Nested Grassmanns for Dimensionality Reduction

Reference:

If you use this code, please cite the following paper that contains the theory, the algorithm, and some experiments showing the performance of this model.

Chun-Hao Yang and Baba C. Vemuri (2021), Nested Grassmanns for Dimensionality Reduction with Applications to Shape Analysis in Proceedings of the International Conference on Information Processing in Medical Imaging, 2021, June 28-30, Bornholm, Denmark, pages 136-149.

Yang, C. H., & Vemuri, B. C. (2022). Nested Grassmannians for Dimensionality Reduction with Applications. Machine Learning for Biomedical Imaging, 1(IPMI 2021 special issue), 1-10.

This software was developed as part of research in part funded by the NSF grant IIS-1724174, the NIH NINDS and NIA via R01NS121099 to Vemuri and the MOST grant 110-2118-M-002-005-MY3 to Yang.

Dependencies

Pymanopt 0.2.4

PyTorch

Usage

Following the convention of pymanopt, $N$ points on $\text{Gr}(p,n)$ are represented as an $(N,n,p)$ numpy array. The function DR_proj takes an $(N, n, p)$ numpy array and an integer $m < n$ as inputs and projects the $N$ points on $\text{Gr}(p, n)$ to $\text{Gr}(p, m)$. The outputs are the ratio of explained variance, the projected points $\hat{X}$ which is an $(N, m ,p)$ numpy array, and the projection parameters $A$ and $B$.

An example can be found in example.ipynb.