List of the algorithms

• RPCA: Robust PCA (44)

• • RPCA: Robust Principal Component Analysis (De la Torre and Black, 2001) website
• • PCP: Principal Component Pursuit (Candes et al. 2009)
• • FPCP: Fast PCP (Rodriguez and Wohlberg, 2013)
• • R2PCP: Riemannian Robust Principal Component Pursuit (Hintermüller and Wu, 2014)
• • AS-RPCA: Active Subspace: Towards Scalable Low-Rank Learning (Liu and Yan, 2012)
• • ALM: Augmented Lagrange Multiplier (Tang and Nehorai 2011)
• • EALM: Exact ALM (Lin et al. 2009) website
• • IALM: Inexact ALM (Lin et al. 2009) website
• • IALM_LMSVDS: IALM with LMSVDS (Liu et al. 2012)
• • IALM_BLWS: IALM with BLWS (Lin and Wei, 2010)
• • APG_PARTIAL: Partial Accelerated Proximal Gradient (Lin et al. 2009) website
• • APG: Accelerated Proximal Gradient (Lin et al. 2009) website
• • DUAL: Dual RPCA (Lin et al. 2009) website
• • SVT: Singular Value Thresholding (Cai et al. 2008) website
• • ADM: Alternating Direction Method (Yuan and Yang, 2009)
• • LSADM: LSADM (Goldfarb et al. 2010)
• • L1F: L1 Filtering (Liu et al. 2011)
• • DECOLOR: Contiguous Outliers in the Low-Rank Representation (Zhou et al. 2011) website1 website2
• • RegL1-ALM: Low-Rank Matrix Approximation under Robust L1-Norm (Zheng et al. 2012) website
• • GA: Grassmann Average (Hauberg et al. 2014) website
• • GM: Grassmann Median (Hauberg et al. 2014) website
• • TGA: Trimmed Grassmann Average (Hauberg et al. 2014) website
• • STOC-RPCA: Online Robust PCA via Stochastic Optimization (Feng et al. 2013) website
• • MoG-RPCA: Mixture of Gaussians RPCA (Zhao et al. 2014) website
• • OP-RPCA: Robust PCA via Outlier Pursuit (Xu et al. 2012) website
• • NSA1: Non-Smooth Augmented Lagrangian v1 (Aybat et al. 2011)
• • NSA2: Non-Smooth Augmented Lagrangian v2 (Aybat et al. 2011)
• • PSPG: Partially Smooth Proximal Gradient (Aybat et al. 2012)
• • flip-SPCP-sum-SPG: Flip-Flop version of Stable PCP-sum solved by Spectral Projected Gradient (Aravkin et al. 2014)
• • flip-SPCP-max-QN: Flip-Flop version of Stable PCP-max solved by Quasi-Newton (Aravkin et al. 2014)
• • Lag-SPCP-SPG: Lagrangian SPCP solved by Spectral Projected Gradient (Aravkin et al. 2014)
• • Lag-SPCP-QN: Lagrangian SPCP solved by Quasi-Newton (Aravkin et al. 2014)
• • FW-T: SPCP solved by Frank-Wolfe method (Mu et al. 2014) website
• • BRPCA-MD: Bayesian Robust PCA with Markov Dependency (Ding et al. 2011) website
• • BRPCA-MD-NSS: BRPCA-MD with Non-Stationary Noise (Ding et al. 2011) website
• • VBRPCA: Variational Bayesian RPCA (Babacan et al. 2011)
• • PRMF: Probabilistic Robust Matrix Factorization (Wang et al. 2012) website
• • OPRMF: Online PRMF (Wang et al. 2012) website
• • MBRMF: Markov BRMF (Wang and Yeung, 2013) website
• • TFOCS-EC: TFOCS with equality constraints (Becker et al. 2011) website
• • TFOCS-IC: TFOCS with inequality constraints (Becker et al. 2011) website
• • GoDec: Go Decomposition (Zhou and Tao, 2011) website
• • SSGoDec: Semi-Soft GoDec (Zhou and Tao, 2011) website
• • GreGoDec: Greedy Semi-Soft GoDec Algotithm (Zhou and Tao, 2013) website

• ST: Subspace Tracking (3)

• • GRASTA: Grassmannian Robust Adaptive Subspace Tracking Algorithm (He et al. 2012) website
• • GOSUS: Grassmannian Online Subspace Updates with Structured-sparsity (Xu et al. 2013) website
• • pROST: Robust PCA and subspace tracking from incomplete observations using L0-surrogates (Hage and Kleinsteuber, 2013) website

• MC: Matrix Completion (5)

