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Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix.
On lines and planes of closest fit to systems of points in space
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Additive structure in qualitative data: An alternating least squares method with optimal scaling features
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Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features
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Regression quantiles
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Robust Statistics
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Least squares quantization in PCM
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Principal component analysis
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Comparison of five rules for determining the number of components to retain
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Neural networks and principal component analysis: Learning from examples without local minima
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Solving multiclass learning problems via error-correcting output codes
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Sparse coding with an overcomplete basis set: A strategy employed by V1?
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Atomic decomposition by basis pursuit
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Personality, motivation and cognitive performance: Final report to the army research institute on contract MDA 903-93-K-0008
W. Revelle and K. Anderson · 1998
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A fuzzy k k -modes algorithm for clustering categorical data
Z. Huang and M. Ng · 1999
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Learning the parts of objects by non-negative matrix factorization
D. Lee and H. Seung · 1999
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Large margin DAGs for multiclass classification
J. Platt, N. Cristianini, and J. Shawe-Taylor · 1999
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Probabilistic principal component analysis
M. Tipping and C. Bishop · 1999
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The information bottleneck method
N. Tishby, F. Pereira, and W. Bialek · 2000
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Nearest q q -flat to m m points
P. Tseng · 2000
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A generalization of principal component analysis to the exponential family
M. Collins, S. Dasgupta, and R. Schapire · 2001
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Algorithms for non-negative matrix factorization
D. Lee and H. Seung · 2001
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Automatic choice of dimensionality for pca
T. Minka · 2001
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On the algorithmic implementation of multiclass kernel-based vector machines
K. Crammer and Y. Singer · 2002
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Generalized 2
G. J. Gordon · 2002
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Branch and bound methods
S. Boyd and J. Mattingley · 2003
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
S. Burer and R. Monteiro · 2003
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Local minima and convergence in low-rank semidefinite programming
S. Burer and R. D. C. Monteiro · 2003
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Subgradient methods
S. Boyd, L. Xiao, and A. Mutapcic · 2003
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Repairing Tom Swift’s electric factor analysis machine
K. Preacher and R. MacCallum · 2003
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Weighted low-rank approximations
N. Srebro and T. Jaakkola · 2003
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A generalized linear model for principal component analysis of binary data
A. Schein, L. Saul, and L. Ungar · 2003
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k k -means projective clustering
P. K. Agarwal and N. H. Mustafa · 2004
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Convex Optimization
S. Boyd and L. Vandenberghe · 2004
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A direct formulation for sparse PCA using semidefinite programming
A. d’Aspremont, L. El Ghaoui, M. I. Jordan, and G. R. Lanckriet · 2004
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Clustering large graphs via the singular value decomposition
P. Drineas, A. Frieze, R. Kannan, S. Vempala, and V. Vinay · 2004
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Rank minimization and applications in system theory
M. Fazel, H. Hindi, and S. Boyd · 2004
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Multicategory support vector machines: Theory and application to the classification of microarray data and satellite radiance data
Y. Lee, Y. Lin, and G. Wahba · 2004
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In defense of one-vs-all classification
R. Rifkin and A. Klautau · 2004
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Learning with Matrix Factorizations
N. Srebro · 2004
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Maximum-margin matrix factorization
N. Srebro, J. Rennie, and T. Jaakkola · 2004
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Topics in Sparse Approximation
J. Tropp · 2004
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Quantile regression
R. Koenker · 2005
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Fast maximum margin matrix factorization for collaborative prediction
J. Rennie and N. Srebro · 2005
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k k -SVD: An algorithm for designing overcomplete dictionaries for sparse representation
M. Aharon, M. Elad, and A. Bruckstein · 2006
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Orthogonal nonnegative matrix t-factorizations for clustering
C. Ding, T. Li, W. Peng, and H. Park · 2006
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Efficient sparse coding algorithms
H. Lee, A. Battle, R. Raina, and A. Ng · 2006
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Document clustering using nonnegative matrix factorization
F. Shahnaz, M. W. Berry, V. P. Pauca, and R. J. Plemmons · 2006
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Sparse principal component analysis
H. Zou, T. Hastie, and R. Tibshirani · 2006
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k k -means + + ++ : The advantages of careful seeding
D. Arthur and S. Vassilvitskii · 2007
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Distributed optimization and statistical learning via the alternating direction method of multipliers
S. Boyd, N. Parikh, E. Chu, B. Peleato, and J. Eckstein · 2011
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Robust principal component analysis?
