What is the role of random projection in scalable dimensionality reduction?

Random projection reduces dimensionality using random matrices while approximately preserving distances.

Random projection is based on the Johnson-Lindenstrauss lemma, which states that high-dimensional points can be projected into lower dimensions with minimal distortion using random linear transformations. It is computationally efficient because it avoids eigen decomposition and works well for very large sparse datasets. It is widely used in preprocessing pipelines for clustering and nearest neighbor search.