Hybrid non-linear dimensionality reduction method framework based on random projections

Abstract

Dimensionality reduction of big data is becoming more and more important in many domains, such as cloud computing, human gene distribution, image processing and smart grids, which all involve high-dimensional data analysis. While traditional linear dimensionality reduction techniques are computationally efficient and simple to implement, they fail to adequately capture the intrinsic structure of complex nonlinear high-dimensional data. To solve this problem, many non-linear dimensionality reduction methods, such as Isometric Embedding, Locally Linear Embedding, Semidefinite Embedding and Laplacian Eigenmaps, have been proposed. Though these approaches can be used to learn the global structure of non-linear manifolds, they are computationally expensive, potentially limiting their use in large-scale applications with high-dimensional data. This paper proposes an innovative hybrid non-linear dimensionality reduction method framework based on random projections, which can save computer memory, enhance computing speed and preserve original data geometry. In addition, experiments under several different combinations of random projections and non-linear dimensionality reduction methods are tested on a document-term dataset to verify the effectiveness of the proposed framework.