A dimensionality reduction method of continuous dependent variables based supervised Laplacian eigenmaps. Issue 11 (24th July 2019)

• Record Type: Journal Article
• Authors: Fan, Zhipeng
• Is Part Of: Journal of statistical computation and simulation. Volume 89:Issue 11(2019)
• Page Start: 2073
• Page End: 2083
• Publication Date: 2019-07-24
• Subjects: Dimensionality reduction -- supervised learning -- continuous dependent variables -- Laplacian graph -- neighbourhood; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1607347
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: Dimensionality reduction is one of the important preprocessing steps in high-dimensional data analysis. In this paper we propose a supervised manifold learning method, it makes use of the information of continuous dependent variables to distinguish intrinsic neighbourhood and extrinsic neighbourhood of data samples, and construct two graphs according to these two kinds of neighbourhoods. Following the idea of Laplacian eigenmaps, we reveal that on the low-dimensional manifold the neighbourhood structure can be preserved or even improved. Our approach has two important characteristics: (i) it uses dependent variables to find an informative low-dimensional projection which is robust to noisy independent variables and (ii) the objective function simultaneously enlarges the distance between dissimilar samples and pushes similar samples close to each other according to the graph constructed with the help of continuous dependent variables. Our experiments demonstrate that the effectiveness of our method is over their traditional rivals.