21
We present a penalized matrix decomposition (PMD), a new framework for computing a rank-K approximation for a matrix. We approximate the matrix X as X ˆ = k K=1 dkukvk T , where dk, uk, and vk m...
Low-Rank and Sparse Matrix Decomposition for Accelerated Dynamic MRI with Separation of Background and Dynamic Components
compressed sensing low-rank matrix completion sparsity dynamic MRI
2015/6/17
Purpose: To apply the low-rank plus sparse (L+S) matrix decomposition model to reconstruct undersampled dynamic MRI as a superposition of background and dynamic components in various problems of clini...
A Generalized Least Squares Matrix Decomposition
matrix decomposition,singular value decomposition,transposable data,principal components analysis,sparse principal components analysis,functional prin-cipal components analysis,spatio-temporal data
2011/3/21
Variables in high-dimensional data sets common in neuroimaging, spatial statistics, time series and genomics often exhibit complex dependencies. Conventional multivariate analysis techniques often ign...
A Generalized Least Squares Matrix Decomposition
matrix decomposition singular value decomposition transposable data principal components analysis, sparse principal components analysis functional prin-cipal components analysis spatio-temporal data
2011/3/23
Variables in high-dimensional data sets common in neuroimaging, spatial statistics, time series and genomics often exhibit complex dependencies. Conventional multivariate analysis techniques often ign...
Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions
Noisy matrix decomposition via convex relaxation high dimensions
2011/3/24
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are the noisy realizations of the sum of an (appproximately) lo...