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

被引：0

作者：

Bian R. ^{[1
]}

Zhang J. ^{[2
]}

Zhou L. ^{[3
]}

Jiang P. ^{[4
]}

Chen B. ^{[1
]}

Wang Y. ^{[1
]}

机构：

[1] School of Computer Science and Technology, Shandong University, Qingdao

[2] Computer Network Information Center, Chinese Academy of Sciences, Beijing

[3] Scientific Computing and Imaging Institute, University of Utah, Salt Lake City

[4] School of Qilu Transportation, Shandong University, Jinan

来源：

Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics | 2021年 / 33卷 / 11期

关键词：

Dimensionality reduction; Local principal component analysis; Multi-manifold; Visualization;

D O I：

10.3724/SP.J.1089.2021.18806

中图分类号：

学科分类号：

摘要：

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. © 2021, Beijing China Science Journal Publishing Co. Ltd. All right reserved.

引用

页码：1746 / 1754

页数：8

共 21 条

[11] Wang Y, Jiang Y, Wu Y, Et al., Spectral clustering on multiple manifolds, IEEE Transactions on Neural Networks, 22, 7, pp. 1149-1161, (2011)
[12] van der Maaten L., Accelerating t-SNE using tree-based algorithms, Journal of Machine Learning Research, 15, 93, pp. 3221-3245, (2014)
[13] Lloyd S., Least squares quantization in PCM, IEEE Transactions on Information Theory, 28, pp. 129-137, (1982)
[14] Ester M, Kriegel H P, Sander J, Et al., A density-based algorithm for discovering clusters in large spatial databases with noise, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, pp. 226-231, (1996)
[15] von Luxburg U., A tutorial on spectral clustering, Statistics and Computing, 17, 4, pp. 395-416, (2007)
[16] Stewart G W, Sun J G., Matrix perturbation theory (computer science and scientific computing), (1990)
[17] Samet H., The design analysis of spatial data structures, pp. 66-80, (1989)
[18] Omohundro S M., Five balltree construction algorithms, (1989)
[19] LeCun Y, Bottou L, Bengio Y, Et al., Gradient-based learning applied to document recognition, Proceedings of the IEEE, 86, 11, pp. 2278-2324, (1998)
[20] Fisher R A., The use of multiple measurements in taxonomic problems, Annals of Eugenics, 7, 2, pp. 179-188, (1936)

← 1 2 3 →