Johnson Lindenstrauss Transform

The Johnson-Lindenstrauss Transform (JL Transform) is a dimensionality reduction technique that efficiently projects high-dimensional data into a lower-dimensional space while approximately preserving pairwise distances. Current research focuses on improving the speed and sparsity of JL transforms, particularly through algorithmic advancements like the Fast JL Transform and exploring variations such as sparse and quantized JL transforms. These improvements are crucial for applications ranging from large-scale data analysis and machine learning (e.g., efficient processing of large language model embeddings) to privacy-preserving data release, where reducing dimensionality is essential for computational efficiency and data protection.