Spectral methods for data science: A statistical perspective

Y Chen, Y Chi, J Fan, C Ma - Foundations and Trends® in …, 2021‏ - nowpublishers.com
Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

Theoretical foundations of t-sne for visualizing high-dimensional clustered data

TT Cai, R Ma - Journal of Machine Learning Research, 2022‏ - jmlr.org
This paper investigates the theoretical foundations of the t-distributed stochastic neighbor
embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data …

[کتاب][B] Handbook of cluster analysis

C Hennig, M Meila, F Murtagh, R Rocci - 2015‏ - books.google.com
This handbook provides a comprehensive and unified account of the main research
developments in cluster analysis. Written by active, distinguished researchers in this area …

Consistency of spectral clustering in stochastic block models

J Lei, A Rinaldo - The Annals of Statistics, 2015‏ - JSTOR
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 …

Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics

TT Cai, A Zhang - 2018‏ - projecteuclid.org
Supplement to “Rate-optimal perturbation bounds for singular subspaces with applications
to high-dimensional statistics”. The supplementary material includes the proofs for Theorem …

Optimality of spectral clustering in the Gaussian mixture model

M Löffler, AY Zhang, HH Zhou - The Annals of Statistics, 2021‏ - projecteuclid.org
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 …

Spectral clustering of graphs with general degrees in the extended planted partition model

K Chaudhuri, F Chung… - Conference on Learning …, 2012‏ - proceedings.mlr.press
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 …

Impact of regularization on spectral clustering

A Joseph, B Yu - 2016‏ - projecteuclid.org
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 …

Estimating mixed memberships with sharp eigenvector deviations

X Mao, P Sarkar, D Chakrabarti - Journal of the American Statistical …, 2021‏ - Taylor & Francis
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 …

Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices

Y Chen, J Xu - Journal of Machine Learning Research, 2016‏ - jmlr.org
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 …