Robust L/sub 1/ norm factorization in the presence of outliers and missing data by alternative convex programming

By Qifa Ke, Takeo Kanade. 2005

693 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

A Unified View of Matrix Factorization Models (2008, neutral): “1-SVD [27] R θ ∑ ij |Wij ( Xij − X̂ij ) | ≥ 0”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “In the seminal work of (Ke and Kanade, 2005), Ke and Kannde designed an alternative convex programming algorithm to solve this `1 norm factorization model.”
Unifying Heterogeneous Classifiers With Distillation (2019, background): “, structure from motion [18] and recommender systems [21].”
Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition (2013, methodology): “Unfortunately, this factorization approach has several caveats: The LS loss is highly susceptible to outliers; also, the presence of missing data in X results in local minima.”
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].”
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization (2006, methodology): “The standard generalization to L1-norm PCA is to solve ( Ke & Kanade, 2004 ).”
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization (2009, result): “We give simulations and real-data examples corroborating the theoretical results.”
Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation (2011, background): “R converges in about 20 iterations for a convergence precision of 10−5. D. Relation to Other Methods 1) Robust Principle Component Analysis: RPCA has drawn a lot of attention in computer vision [49], [50]. Recently, the seminal work [13] shows that, under some mild conditions, the low-rank model can”
Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, methodology): “Note that in this algorithm, we apply the weighted median algorithm to update either P or X at a time, to reduce the total computation time and this is different from Ke and Kanade [3], where the algorithm is applied columnwise.”
Principal Component Analysis Based on L1-Norm Maximization (2008, methodology): “In order to obtain a solution of L1-PCA, a heuristic estimate for the general L1 problem was used in [5], while, in [6] and [7], the weighted median method and convex programming methods were proposed.”
Motion Segmentation in the Presence of Outlying, Incomplete, or Corrupted Trajectories (2010, methodology): “In practice, due to occlusions or limitations of the tracker, some features may be missing in some image frames and lead to incomplete trajectories in Y .T here are many methods in the computer vision literature for filling in the missing entries of a matrix of motion trajectories [14], [15], [ 19 ]”
Efficient Computation of Robust Weighted Low-Rank Matrix Approximations Using the L_1 Norm (2012, methodology): “The method is unfortunately very sensitive to initialization (see [13] for more detail).”
Robust Principal Component Analysis Based on Maximum Correntropy Criterion (2011, methodology): “Although methods based on (3) can improve robustness to outliers, those methods based on -norm [6], [7] and [21] are not invariant to rotation of input feature space and the equidistance surface will be very skewed [4].”
On the Complexity of Robust PCA and ℓ1-norm Low-Rank Matrix Approximation (2015, background): “However, in some applications, other metrics might have to be used; here are two important examples: • Weights and missing data.”
Robust (Semi) Nonnegative Graph Embedding (2014, methodology): “[24] proposed a unified 1-norm subspace learning framework based on linear programming technique, however it is time consuming.”
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices (2009, methodology): “er of natural approaches to robustifying PCA have been explored in the literature. These approaches include in uence function techniques [19, 28], multivariate trimming [18], alternating minimization [21], and random sampling techniques [16]. Unfortunately, none of these existing approaches yields a”