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

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, Euclidean metric and local PCA are considered when calculating high-dimensional probability to distinguish different 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 quantitatively 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 manifold well.