Random Projection is a technique used in data science for dimensionality reduction, particularly effective when dealing with high-dimensional datasets. The core idea is to project data from a high-dimensional space into a lower-dimensional space while preserving the pairwise distances between data points, as supported by the Johnson-Lindenstrauss lemma. This lemma states that a small set of points in a high-dimensional space can be embedded into a much lower-dimensional space with minimal distortion of distances ¹⁵.

The sklearn.random_projection module provides two main types of random projection: Gaussian random projection and sparse random projection. In Gaussian random projection, the projection matrix is generated using a Gaussian distribution, while in sparse random projection, a sparse random matrix is used. Both methods aim to reduce the computational burden associated with high-dimensional data while maintaining the essential structure of the dataset ¹³.

Random Projection is particularly advantageous compared to other methods like Principal Component Analysis (PCA), as it is less computationally expensive and can handle large datasets more efficiently ²³.