Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Executive Summary
- 1 Rudiments of Statistical Learning Theory
- 2 Vapnik–Chervonenkis Dimension
- 3 Learnability for Binary Classification
- 4 Support Vector Machines
- 5 Reproducing Kernel Hilbert Spaces
- 6 Regression and Regularization
- 7 Clustering
- 8 Dimension Reduction
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
8 - Dimension Reduction
from Part One - Machine Learning
Published online by Cambridge University Press: 21 April 2022
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Executive Summary
- 1 Rudiments of Statistical Learning Theory
- 2 Vapnik–Chervonenkis Dimension
- 3 Learnability for Binary Classification
- 4 Support Vector Machines
- 5 Reproducing Kernel Hilbert Spaces
- 6 Regression and Regularization
- 7 Clustering
- 8 Dimension Reduction
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
Summary
The high dimensionality of datapoints often constitutes an obstacle to efficient computations. This chapter investigates three workarounds that replace the datapoints by some substitutes selected in a lower dimensional set. The first workaround is principal component analysis, where the lower dimensional set is a linear space spanned by the top singular vectors of the data matrix. The second workaround is a Johnson–Lindenstrauss projection, where the lower dimensional set is a random linear space. The third workaround is locally linear embedding, where the lower dimensional set is not chosen as a linear space anymore.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 56 - 64Publisher: Cambridge University PressPrint publication year: 2022