A survey of dimensionality reduction techniques based on random projection

TL;DR

This survey reviews random projection-based dimensionality reduction techniques, highlighting their advantages, limitations, and applications in handling high-dimensional data efficiently.

Contribution

It provides a comprehensive summary of various RP methods, their benefits, limitations, and guidance for selecting suitable techniques for different scenarios.

Findings

RP techniques significantly reduce computational costs for high-dimensional data

Different RP methods have varying levels of data distortion and structure preservation

The survey offers references for developing new RP-based approaches

Abstract

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied extensively in the past few decades. However, as the dimensionality of data increases, the computational cost of traditional dimensionality reduction methods grows exponentially, and the computation becomes prohibitively intractable. These drawbacks have triggered the development of random projection (RP) techniques, which map high-dimensional data onto a low-dimensional subspace with extremely reduced time cost. However, the RP transformation matrix is generated without considering the intrinsic structure of the original data and usually leads to relatively high distortion. Therefore, in recent years, methods based on RP have been proposed to address this problem. In this paper, we summarize the methods used in different situations to help practitioners to employ the proper techniques for their specific applications. Meanwhile, we enumerate the benefits and limitations of the various methods and provide further references for researchers to develop novel RP-based approaches.