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Probabilistic distribution model based on Wasserstein distance for nonlinear dimensionality reduction
CAO Xiaolu, XIN Yunhong
Journal of Computer Applications
2017, 37 (10):
2819-2822.
DOI: 10.11772/j.issn.1001-9081.2017.10.2819
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.
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