E. Candès, X. Li, Y. Ma, and J. Wright · 2011
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Low-rank matrix approximation with weights or missing data is NP-hard
N. Gillis and F. Glineur · 2011
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Nonnegative matrix factorization: Complexity, algorithms and applications
N. Gillis · 2011
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
N. Halko, P.-G. Martinsson, and J. Tropp · 2011
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Fast nonnegative matrix factorization: An active-set-like method and comparisons
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Algorithms and applications for approximate nonnegative matrix factorization
M. Berry, M. Browne, A. Langville, V. Pauca, and R. Plemmons · 2007
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Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis
H. Kim and H. Park · 2007
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Projected gradient methods for nonnegative matrix factorization
C. Lin · 2007
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Self-taught learning: Transfer learning from unlabeled data
R. Raina, A. Battle, H. Lee, B. Packer, and A. Ng · 2007
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Hinge rank loss and the area under the ROC curve
H. Steck · 2007
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Signal recovery from random measurements via orthogonal matching pursuit
J. Tropp and A. Gilbert · 2007
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J. Kim and H. Park · 2011
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Hogwild!: A lock-free approach to parallelizing stochastic gradient descent
F. Niu, B. Recht, C. Ré, and S. Wright · 2011
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Hogwild: A lock-free approach to parallelizing stochastic gradient descent
B. Recht, C. Ré, S. Wright, and F. Niu · 2011
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Large-scale convex minimization with a low-rank constraint
S. Shalev-Shwartz, A. Gonen, and O. Shamir · 2011
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Accuracy at the top
S. Boyd, C. Cortes, M. Mohri, and A. Radovanovic · 2012
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Julia: A fast dynamic language for technical computing
J. Bezanson, S. Karpinski, V. B. Shah, and A. Edelman · 2012
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Factoring nonnegative matrices with linear programs
V. Bittorf, B. Recht, C. Ré, and J. A. Tropp · 2012
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M. Davenport, Y. Plan, E. Berg, and M. Wootters · 2012
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Efficient algorithms for collaborative filtering
R. Keshavan · 2012
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Low Rank Approximation: Algorithms, Implementation, Applications
I. Markovsky · 2012
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P. Richtárik, M. Takáč, and S. Ahipaşaoğlu · 2012
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A geometric analysis of subspace clustering with outliers
M. Soltanolkotabi and E. Candes · 2012
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Nuclear norm minimization methods for frequency domain subspace identification
R. Smith · 2012
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Robust PCA via outlier pursuit
H. Xu, C. Caramanis, and S. Sanghavi · 2012
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Learning sparsely used overcomplete dictionaries via alternating minimization
A. Agarwal, A. Anandkumar, P. Jain, and P. Netrapalli · 2013
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
J. Bolte, S. Sabach, and M. Teboulle · 2013
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Scalable convex methods for flexible low-rank matrix modeling
W. Fithian and R. Mazumder · 2013
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Noisy matrix completion using alternating minimization
S. Gunasekar, A. Acharya, N. Gaur, and J. Ghosh · 2013
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On the provable convergence of alternating minimization for matrix completion
M. Hardt · 2013
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Low-rank matrix completion using alternating minimization
P. Jain, P. Netrapalli, and S. Sanghavi · 2013
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Efficient estimation of word representations in vector space
T. Mikolov, K. Chen, G. Corrado, and J. Dean · 2013
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Distributed representations of words and phrases and their compositionality
T. Mikolov, I. Sutskever, K. Chen, G. Corrado, and J. Dean · 2013
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Proximal algorithms
N. Parikh and S. Boyd · 2013
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Parallel stochastic gradient algorithms for large-scale matrix completion
B. Recht and C. Ré · 2013
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M. Soltanolkotabi, E. Elhamifar, and E. Candes · 2013
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Fantope projection and selection: A near-optimal convex relaxation of sparse PCA
V. Vu, J. Cho, J. Lei, and K. Rohe · 2013
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Learning to rank recommendations with the k k -order statistic loss
J. Weston, H. Yee, and R. J. Weiss · 2013
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H. Yun, H.-F. Yu, C.-J. Hsieh, S. V. N. Vishwanathan, and I. Dhillon · 2013
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Smallk is a C++/Python high-performance software library for nonnegative matrix factorization (NMF) and hierarchical and flat clustering using the NMF; current version 1.2.0
R. Boyd, B. Drake, D. Kuang, and H. Park · 2014
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Parallel prefix polymorphism permits parallelization, presentation & proof
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Matrix estimation by universal singular value thresholding
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CVXPY: A Python-embedded modeling language for convex optimization, version 0.2
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Quadratic programing solver for non-negative matrix factorization with spark
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Random projections for non-negative matrix factorization
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Training highly multiclass classifiers
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A flexible framework for projecting heterogeneous data
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Matrix completion and low-rank svd via fast alternating least squares
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Stable autoencoding: A flexible framework for regularized low-rank matrix estimation
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Confidence areas for fixed-effects pca
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Algorithms for nonnegative matrix and tensor factorizations: A unified view based on block coordinate descent framework
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Provable non-convex robust PCA
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Low Rank Representations of Matrices using Nuclear Norm Heuristics
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Glove: Global vectors for word representation
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Alternating direction method of multipliers for non-negative matrix factorization with the beta-divergence
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