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840
On the provable convergence of alternating minimization for matrix completion. arXiv
, 1312
"... Abstract—Alternating Minimization is a widely used and empirically successful framework for Matrix Completion and related lowrank optimization problems. We give a new algorithm based on Alternating Minimization that provably recovers an unknown lowrank matrix from a random subsample of its entries ..."
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Cited by 9 (1 self)
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Abstract—Alternating Minimization is a widely used and empirically successful framework for Matrix Completion and related lowrank optimization problems. We give a new algorithm based on Alternating Minimization that provably recovers an unknown lowrank matrix from a random subsample of its
Introduction to nonlinear mechanics
, 1947
"... A little used parameterization of the threedimensional rotation group is taken as basis in deriving an easily integrable kinematic relation (a 4vector linear differential equation) for the attitude rate, in terms of the present attitude and angular velocity of one reference frame relative to anot ..."
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Cited by 22 (0 self)
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geometric aspect. A special set of coordinate variables is introduced which after much manipulation results in a linear differential equation for the attitude (a 4vector) with its timevarying matrix constructed solely from the angular velocity (a 3vector). An infinite series expansion in integrals
SOLVING A LOWRANK FACTORIZATION MODEL FOR MATRIX COMPLETION BY A NONLINEAR SUCCESSIVE OVERRELAXATION ALGORITHM
"... Abstract. The matrix completion problem is to recover a lowrank matrix from a subset of its entries. The main solution strategy for this problem has been based on nuclearnorm minimization which requires computing singular value decompositions – a task that is increasingly costly as matrix sizes an ..."
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Cited by 91 (10 self)
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is analyzed. Numerical results show that the algorithm can reliably solve a wide range of problems at a speed at least several times faster than many nuclearnorm minimization algorithms. Key words. Matrix Completion, alternating minimization, nonlinear GS method, nonlinear SOR method AMS subject
Inertias of Block Band Matrix Completions
"... . This paper classifies the ranks and inertias of hermitian completion for the partially specified 3x3 block band hermitian matrix, (also known as a "bordered matrix") P = 0 B B @ A B ? B C D ? D E 1 C C A : The full set of completion inertias is described in terms of seven li ..."
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Cited by 5 (0 self)
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linear inequalities involving inertias and ranks of specified submatrices. The minimal completion rank for P is computed. We study the completion inertias of partially specified hermitian blockband matrices, using a block generalization of the DymGohberg algorithm. At each inductive step, we use our
Lineartime dynamics using lagrange multipliers
 In SIGGRAPH 96 Conference Proceedings, Computer Graphics Proceedings, Annual Conference Series
, 1996
"... Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics ..."
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Cited by 139 (0 self)
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Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics
Exploiting sparsity in linear and nonlinear matrix inequalities via positive semidefinite matrix completion
, 2010
"... ..."
Computing person and firm effects using linked longitudinal employeremployee data,” Center for Economic Studies, US Census Bureau,
, 2002
"... Abstract In this paper we provide the exact formulas for the direct least squares estimation of statistical models that include both person and firm effects. We also provide an algorithm for determining the estimable functions of the person and firm effects (the identifiable effects). The computati ..."
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Cited by 141 (16 self)
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). The computational techniques are also directly applicable to any linear twofactor analysis of covariance with two highdimension nonorthogonal factors. We show that the application of the exact solution does not change the substantive conclusions about the relative importance of person and firm effects
Praneeth Netrapalli Provable Matrix Completion using Alternating Minimization AltMin Sensing Completion Proof References
, 2013
"... To minimize f (X) over rankk matrices X, repeat the following: fix U and minimize f (UV †)over V fix V and minimize f (UV †)over U X U V' A popular Empirical approach to solve low rank matrix problems eg. matrix completion, clustering etc. Challenge: few theoretical guarantees ..."
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To minimize f (X) over rankk matrices X, repeat the following: fix U and minimize f (UV †)over V fix V and minimize f (UV †)over U X U V' A popular Empirical approach to solve low rank matrix problems eg. matrix completion, clustering etc. Challenge: few theoretical guarantees
Lowrank matrix completion by riemannian optimization
 ANCHPMATHICSE, Mathematics Section, École Polytechnique Fédérale de
"... The matrix completion problem consists of finding or approximating a lowrank matrix based on a few samples of this matrix. We propose a novel algorithm for matrix completion that minimizes the least square distance on the sampling set over the Riemannian manifold of fixedrank matrices. The algorit ..."
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Cited by 40 (4 self)
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. The algorithm is an adaptation of classical nonlinear conjugate gradients, developed within the framework of retractionbased optimization on manifolds. We describe all the necessary objects from differential geometry necessary to perform optimization over this lowrank matrix manifold, seen as a submanifold
Inductive Matrix Completion for Predicting GeneDisease Associations
"... Motivation: Most existing methods for predicting causal disease genes rely on specific type of evidence, and are therefore limited in terms of applicability. More often than not, the type of evidence available for diseases varies — for example, we may know linked genes, keywords associated with the ..."
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Cited by 9 (3 self)
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Inductive Matrix Completion to the problem of predicting genedisease associations; it combines multiple types of evidence (features) for diseases and genes to learn latent factors that explain the observed genedisease associations. We construct features from different biological sources such as microarray
Results 11  20
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840