Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as Principle Component Analysis (PCA) and Linear Discriminant Analysis (LDA), have been studied extensively in the past few decades. However, as the dimension of huge data increases, the computational cost of traditional dimensionality reduction approaches grows dramatically and becomes prohibitive. It has also triggered the development of Random Projection (RP) technique which maps high-dimensional data onto low-dimensional subspace within short time. However, RP generates transformation matrix without considering intrinsic structure of original data and usually leads to relatively high distortion. Therefore, in the past few years, some approaches based on RP have been proposed to address this problem. In this paper, we summarized these approaches in different applications to help practitioners to employ proper approaches in their specific applications. Also, we enumerated their benefits and limitations to provide further references for researchers to develop novel RP-based approaches. A survey of dimensionality reduction techniques based on random projection