Random Projection is a technique used to reduce the dimensionality of data, which is particularly useful when dealing with high-dimensional datasets. The core idea is to project the data from a high-dimensional space to a lower-dimensional space using a randomly generated projection matrix. This method is computationally efficient and can help in speeding up processing times while maintaining a controlled level of accuracy in the data representation.

The effectiveness of Random Projection is supported by the Johnson-Lindenstrauss lemma, which 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 between the points. This means that while the pairwise distances may not be perfectly preserved, they remain approximately intact, allowing for meaningful analysis of the data in its reduced form ¹³⁵.

There are two main types of projection matrices used in Random Projection: Gaussian random matrices and sparse random matrices. Each has its own advantages, with sparse random matrices being less computationally expensive due to their structure ²³.