A closed form solution to robust subspace estimation and clustering

By Paolo Favaro, René Vidal, Avinash Ravichandran. Computer Vision and Pattern Recognition, 2011

342 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Signal Processing

View Paper: https://www.semanticscholar.org/paper/9839ba5f1208f715ff60609fc112a77bc69ec791

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In Civil and Structural Engineering

In Computational Mechanics

In Signal Processing

Citations in the corpus

Unifying Nuclear Norm and Bilinear Factorization Approaches for Low-Rank Matrix Decomposition (2013, methodology): “Since the nuclear norm yields a SDP, several methods try to optimize it efficiently [8, 9, 16, 24] by exploiting a closed form solution of its proximal operator.”
A Geometric Analysis of Subspace Clustering with Outliers (2011, methodology): “We believe that a major advantage of SSC vis a vis more recent approaches [13, 28] is that the eigen-gap heuristic is applicable under broader circumstances.”
Structured AutoEncoders for Subspace Clustering (2018, background): “1) Baseline Algorithms: We compare the proposed StructAEs with SSC [7], LRR [8], low rank based subspace clustering (LRSC) [41], LSR [6], smooth representation clustering (SMR) [42], kernel SSC (KSSC) [24], kernel LRR (KLRR) [23], latent subspace sparse subspace clustering (LS3C) [30] and stacked sp”
See all by looking at a few: Sparse modeling for finding representative objects (2012, background): “In this section, we formulate the problem of finding representative objects from the collection of data points.”
A Weakly Supervised Fine Label Classifier Enhanced by Coarse Supervision (2019, methodology): “Matrices are partitioned according to the sets I1 = {i : σi > 1 √ λ } and I2 = {i : σi ≤ 1 √ λ } [9].”
Deep Subspace Clustering Networks (2017, background): “We compare our methods against the following baselines: Low Rank Representation (LRR) [23], Low Rank Subspace Clustering (LRSC) [43], Sparse Subspace Clustering (SSC) [10], Kernel Sparse Subspace Clustering (KSSC) [35], SSC by Orthogonal Matching Pursuit (SSCOMP) [53], Efficient Dense Subspace Clust”
Robust Recovery of Subspace Structures by Low-Rank Representation (2010, methodology): “In [51] and [42], a non-convex formulation is adopted to learn the original data X 0 and its row space V 0 V T 0 simultaneously: where the unknown variable D is used as the dictionary.”
Low rank subspace clustering (LRSC) (2014, result): “Likewise, our results for LRSC are different from those in our prior work Favaro et al. (2011), where we had also used the erroneous function “compacc.”
Robust Online Multi-Task Learning with Correlative and Personalized Structures (2017, methodology): “To learn low-dimensional subspaces, recently proposed methods, such as Low-Rank Representation (LRR) [41] and Low-Rank Subspace and Clustering (LRSC) [42], usually depended on the nuclear norm as a convex rank approximation function to seek low-rank subspaces.”
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit (2015, result): “In particular, our result for deterministic arbitrary models is much stronger than the main result in [40].”
Multi-view low-rank sparse subspace clustering (2017, methodology): “Sparse subspace clustering [15] and low-rank subspace clustering [16, 17, 18, 19] are among most eﬀective methods that solve this problem.”