• • LRGeomCG: Low-rank matrix completion by Riemannian optimization (Bart Vandereycken, 2013) website1 website2
• • GROUSE: Grassmannian Rank-One Update Subspace Estimation (Balzano et al. 2010) website
• • OptSpace: Matrix Completion from Noisy Entries (Keshavan et al. 2009) website
• • FPC: Fixed point and Bregman iterative methods for matrix rank minimization (Ma et al. 2008) website
• • SVT: A singular value thresholding algorithm for matrix completion (Cai et al. 2008) website

• LRR: Low Rank Recovery (6)

• • EALM: Exact ALM (Lin et al. 2009)
• • IALM: Inexact ALM (Lin et al. 2009)
• • ADM: Alternating Direction Method (Lin et al. 2011)
• • LADMAP: Linearized ADM with Adaptive Penalty (Lin et al. 2011)
• • FastLADMAP: Fast LADMAP (Lin et al. 2011)
• • ROSL: Robust Orthonormal Subspace Learning (Shu et al. 2014) website

• TTD: Three-Term Decomposition (4)

• • 3WD: 3-Way-Decomposition (Oreifej et al. 2012) website
• • MAMR: Motion-Assisted Matrix Restoration (Ye et al. 2015) website
• • RMAMR: Robust Motion-Assisted Matrix Restoration (Ye et al. 2015) website
• • ADMM: Alternating Direction Method of Multipliers (Parikh and Boyd, 2014) website1 website2

• NMF: Non-Negative Matrix Factorization (14)

• • NMF-MU: NMF solved by Multiplicative Updates
• • NMF-PG: NMF solved by Projected Gradient
• • NMF-ALS: NMF solved by Alternating Least Squares
• • NMF-ALS-OBS: NMF solved by Alternating Least Squares with Optimal Brain Surgeon
• • PNMF: Probabilistic Non-negative Matrix Factorization
• • ManhNMF: Manhattan NMF (Guan et al. 2013) website
• • NeNMF: NMF via Nesterovs Optimal Gradient Method (Guan et al. 2012) website
• • LNMF: Spatially Localized NMF (Li et al. 2001)
• • ENMF: Exact NMF (Gillis and Glineur, 2012) website
• • nmfLS2: Non-negative Matrix Factorization with sparse matrix (Ji and Eisenstein, 2013) website
• • Semi-NMF: Semi Non-negative Matrix Factorization
• • Deep-Semi-NMF: Deep Semi Non-negative Matrix Factorization (Trigeorgis et al. 2014) website
• • iNMF: Incremental Subspace Learning via NMF (Bucak and Gunsel, 2009) website
• • DRMF: Direct Robust Matrix Factorization (Xiong et al. 2011) website

• NTF: Non-Negative Tensor Factorization (6)

• • betaNTF: Simple beta-NTF implementation (Antoine Liutkus, 2012)
• • bcuNTD: Non-negative Tucker Decomposition by block-coordinate update (Xu and Yin, 2012) website
• • bcuNCP: Non-negative CP Decomposition by block-coordinate update (Xu and Yin, 2012) website
• • NTD-MU: Non-negative Tucker Decomposition solved by Multiplicative Updates (Zhou et al. 2012)
• • NTD-APG: Non-negative Tucker Decomposition solved by Accelerated Proximal Gradient (Zhou et al. 2012)
• • NTD-HALS: Non-negative Tucker Decomposition solved by Hierarchical ALS (Zhou et al. 2012)

• TD: Tensor Decomposition (11)

• • HoSVD: Higher-order Singular Value Decomposition (Tucker Decomposition)
• • HoRPCA-IALM: HoRPCA solved by IALM (Goldfarb and Qin, 2013) website
• • HoRPCA-S: HoRPCA with Singleton model solved by ADAL (Goldfarb and Qin, 2013) website
• • HoRPCA-S-NCX: HoRPCA with Singleton model solved by ADAL (non-convex) (Goldfarb and Qin, 2013) website
• • Tucker-ADAL: Tucker Decomposition solved by ADAL (Goldfarb and Qin, 2013) website
• • Tucker-ALS: Tucker Decomposition solved by ALS
• • CP-ALS: PARAFAC/CP decomposition solved by ALS
• • CP-APR: PARAFAC/CP decomposition solved by Alternating Poisson Regression (Chi et al. 2011)
• • CP2: PARAFAC2 decomposition solved by ALS (Bro et al. 1999)
• • RSTD: Rank Sparsity Tensor Decomposition (Yin Li, 2010) website
• • t-SVD: Tensor SVD in Fourrier Domain (Zhang et al. 2013)

• Some remarks:

• • The FW-T algorithm of Mu et al. (2014) works only with CVX library. Download and install it in: lrslibrary/libs/cvx/.
• • The DECOLOR algorithm of Zhou et al. (2011) don't works in MATLAB R2014a(x64), but works successfully in MATLAB R2013b(x64) and both R2014a(x86) and R2013b(x86).