关键词: 降维, Wasserstein距离, 最小运输问题, 非线性方法, 概率分布模型

Abstract: Dimensionality reduction plays an important role in big data analysis and visualization. Many dimensionality reduction techniques with probabilistic distribution models rely on the optimizaition of cost function between low-dimensional model distribution and high-dimensional real distribution. The key issue of this type of technology is to efficiently construct the probabilistic distribution model representing the feature of original high-dimensional dataset most. In this paper, Wasserstein distance was introduced to dimensionality reduction, and a novel method named Wasserstein Embedded Map (W-map) was presented for high-dimensional data reduction and visualization. W-map converts dimensionality reduction problem into optimal transportation problem by constructing the similar Wasserstein flow in the high-dimensional dataset and its corresponding low-dimensional representation, and then the best matched low-dimensional visualization was found by solving the optimal transportation problem of Wasserstein distance. Experimental results demonstrate that the presented method performs well in dimensionality reduction and visualization for high-dimensional data.

Key words: dimensionality reduction, Wasserstein distance, optimal transportation problem, nonlinear technique, probabilistic model