A Comprehensive Review on Data Dimension Reduction through Random Projection Techniques

high-dimensional data presents serious research challenges in modern data analysis as it is computationally difficult, redundant, and hard to extract meaningful structure. Random Projection (RP) has been proposed as a fast and data-neutral dimensionality reduction method that has good theoretical guarantees provided by the JohnsonLindaastrass (JL) Lemma. The review includes a detailed analysis of the RP techniques, such as Gaussian, sparse, Achlioptas, and structured ones, and compares them to their applicability in the different application areas. The paper summarizes existing literature, lists some existing practical benefits including scalability and low cost of computation, and the limitations and future research directions. It is illustrated in the analysis that RP provides a good compromise between the efficiency and preservation of the structure and, thus, is a competitive alternative to some classical methods, including Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA).