关键词: 扩散映射, 非线性降维, 判别核方案, 类别标签, 核函数, 流形学习

Abstract:

Aiming at that high-dimensional data is hard to be understood intuitively, and cannot be effectively processed by traditional machine learning and data mining techniques, a new method for nonlinear dimensionality reduction called Discriminant Diffusion Maps Analysis (DDMA) was proposed. It was implemented by applying a discriminant kernel scheme to the framework of the diffusion maps. The Gaussian kernel window width was selected from the within-class width and the between-class width according to discriminating sample category labels, it made kernel function effectively extract data correlation features and exactly describe the structure characteristics of data space. The DDMA was used in artificial Swiss-roll test and penicillin fermentation process, with comparisons with Principle Component Analysis (PCA), Linear Discriminant Analysis (LDA), Kernel Principle Components Analysis (KPCA), Laplacian Eigenmaps (LE) and Diffusion Maps (DM). The results show that DDMA represents the high-dimensional data in a low-dimensional space while successfully retaining original characteristics of the data; in addition, the data structure features in low-dimensional space generated by DDMA are superior to those generated by the comparison methods, the performance of data dimension reduction and feature extraction verifies effectiveness of the proposed scheme.

Key words: Diffusion Maps (DM), nonlinear dimensionality reduction, discriminant kernel scheme, category label, kernel function, manifold learning