Johnson Lindenstrauss

The Johnson-Lindenstrauss Lemma provides a powerful framework for dimensionality reduction, guaranteeing that high-dimensional data can be projected into a lower-dimensional space while approximately preserving pairwise distances. Current research focuses on refining the theoretical understanding of this lemma, particularly analyzing the performance of various projection methods (e.g., random projections, hashing, subsampling) under different data characteristics and noise conditions, and exploring its application in diverse areas such as graph learning and neural networks. These advancements lead to more efficient algorithms for handling high-dimensional data in machine learning, signal processing, and other fields where computational cost is a major constraint.