R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization

By Chris H. Q. Ding, Ding Zhou, Xiaofeng He, Hongyuan Zha. International Conference on Machine Learning, 2006

704 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0439f9ea8dabf18581322f33aa25424851251d21

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Citations in the corpus

Low rank approximation with entrywise l1-norm error (2017, methodology): “Then any of the four heuristic algorithms [17, 34, 56, 59] is not able to achieve better than an nmin(γ ,0.”
Multiple Incomplete Views Clustering via Weighted Nonnegative Matrix Factorization with L2, 1 Regularization (2015, background): “L2,1 norm of a matrix was first introduced in [9] as rotational invariant L1 norm.”
Maximizing boosted top identification by minimizing N-subjettiness (2011, methodology): “ˆn(n) J ,nˆ (n+1) J ) (3.5) is smaller than the desired precision threshold (∆ < 10−4 in this paper). In the computer science literature, a similar algorithm called R1-k-means was proposed in Ref. [45] for β = 1. The R1-k-means algorithm should not be confused with the k-medians algorithm, as k-m”
Robust Principal Component Analysis Based on Maximum Correntropy Criterion (2011, methodology): “Here, we verify the robustness of our proposed rotationally invariant HQ-PCA algorithm and compare the performance with two state-of-the-art PCAs: R1-PCA [4] and PCA- [10].”
Robust nonnegative matrix factorization using L21-norm (2011, background): “L2,1 norm of a matrix A is first introduced in [9] and is defined as”
Principal Component Analysis Based on L1-Norm Maximization (2008, methodology): “In addition, the minimization of (4) is also very difficult an d a subspace iteration algorithm based on L1 norm estimation techniques such as Huber’s M-estimato r was used in [4].”
Robust and Discriminative Self-Taught Learning (2013, methodology): “Instead of using traditional squared ℓ2-norm loss function when learning the feature dictionary, we use the ℓ2,1-norm loss function, which is robust to outlier samples (Ding et al., 2006; Nie et al., 2010).”
Discriminative Least Squares Regression for Multiclass Classification and Feature Selection (2012, background): “However, L 2 , 1 norm-based loss function is rotational invariant [45], and will lead to unchanged loss value under orthogonal transformations.”
Efficient and Robust Feature Selection via Joint ℓ2, 1-Norms Minimization (2010, methodology): “This loss function has a rotational invariant property while the pure `1-norm loss function does not has such desirable property [5].”
Robust Computation of Linear Models by Convex Relaxation (2012, background): “Although many algorithms [2,12,25,58,74,81] attempt (1.”
Efficient $l_{1}$ -Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method (2015, methodology): “[4] proposed r1-PCA, which combines the merits of the l1-norm and l2-norm.”
Outlier Detection for Text Data (2017, methodology): “We will relate the BCD framework to our non-negative matrix factorization problem, and explain our algorithm Text Outliers using Nonnegative Matrix Factorization(TONMF) in detail.”
Face2Face: Real-Time Face Capture and Reenactment of RGB Videos (2016, methodology): “We use the 2,1-norm [12] instead of a least-squares formulation to be robust against outliers.”
A survey of dimensionality reduction techniques (2014, methodology): “However, these modifications are not invariant to rotations of the input features [Ding2006].”