DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling

Gautam Pai, Ronen Talmon, Alexander M. Bronstein, Ron Kimmel

WACV 2019 pp. 819-828

doi:10.1109/WACV.2019.00092 /wacv/2019/pai2019wacv-dimal/

Abstract

This paper explores a fully unsupervised deep learning approach for computing distance-preserving maps that generate low-dimensional embeddings for a certain class of manifolds. We use the Siamese configuration to train a neural network to solve the problem of least squares multidimensional scaling for generating maps that approximately preserve geodesic distances. By training with only a few landmarks, we show a significantly improved local and nonlocal generalization of the isometric mapping as compared to analogous non-parametric counterparts. Importantly, the combination of a deep-learning framework with a multidimensional scaling objective enables a numerical analysis of network architectures to aid in understanding their representation power. This provides a geometric perspective to the generalizability of deep learning.

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Cite

Text

Pai et al. "DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling." IEEE/CVF Winter Conference on Applications of Computer Vision, 2019. doi:10.1109/WACV.2019.00092

Markdown

[Pai et al. "DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling." IEEE/CVF Winter Conference on Applications of Computer Vision, 2019.](https://mlanthology.org/wacv/2019/pai2019wacv-dimal/) doi:10.1109/WACV.2019.00092

BibTeX

@inproceedings{pai2019wacv-dimal,
  title     = {{DIMAL: Deep Isometric Manifold Learning Using Sparse Geodesic Sampling}},
  author    = {Pai, Gautam and Talmon, Ronen and Bronstein, Alexander M. and Kimmel, Ron},
  booktitle = {IEEE/CVF Winter Conference on Applications of Computer Vision},
  year      = {2019},
  pages     = {819-828},
  doi       = {10.1109/WACV.2019.00092},
  url       = {https://mlanthology.org/wacv/2019/pai2019wacv-dimal/}
}