publication . Preprint . 2009

Introduction to Machine Learning: Class Notes 67577

Shashua, Amnon;
Open Access English
  • Published: 23 Apr 2009
Abstract
Comment: 109 pages, class notes of Machine Learning course given at the Hebrew University of Jerusalem
Subjects
arXiv: Computer Science::Machine Learning
free text keywords: Computer Science - Learning
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5 Spectral Analysis I: PCA, LDA, CCA 5.1 PCA: Statistical Perspective 5.1.1 Maximizing the Variance of Output Coordinates 5.1.2 Decorrelation: Diagonalization of the Covariance Matrix 5.2 PCA: Optimal Reconstruction 5.3 The Case n >> m 5.4 Kernel PCA 5.5 Fisher's LDA: Basic Idea 5.6 Fisher's LDA: General Derivation 5.7 Fisher's LDA: 2-class 5.8 LDA versus SVM 5.9 Canonical Correlation Analysis

6 Spectral Analysis II: Clustering 6.1 K-means Algorithm for Clustering 6.1.1 Matrix Formulation of K-means 6.2 Min-Cut 6.3 Spectral Clustering: Ratio-Cuts and Normalized-Cuts 6.3.1 Ratio-Cuts 6.3.2 Normalized-Cuts

7 The Formal (PAC) Learning Model 7.1 The Formal Model 7.2 The Rectangle Learning Problem 7.3 Learnability of Finite Concept Classes 7.3.1 The Realizable Case 7.3.2 The Unrealizable Case

8 The VC Dimension 8.1 The VC Dimension 8.2 The Relation between VC dimension and PAC Learning

9 The Double-Sampling Theorem 9.1 A Polynomial Bound on the Sample Size m for PAC Learning 9.2 Optimality of SVM Revisited

10 Appendix Bibliography

41 42 43 46 47 49 49 50 52 54 54 55 58 59 60 62 63 64 65 69 69 73 75 76 77 80 81 85 89 M. Anthony and P.L. Bartlett. Neural Neteowk Learning: Theoretical Foundations. Cambridge University Press, 1999.

K.M. Hall. An r-dimensional quadratic placement algorithm. Manag. Sci., 17:219{ 229, 1970.

M.J. Kearns and U.V. Vazirani. An Introduction to Computational Learning Theory. MIT Press, 1997.

Y. Linde, A. Buzo, and R.M. Gray. An algorithm for vector quantizer design. IEEE Transactions on Communications, 1:84{95, 1980. [OpenAIRE]

A.Y. Ng, M.I. Jordan, and Y. Weiss. On spectral clustering: Analysis and an algorithm. In Proceedings of the conference on Neural Information Processing Systems (NIPS), 2001.

J. Shi and J. Malik. Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(8), 2000.

R. Zass and A. Shashua. A unifying approach to hard and probabilistic clustering. In Proceedings of the International Conference on Computer Vision, Beijing, China, Oct. 2005. [OpenAIRE]

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