https://blog.csdn.net/rosenor1/article/details/52278116
https://blog.csdn.net/u013250861/article/details/111658629
https://zhuanlan.zhihu.com/p/157482881

https://github.com/heucoder/dimensionality_reduction_alo_codes

PCA、LDA、LFA、LPP、LE、FastICA、SVD、ICA

KPCA 、KICA、KDA

LLE、t-SNE、MDS、ISOMAP、MVU、LTSA、

AutoEncoder

  • 线性降维方法：PCA 、ICA LDA、LFA、LPP(LE 的线性表示)
  • 非线性降维方法：
  • 基于核函数的非线性降维方法——KPCA 、KICA、KDA
  • 基于特征值的非线性降维方法(流型学习)——ISOMAP、LLE、LE、LPP、LTSA、MVU

image.png

Manifold learning (Isomap, LLE, t SNE, UMAP)

umap

Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. The algorithm is founded on three assumptions about the data:

  1. The data is uniformly distributed on a Riemannian manifold;
  2. The Riemannian metric is locally constant (or can be approximated as such);
  3. The manifold is locally connected.

统一流形近似和投影（UMAP）是一种降维技术，可用于可视化，类似于t-SNE，但也可用于一般非线性降维。该算法基于对数据的三个假设：
1.数据均匀分布在黎曼流形上；
2.Riemannian metric 黎曼度量是局部常数（或可以近似为局部常数）；
3.流形是局部连通的。

image.png
https://github.com/lmcinnes/umap

https://github.com/timsainb/ParametricUMAP_paper
https://cloud.tencent.com/developer/article/1549795