Damped Newton algorithms for matrix factorization with missing data

By Aeron Buchanan, Andrew William Fitzgibbon. Computer Vision and Pattern Recognition, 2005

346 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/471d0a8a251255e9f7513c0c0315e588817c1764

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In Aerospace Engineering

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA (2008, neutral): “Similar (not identical) alternation algorithms have been proposed in (Shum et al. 1995; De la Torre and Black 2001; Buchanan and Fitzgibbon 2000 ).”
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors (2008, background): “(In real situations, occlusions typically occur in a much more structured manner [8]).”
Supervised Descent Method and Its Applications to Face Alignment (2013, methodology): “There are a large number of different approaches to solve these continuous nonlinear optimization problems based on first and second order methods, such as gradient descent [1] for dimensionality reduction, Gauss-Newton for image alignment [22, 5, 14] or Levenberg-Marquardt for structure from motion”
Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm (2012, methodology): “This is a behavior that has also been observed for alternated approaches in the L2 instance, see [7].”
Weighted Nuclear Norm Minimization with Application to Image Denoising (2014, methodology): “Low rank matrix approximation methods can be generally categorized into two categories: the low rank matrix factorization (LRMF) methods [25, 2, 16, 13] and the nuclear norm minimization (NNM) methods [14, 4, 27, 3, 20, 19, 21, 11].”
Robust Rotation and Translation Estimation in Multiview Reconstruction (2007, background): “• 99.9% occlusions =) imputation, damped Newton [ 1 ] with random initialization impossible”
Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition (2013, methodology): “Following results reported in the detailed comparisons of [4, 15, 29, 30, 33, 41], we dismissed alternated methods due to their flatlining tendency.”
Unifying Heterogeneous Classifiers With Distillation (2019, methodology): “3We note there are more effective algorithms for matrix factorisation than ALS [7, 29, 11].”
A Benchmark for the Comparison of 3-D Motion Segmentation Algorithms (2007, methodology): “Another advantage of the projection, is that it allows one to deal with missing data, as a rank-5 factorization of W can be computed using matrix factorization techniques for missing data (see [2] for a review).”
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization (2012, neutral): “[8, 10, 12]), outlier case (e.”
Mnemonic Descent Method: A Recurrent Process Applied for End-to-End Face Alignment (2016, background): “Non-linear least squares optimisation problems often arise in computer vision, including but not limited to Structure-from-Motion [9, 23], rigid and deformable image alignment [33, 35], optical flow estimation [33, 66, 46, 45], CNN RNN”
Estimating 3D shape from degenerate sequences with missing data (2009, methodology): “To our knowledge, the Damped Newton algorithm of Buchanan&Fitzgibbon [2] produces the least reconstruction error (it is optimal”
Practical low-rank matrix approximation under robust L1-norm (2012, methodology): “In computer vision literature [5, 15, 14], various optimization methods have been proposed and proven to be successful even in the presence of high ratio of missing data.”
All-at-once Optimization for Coupled Matrix and Tensor Factorizations (2011, methodology): “…is deﬁned as , where ˆ X corresponds to the data reconstructed using the extracted factor matrices, i.e., ˆA , ˆB , and ˆ C , as ˆ X = ˆ A , ˆ B , ˆ C . the presence of missing data, ALS-based imputation techniques may suﬀer from poor convergence [8] and do not scale to large-scale data sets [1].”
Subspace video stabilization (2011, methodology): “Next, we experimented with several iterative global optimization techniques such as the damped Newton method [Buchanan and Fitzgibbon 2005] and LevenbergMarquardt [Chen 2008].”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “…techniques in past decades, there are a flurry of studies in LRMA, and many important models and algorithms have been reported (Srebro et al, 2003; Buchanan and Fitzgibbon, 2005; Ke and Kanade, 2005; Eriksson and Van Den Hengel, 2010; Fazel et al, 2001; Wright et al, 2009; Candès and Recht,…”
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, background): “Both of these two categories have a variety of extensions as proposed in [5], [6], [19], [30], [61].”
Weighted Schatten $p$ -Norm Minimization for Image Denoising and Background Subtraction (2015, methodology): “Speaking, LRMA can be achieved by factorization based models [15], [16], [17], [18] and regularization based models.”