The Empirical Gram Matrix

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Table of contents

1 The Gram Matrix 
1.1 Introduction
1.2 Estimate of the Gram matrix
1.3 Gram operators in Hilbert spaces
1.4 Symmetric random matrices
1.5 Covariance matrix
1.6 Empirical results
2 The Empirical Gram Matrix 
2.1 Introduction
2.2 Estimate of the Gram matrix via the empirical Gram matrix
3 Principal Component Analysis 
3.1 Introduction
3.2 Estimate of the eigenvalues
3.3 Standard Principal Component Analysis
3.4 Robust Principal Component Analysis
4 Spectral Clustering 
4.1 Introduction
4.2 Description of an ideal algorithm
4.3 Estimation of the ideal algorithm by an empirical one
4.4 Empirical results