Dimensionality Reduction - Part 2

Mahmood Amintoosi, Fall 2024

Computer Science Dept, Ferdowsi University of Mashhad

Linear Discriminant Analysis

• Linear Discriminant Analysis (LDA)

From high-dimensional into low-dimensional Euclidean space

• Johnson–Lindenstrauss lemma

• Gaussian random projection

• Random Projection: Theory and Implementation in Python with Scikit-Learn

Further Reading

• Scikit-learn: The Johnson-Lindenstrauss bound for embedding with random projections

• Paper: Supervised dimensionality reduction for big data

• Paper: An Introduction to Johnson–Lindenstrauss Transforms

• Sketching Algorithms for Big Data, Harvard

  • JL Lemma, History of lower bounds

  • JL Lower bound Optimality