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Spectral methods for data science: A statistical perspective
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …
Theoretical foundations of t-sne for visualizing high-dimensional clustered data
This paper investigates the theoretical foundations of the t-distributed stochastic neighbor
embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data …
embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data …
[کتاب][B] Handbook of cluster analysis
This handbook provides a comprehensive and unified account of the main research
developments in cluster analysis. Written by active, distinguished researchers in this area …
developments in cluster analysis. Written by active, distinguished researchers in this area …
Consistency of spectral clustering in stochastic block models
We analyze the performance of spectral clustering for community extraction in stochastic
block models. We show that, under mild conditions, spectral clustering applied to the …
block models. We show that, under mild conditions, spectral clustering applied to the …
Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics
Supplement to “Rate-optimal perturbation bounds for singular subspaces with applications
to high-dimensional statistics”. The supplementary material includes the proofs for Theorem …
to high-dimensional statistics”. The supplementary material includes the proofs for Theorem …
Optimality of spectral clustering in the Gaussian mixture model
In the Supplementary Material [42], we first present some propositions that characterize the
population quantities in Appendix A. Then in Appendix B, we give several auxiliary lemmas …
population quantities in Appendix A. Then in Appendix B, we give several auxiliary lemmas …
Spectral clustering of graphs with general degrees in the extended planted partition model
In this paper, we examine a spectral clustering algorithm for similarity graphs drawn from a
simple random graph model, where nodes are allowed to have varying degrees, and we …
simple random graph model, where nodes are allowed to have varying degrees, and we …
Impact of regularization on spectral clustering
Impact of regularization on spectral clustering Page 1 The Annals of Statistics 2016, Vol. 44, No.
4, 1765–1791 DOI: 10.1214/16-AOS1447 © Institute of Mathematical Statistics, 2016 IMPACT …
4, 1765–1791 DOI: 10.1214/16-AOS1447 © Institute of Mathematical Statistics, 2016 IMPACT …
Estimating mixed memberships with sharp eigenvector deviations
We consider the problem of estimating community memberships of nodes in a network,
where every node is associated with a vector determining its degree of membership in each …
where every node is associated with a vector determining its degree of membership in each …
Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices
We consider two closely related problems: planted clustering and submatrix localization. In
the planted clustering problem, a random graph is generated based on an underlying cluster …
the planted clustering problem, a random graph is generated based on an underlying cluster …