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Singular values of a data in a matrix form provide insights on the structure of the data, the effective dimensionality, and the choice of hyper-parameters on higher-level data analysis tools.
Characteristic vectors of bordered matrices with infinite dimensions
E. P. Wigner · 1955
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On the second eigenvalue in random regular graphs
J. Friedman, J. Kahn, and E. Szemerédi · 1989
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A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines
Michael F Hutchinson · 1990
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Finding and counting given length cycles
N. Alon, R. Yuster, and U. Zwick · 1997
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Characterization of 3d molecular structure
E. Estrada · 2000
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Finding and counting small induced subgraphs efficiently
T. Kloks, D. Kratsch, and H. Müller · 2000
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Fast computation of low rank matrix approximations
Dimitris Achlioptas and Frank McSherry · 2001
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Chebyshev polynomials
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Network motifs in the transcriptional regulation network of escherichia coli
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The parameterized complexity of counting problems
J. Flum and M. Grohe · 2004
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Chebyshev approximation of log-determinants of spatial weight matrices
R. K. Pace and J. P. LeSage · 2004
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Selective avoidance of cycles in irregular ldpc code construction
T. Tian, C. R. Jones, J. D. Villasenor, and R. D. Wesel · 2004
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Spectral measures of bipartivity in complex networks
E. Estrada and J. A. Rodriguez-Velázquez · 2005
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Spectral techniques applied to sparse random graphs
U. Feige and E. Ofek · 2005
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Gaussian Markov random fields: theory and applications
H. Rue and L. Held · 2005
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An algorithm for counting short cycles in bipartite graphs
T. R. Halford and K. M. Chugg · 2006
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A new way to enumerate cycles in graph
H. Liu and J. Wang · 2006
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Information-theoretic metric learning
J. V. Davis, B. Kulis, P. Jain, S. Sra, and I. S. Dhillon · 2007
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Statistical-mechanical approach to subgraph centrality in complex networks
E. Estrada and N. Hatano · 2007
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Approximate implementation of the logarithm of the matrix determinant in gaussian process regression
Y. Zhang and W. E. Leithead · 2007
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Smooth function topological structure descriptors based on graph-spectra
R. Carbó-Dorca · 2008
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Exact matrix completion via convex optimization
E. J. Candès and B. Recht · 2009
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A gradient descent algorithm on the Grassman manifold for matrix completion
R. H. Keshavan and S. Oh · 2009
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Density-matrix-based algorithm for solving eigenvalue problems
Eric Polizzi · 2009
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Minimum volume ellipsoid
S. Van Aelst and P. Rousseeuw · 2009
Parameter estimation in high dimensional gaussian distributions
E. Aune, D. P. Simpson, and J. Eidsvik · 2014
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Universal matrix completion
S. Bhojanapalli and P. Jain · 2014
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On sketching matrix norms and the top singular vector
Y. Li, H. L. Nguyên, and D. P. Woodruff · 2014
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Non-convex robust pca
Praneeth Netrapalli, UN Niranjan, Sujay Sanghavi, Animashree Anandkumar, and Prateek Jain · 2014
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Efficiently estimating motif statistics of large networks
P. Wang, J. Lui, B. Ribeiro, D. Towsley, J. Zhao, and X. Guan · 2014
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A randomized algorithm for approximating the log determinant of a symmetric positive definite matrix
C. Boutsidis, P. Drineas, P. Kambadur, E.-M. Kontopoulou, and A. Zouzias · 2015
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Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix
H. Avron and S. Toledo · 2011
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Robust principal component analysis?
Emmanuel J Candès, Xiaodong Li, Yi Ma, and John Wright · 2011
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On the rate of convergence to the semicircular law, preprint (2011)
F. Götze and A. Tikhomirov · 2011
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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
Nathan Halko, Per-Gunnar Martinsson, and Joel A Tropp · 2011
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Randomized algorithms for matrices and data
Michael W Mahoney et al · 2011
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W. Schudy and M. Sviridenko · 2011
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Beyond triangles: A distributed framework for estimating 3-profiles of large graphs
E. R. Elenberg, K. Shanmugam, M. Borokhovich, and A. G. Dimakis · 2015
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Large-scale log-determinant computation through stochastic chebyshev expansions
I. Han, D. Malioutov, and J. Shin · 2015
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Sparse random graphs: regularization and concentration of the laplacian
C. M. Le, E. Levina, and R. Vershynin · 2015
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Improved bounds on sample size for implicit matrix trace estimators
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Matrix completion from fewer entries: Spectral detectability and rank estimation
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Distributed estimation of generalized matrix rank: Efficient algorithms and lower bounds
Y. Zhang, M. J. Wainwright, and M. I. Jordan · 2015
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How accurately should i compute implicit matrix-vector products when applying the hutchinson trace estimator?
J. Chen · 2016
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Efficient estimation of eigenvalue counts in an interval
E. Di Napoli, E. Polizzi, and Y. Saad · 2016
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Distributed estimation of graph 4-profiles
E. R. Elenberg, K. Shanmugam, M. Borokhovich, and A. G. Dimakis · 2016
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Approximating the spectral sums of large-scale matrices using chebyshev approximations
I. Han, D. Malioutov, H. Avron, and J. Shin · 2016
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Spectrum estimation from samples
W. Kong and G. Valiant · 2016
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On approximating functions of the singular values in a stream
Y. Li and D. P. Woodruff · 2016
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Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse
L. Wu, J. Laeuchli, V. Kalantzis, A. Stathopoulos, and E. Gallopoulos · 2016
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Matrix completion from noisy entries
R. H Keshavan, A. Montanari, and S. Oh · 2078
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