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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.
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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...
Grouping tasks and data display items via the non-negative matrix factorization
Grouping tasks non-negative matrix factorization
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2015/8/21
Analyzing work functions and the IO variables they
need is an important component of designing and evaluating
complex systems. We develop a biclustering method for jointly
grouping work functions a...
Matrix Completion from Noisy Entries
matrix completion low-rank matrices spectral methods manifold optimization
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2015/8/21
Given a matrix M of low-rank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from colla...
Matrix Completion from a Few Entries
Random matrix random matrix ge matrix rank lower
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2015/8/21
Let M be a random nα × n matrix of rank r ≪ n, and assume that a uniformly random subset E of its entries is observed. We describe an efficient algorithm that reconstructs M from |E| = O(r ...
A bisection method for computing the H_infinity-norm of a transfer matrix and related problems
Transfer matrix singular value assessment the Hamiltonian matrix characteristic values of linear algebra
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2015/8/13
Inspired by recent work of Byers we establish a simple connection between the singular values of a transfer matrix evaluated along the imaginary axis and the imaginary eigenvalues of a related Hamilto...
A branch and bound methodology for matrix polytope stability problems arising in power systems
Robust matrix of power system the linearized dynamics linear system model robust stability
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2015/8/12
This paper proposes a formulation to provide necessary and sufficient conditions for robust stability of a family of matrices modeling linearized power system dynamics. A construction for transforming...
A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L_infinity-norm
Matrix and singular value differentiable function frequency singular value lipschitz second derivative
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2015/8/12
The ith singular value of a transfer matrix need not be a differentiable function of frequency where its multiplicity is greater than one. We show that near a local maximum, however, the largest singu...
Linear matrix inequalities in system and control theory
Linear matrix inequality system the control theory and linear matrix inequality affine combination symmetric positive semidefinite matrix
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2015/8/12
A wide variety of problems in system and control theory can be formulated (or reformulated) as convex optimization problems involving linear matrix inequalities, that is, constraints requiring an affi...
Control systems analysis and synthesis via linear matrix inequalities
Control theory and linear matrix inequality the numerical algebraic riccati inequality lyapunov
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2015/8/12
A wide variety of problems in systems and control theory can be cast or recast as convex problems that involve linear matrix inequalities (LMIs). For a few very special cases there are “analytical sol...
History of linear matrix inequalities in control theory
Linear matrix inequality control control theory tool control applications
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2015/8/12
The purpose of this paper is to give a historical view of Linear Matrix Inequalities in control and system theory. Not surprisingly, it appears that LMIs have been involved in some of the major events...
Existence and uniqueness of optimal matrix scalings
diagonal similarity scalings scaled singular value minimization irreducible matrices
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2015/8/12
We show that the set of diagonal similarity scalings that minimize the scaled singular value of a matrix is nonempty and bounded if and only if the matrix that is being scaled is irreducible. For an i...
A primal-dual potential reduction method for problems involving matrix inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
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2015/8/11
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
Multiobjective H_2/H_infinity-optimal control via finite dimensional Q-parametrization and linear matrix inequalities
Controller design convex semidefinite programming impulse response
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2015/8/11
The problem of multi-objective H2/H-infinity optimal controller design is reviewed. There is as yet no exact solution to this problem. We present a method based on that proposed by Scherer. The proble...
Determinant maximization with linear matrix inequality constraints
Matrix linear matrix inequality (lmi) computational geometry statistics system identification communication theory
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2015/8/11
The problem of maximizing the determinant of a matrix subject to linear matrix inequalities arises in many fields, including computational geometry, statistics, system identification, experiment desig...
Least-squares covariance matrix adjustment
Symmetric matrices linear equations inequalities the original matrix
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2015/8/10
We consider the problem of finding the smallest adjustment to a given symmetric n by n matrix, as measured by the Euclidean or Frobenius norm, so that it satisfies some given linear equalities and ine...