Efficient-Non-Linear-Dimensionality-Reduction

[Paper 1] [Paper 2]

Matlab code for a very efficient and accurate approximation of non-linear dimensionality reduction "Classical Scaling" (also known as Multidimensional Scaling (MDS) or Isomap). The code works on 3D triangle meshes, as well as graphs of point clouds of any dimension. The graph should be created by connecting near points.

Setup & Usage

The project was tested on OSX with Matlab R2019a, and should work on windows 64 as well, to run it:

1. Download files
2. Run DEMO_detailed.m

For your convenience, the code is also consiced in DEMO_only_code.m without the comments, visualizations, and options.

Citation

If you use these ideas, please cite the papers (1) Efficient Inter-Geodesic Distance Computation and Fast Classical Scaling and (2) Accelerating the computation of canonical forms for 3D nonrigid objects using Multidimensional Scaling :

@article{shamai2018efficient,
  title={Efficient Inter-Geodesic Distance Computation and Fast Classical Scaling},
  author={Shamai, Gil and Zibulevsky, Michael and Kimmel, Ron},
  journal={IEEE transactions on pattern analysis and machine intelligence},
  year={2018},
  publisher={IEEE}
}

@inproceedings{shamai2015accelerating,
  title={Accelerating the computation of canonical forms for 3D nonrigid objects using multidimensional scaling},
  author={Shamai, Gil and Zibulevsky, Michael and Kimmel, Ron},
  booktitle={Proceedings of the 2015 Eurographics Workshop on 3D Object Retrieval},
  pages={71--78},
  year={2015},
  organization={Eurographics Association}
}