面向复杂多流形高维数据的t-SNE降维方法

t-SNE for Complex Multi-Manifold High-Dimensional Data

针对t-SNE方法不能很好地区分相互交叉的多个流形的问题,提出一种可视化降维方法.在t-SNE方法的基础上,在计算高维概率时考虑欧几里得度量和局部主成分分析以区分不同流形.然后可直接使用t-SNE的梯度求解方法得到降维结果.最后分别用3个人工生成的三维数据集和2个通用的机器学习数据集进行实验,并根据不同流形的区分度和流形内的邻域可信度2个指标对降维结果进行量化分析.结果表明,该方法在处理有交叉的多流形数据时的效果要明显优于原来的t-SNE方法,并能够较好地保持每个流形的邻域结构.

To solve the problem that the t-SNE method cannot distinguish multiple manifolds that intersect each other well,a visual dimensionality reduction method is proposed.Based on the t-SNE method,Euclid-ean metric and local PCA are considered when calculating high-dimensional probability to distinguish dif-ferent manifolds.Then the t-SNE gradient solution method can be directly used to get the dimensionality reduction result.Finally,three generated data and two real data are used to test proposed method,and quan-titatively evaluate the discrimination of different manifolds and the degree of neighborhood preservation within the manifold in the dimensionality reduction results.These results show that proposed method is more useful when processing multi-manifold data,and can keep the neighborhood structure of each mani-fold well.