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Matrix perturbation theory

TLDR
In this article, the Perturbation of Eigenvalues and Generalized Eigenvalue Problems are studied. But they focus on linear systems and Least Squares problems and do not consider invariant subspaces.
Abstract
Preliminaries. Norms and Metrics. Linear Systems and Least Squares Problems. The Perturbation of Eigenvalues. Invariant Subspaces. Generalized Eigenvalue Problems.

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A tutorial on spectral clustering

TL;DR: In this article, the authors present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches, and discuss the advantages and disadvantages of these algorithms.
Journal ArticleDOI

Community detection in graphs

TL;DR: A thorough exposition of community structure, or clustering, is attempted, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists.
Proceedings Article

On Spectral Clustering: Analysis and an algorithm

TL;DR: A simple spectral clustering algorithm that can be implemented using a few lines of Matlab is presented, and tools from matrix perturbation theory are used to analyze the algorithm, and give conditions under which it can be expected to do well.
Journal ArticleDOI

Community detection in graphs

TL;DR: A thorough exposition of the main elements of the clustering problem can be found in this paper, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.
Proceedings Article

Improved Algorithms for Linear Stochastic Bandits

TL;DR: A simple modification of Auer's UCB algorithm achieves with high probability constant regret and improves the regret bound by a logarithmic factor, though experiments show a vast improvement.