Fast Multi-scale Neighbor Embedding

This project and the codes in this repository implement fast multi-scale neighbor embedding algorithms for nonlinear dimensionality reduction (DR).

The fast algorithms which are implemented are described in the article Fast Multiscale Neighbor Embedding, from Cyril de Bodt, Dounia Mulders, Michel Verleysen and John A. Lee, published in IEEE Transactions on Neural Networks and Learning Systems, in 2020.

The implementations are provided using the python programming language, but involve some C and Cython codes for performance purposes.

If you use the codes in this repository or the article, please cite as:

C. de Bodt, D. Mulders, M. Verleysen and J. A. Lee, "Fast Multiscale Neighbor Embedding," in IEEE Transactions on Neural Networks and Learning Systems, 2020, doi: 10.1109/TNNLS.2020.3042807.

BibTeX entry:

@article{CdB2020FMsNE,
 author={C. {de Bodt} and D. {Mulders} and M. {Verleysen} and J. A. {Lee}},
 journal={{IEEE} Trans. Neural Netw. Learn. Syst.},
 title={{F}ast {M}ultiscale {N}eighbor {E}mbedding},
 year={2020},
 volume={},
 number={},
 pages={1-15},
 doi={10.1109/TNNLS.2020.3042807}}

Installation

Clone the repository and install locally

pip install .

Or install from PyPI

pip install fmsne

Make sure to have Cython installed on your system - Check instructions here. Note that this web link mentions that Cython requires a C compiler to be present on the system, and provides further information to get such a C compiler according to your system. Note also that Cython is available from the Anaconda Python distribution.

Package functionality

Neighbor Embedding

• mssne: nonlinear dimensionality reduction through multi-scale SNE (Ms SNE), as presented in the reference [2] below and summarized in [1]. This function enables reducing the dimension of a data set. Given a data set with N samples, the 'mssne' function has O(N**2 log(N)) time complexity. It can hence run on databases with up to a few thousands of samples. This function is based on the Cython implementations in fmsne_implem.pyx.

• mstsne: nonlinear dimensionality reduction through multi-scale t-SNE (Ms t-SNE), as presented in the reference [6] below and summarized in [1]. This function enables reducing the dimension of a data set. Given a data set with N samples, the 'mstsne' function has O(N**2 log(N)) time complexity. It can hence run on databases with up to a few thousands of samples. This function is based on the Cython implementations in fmsne_implem.pyx.

• fmssne: nonlinear dimensionality reduction through fast multi-scale SNE (FMs SNE), as presented in the reference [1] below. This function enables reducing the dimension of a data set. Given a data set with N samples, the 'fmssne' function has O(N (log(N))**2) time complexity. It can hence run on very large-scale databases. This function is based on the Cython implementations in fmsne_implem.pyx.

• fmstsne: nonlinear dimensionality reduction through fast multi-scale t-SNE (FMs t-SNE), as presented in the reference [1] below. This function enables reducing the dimension of a data set. Given a data set with N samples, the 'fmstsne' function has O(N (log(N))**2) time complexity. It can hence run on very large-scale databases. This function is based on the Cython implementations in fmsne_implem.pyx.

Quality control

• eval_dr_quality: unsupervised evaluation of the quality of a low-dimensional embedding, as introduced in [3, 4] and employed and summarized in [1, 2, 5]. This function enables computing DR quality assessment criteria measuring the neighborhood preservation from the high-dimensional space to the low-dimensional one. The documentation of the function explains the meaning of the criteria and how to interpret them. Given a data set with N samples, the 'eval_dr_quality' function has O(N**2 log(N)) time complexity. It can hence run using databases with up to a few thousands of samples. This function is not based on the Cython implementations in fmsne_implem.pyx.

• red_rnx_auc: this function is similar to the eval_dr_quality function, but given a data set with N samples, the red_rnx_auc function has O(NKuplog(N)) time complexity, where Kup is the maximum neighborhood size accounted when computing the quality criteria. This function can hence run using much larger databases than eval_dr_quality, provided that Kup is small compared to N. This function is based on the Cython implementations in fmsne_implem.pyx.

Visualization of a 2-D embedding and of the quality criteria.

• viz_2d_emb: plot a 2-D embedding.

• viz_qa: depict the quality criteria computed by eval_dr_quality and red_rnx_auc.

The documentations of the functions describe their parameters.

The fmsne_demo.py file, illustrates how to use to apply fast multi-scale neighbor embedding .

Notations

• DR: dimensionality reduction.
• HD: high-dimensional.
• LD: low-dimensional.
• HDS: HD space.
• LDS: LD space.
• SNE: stochastic neighbor embedding.
• t-SNE: t-distributed SNE.
• Ms SNE: multi-scale SNE.
• Ms t-SNE: multi-scale t-SNE.
• BH t-SNE: Barnes-Hut t-SNE.

References

[1] C. de Bodt, D. Mulders, M. Verleysen and J. A. Lee, "Fast Multiscale Neighbor Embedding," in IEEE Transactions on Neural Networks and Learning Systems, 2020, doi: 10.1109/TNNLS.2020.3042807.

[2] Lee, J. A., Peluffo-Ordóñez, D. H., & Verleysen, M. (2015). Multi-scale similarities in stochastic neighbour embedding: Reducing dimensionality while preserving both local and global structure. Neurocomputing, 169, 246-261.

[3] Lee, J. A., & Verleysen, M. (2009). Quality assessment of dimensionality reduction: Rank-based criteria. Neurocomputing, 72(7-9), 1431-1443.

[4] Lee, J. A., & Verleysen, M. (2010). Scale-independent quality criteria for dimensionality reduction. Pattern Recognition Letters, 31(14), 2248-2257.

[5] Lee, J. A., Renard, E., Bernard, G., Dupont, P., & Verleysen, M. (2013). Type 1 and 2 mixtures of Kullback–Leibler divergences as cost functions in dimensionality reduction based on similarity preservation. Neurocomputing, 112, 92-108.

[6] de Bodt, C., Mulders, D., Verleysen, M., & Lee, J. A. (2018). Perplexity-free t-SNE and twice Student tt-SNE. In ESANN (pp. 123-128).

[7] van der Maaten, L., & Hinton, G. (2008). Visualizing data using t-SNE. Journal of Machine Learning Research, 9(Nov), 2579-2605.

[8] van der Maaten, L. (2014). Accelerating t-SNE using tree-based algorithms. Journal of Machine Learning Research, 15(1), 3221-3245.

Author

Cyril de Bodt (Human Dynamics - MIT Media Lab, and ICTEAM - UCLouvain)

@email: cdebodt at mit dot edu, or cyril dot debodt at uclouvain.be

The code was packaged by Laurent Gatto (Compuational Biology and Bioinformatics - UCLouvain).

License

Copyright <2023> Université catholique de Louvain (UCLouvain), Belgium

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.