Dimensionality Reduction by Using Sparse Reconstruction Embedding

Abstract

Traditional algorithms for dimensionality reduction attempt to preserve the intrinsic geometric properties from high-dimensional space to low-dimensional space. However, these algorithms have poor discrimination on intersecting data and poorly sampled data for classification tasks, because the distance metric methods used for describing the geometric properties are meaningless when processing under-sampled or intersection data. In this paper, we provide a new perspective on solving the problem of dimensionality reduction and propose a novel and parameter-free algorithm called Sparse Reconstruction Embedding(SRE). In SRE, each point is first reconstructed from all the other points by minimizing the reconstruction errors and L ₀ norm, and then mapped into low-dimensional coordinates by preserving the minimum of reconstruction errors. Experimental results show that our approach is much more discriminant and insensitive to under-sampled and intersecting data. We also demonstrate that SRE outperforms the state-of-art algorithms both on artificial datasets and natural datasets in classification tasks.