A Framework for Robust Subspace Learning

By Fernando De la Torre, Michael J. Black. International Journal of Computer Vision, 2003

662 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3f5dfbd571ef719a2c5dc1ed63ca6a3702f7861e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “…facial images can be modeled as reflections of a Lambertian object and approximated by a low dimensional linear subspace; this low rank nature leads to a proper reconstruction of a face model from occluded/corrupted face images (De La Torre and Black, 2003; Liu et al, 2010; Zheng et al, 2012).”
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, background): “…as well as their relaxation forms (e.g., l 1 norm and nuclear norm), have been shown to be helpful to ﬁnely encode the data sparsity in applications, and has inspired various sparse/low-rank models and algorithms against different practical problem [6], [9], [14], [26], [47], [50], [68], [75].”
Incremental gradient on the Grassmannian for online foreground and background separation in subsampled video (2012, methodology): “On the other hand, there has been a large amount of recent work on low-rank models which are more robust to gross corruptions [25, 8, 7].”
Synthesizing physically realistic human motion in low-dimensional, behavior-specific spaces (2004, neutral): “CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation, G.1.6 [Numerical Analysis]: Optimization—Constrained Optimization Keywords: physically based animation, optimization, motion capture”
Robust PCA via Outlier Pursuit (2010, background): “, [3, 5–11]).”
Appearance-based face recognition and light-fields (2004, methodology): “In order to include gallery subjects during training, an algorithm performing PCA with missing data would have to be used to compute the eigen light-fields [ 11 ], [25].)”
Principal Component Analysis Based on L1-Norm Maximization (2008, background): “In order to alleviate this problem and achieve robustness, much research has been performed [2], [3], [4], [5], [6], [7].”
Robust Structured Subspace Learning for Data Representation (2015, background): “In this section, we briefly review the related research on feature learning including feature selection [3], [4], [5], [13] and subspace learning [2], [14].”
Weighted Nuclear Norm Minimization with Application to Image Denoising (2014, background): “For instance, the low rank nature of matrix formed by human facial images allows us to reconstruct the occluded/corrupted faces [8, 20, 30].”
Moving Object Detection by Detecting Contiguous Outliers in the Low-Rank Representation (2011, background): “RPCA has drawn a lot of attention in computer vision [49], [50].”
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.”
RASL: Robust alignment by sparse and low-rank decomposition for linearly correlated images (2010, background): “This somewhat unsatisfactory status quo is mainly due to the extremely difficult nature of the core problem of fitting a low-rank model to highly corrupted data [8], a problem that until recently lacked a polynomial-time algorithm with strong performance guarantees.”
Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recovery (2017, methodology): “A key motivating application is video analytics: decomposing a video into a slowly changing background video and a sparse foreground video [2], [4].”
R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization (2006, methodology): “Several robust PCA have been proposed(Torre & Black, 2003; Aanas et al., 2002).”
Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation (2014, methodology): “Since our investigation is relying on the half-quadratic theory, we first review some theoretical background and half-quadratic modeling based on conjugate function theory [36], [37] for convex or nonconvex minimization.”
Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices (2009, methodology): “y irrelevant to the structure we are trying to identify. A number 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 ”