Optimal instantaneous rigid motion estimation insensitive to local minima
Computer Vision and Image Understanding
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components
International Journal of Computer Vision
Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Nonconvergence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
Implicit Non-Rigid Structure-from-Motion with Priors
Journal of Mathematical Imaging and Vision
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Motion Segmentation from Feature Trajectories with Missing Data
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
Extracting Average Shapes from Occluded Non-rigid Motion
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
An Iterative Multiresolution Scheme for SFM with Missing Data
Journal of Mathematical Imaging and Vision
A Convex Approach to Low Rank Matrix Approximation with Missing Data
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
An iterative multiresolution scheme for SFM with missing data: Single and multiple object scenes
Image and Vision Computing
Interpolation of signals with missing data using Principal Component Analysis
Multidimensional Systems and Signal Processing
International Journal of Computer Vision
Predicting Missing Ratings in Recommender Systems: Adapted Factorization Approach
International Journal of Electronic Commerce
Fast and precise weak-perspective factorization
CAIP'07 Proceedings of the 12th international conference on Computer analysis of images and patterns
Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion
Image and Vision Computing
Rigid Structure from Motion from a Blind Source Separation Perspective
International Journal of Computer Vision
Successively alternate least square for low-rank matrix factorization with bounded missing data
Computer Vision and Image Understanding
Shape-based image segmentation through photometric stereo
Computer Vision and Image Understanding
Bilinear factorization via augmented lagrange multipliers
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Element-wise factorization for N-View projective reconstruction
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
ACM Transactions on Graphics (TOG)
Rank Estimation in Missing Data Matrix Problems
Journal of Mathematical Imaging and Vision
A linear solution to 1-dimensional subspace fitting under incomplete data
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Multilinear model estimation with L2-regularization
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Scene reconstruction and visualization from internet photo collections
Scene reconstruction and visualization from internet photo collections
Hessian Matrix vs. Gauss-Newton Hessian Matrix
SIAM Journal on Numerical Analysis
Decentralized prediction of end-to-end network performance classes
Proceedings of the Seventh COnference on emerging Networking EXperiments and Technologies
An iterative multiresolution scheme for SFM
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Controlling sparseness in non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Iterative extensions of the sturm/triggs algorithm: convergence and nonconvergence
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Factorization with missing and noisy data
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
Optimal Metric Projections for Deformable and Articulated Structure-from-Motion
International Journal of Computer Vision
Towards a robust framework of network coordinate systems
IFIP'12 Proceedings of the 11th international IFIP TC 6 conference on Networking - Volume Part I
Low-rank matrix decomposition in L1-norm by dynamic systems
Image and Vision Computing
Simultaneous compaction and factorization of sparse image motion matrices
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
MATRI: a multi-aspect and transitive trust inference model
Proceedings of the 22nd international conference on World Wide Web
An algorithmic approach to missing data problem in modeling human aspects in software development
Proceedings of the 9th International Conference on Predictive Models in Software Engineering
Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics
International Journal of Knowledge Discovery in Bioinformatics
Coupled Matrix Factorization with Sparse Factors to Identify Potential Biomarkers in Metabolomics
International Journal of Knowledge Discovery in Bioinformatics
DMFSGD: a decentralized matrix factorization algorithm for network distance prediction
IEEE/ACM Transactions on Networking (TON)
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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The problem of low-rank matrix factorization in the presence of missing data has seen significant attention in recent computer vision research. The approach that dominates the literature is EM-like alternation of closed-form solutions for the two factors of the matrix. An obvious alternative is non-linear optimization of both factors simultaneously, a strategy which has seen little published research. This paper provides a comprehensive comparison of the two strategies by evaluating previously published factorization algorithms as well as some second order methods not previously presented for this problem. We conclude that, although alternation approaches can be very quick, their propensity to glacial convergence in narrow valleys of the cost function means that average-case performance is worse than second-order strategies. Further, we demonstrate the importance of two main observations: one, that schemes based on closed-form solutions alone are not suitable and that non-linear optimization strategies are faster, more accurate and provide more flexible frameworks for continued progress; and two, that basic objective functions are not adequate and that regularization priors must be incorporated, a process that is easier with nonlinear methods.