2000 character limit reached
Formation-Controlled Dimensionality Reduction (2404.06808v2)
Published 10 Apr 2024 in cs.LG
Abstract: Dimensionality reduction represents the process of generating a low dimensional representation of high dimensional data. Motivated by the formation control of mobile agents, we propose a nonlinear dynamical system for dimensionality reduction. The system consists of two parts; the control of neighbor points, addressing local structures, and the control of remote points, accounting for global structures.We also include a brief mathematical analysis of the model and its numerical procedure. Numerical experiments are performed on both synthetic and real datasets and comparisons with existing models demonstrate the soundness and effectiveness of the proposed model.
- Hyo-Sung Ahn. Formation control, volume 205 of Studies in Systems, Decision and Control. Springer, 2020.
- Linear dimensionality reduction: Survey, insights, and generalizations. Journal of Machine Learning Research, 16(89):2859–2900, 2015.
- Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control. Automatica J. IFAC, 46(4):695–700, 2010.
- Ali Ghodsi. Dimensionality reduction a short tutorial. 2006.
- Bruce Hendrickson. Conditions for unique graph realizations. SIAM J. Comput., 21(1):65–84, 1992.
- Stabilisation of infinitesimally rigid formations of multi-robot networks. Internat. J. Control, 82(3):423–439, 2009.
- Distance-based undirected formations of single-integrator and double-integrator modeled agents in n𝑛nitalic_n-dimensional space. Internat. J. Robust Nonlinear Control, 24(12):1809–1820, 2014.
- A survey of multi-agent formation control. Automatica J. IFAC, 53:424–440, 2015.
- Reza Olfati-Saber. Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Transactions on Automatic Control, 51(3):401–420, 2006.
- Guido Sanguinetti. Dimensionality reduction of clustered data sets. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(3):535–540, 2008.
- Spectral methods for dimensionality reduction. In Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien, editors, Semi-supervised learning, pages 293–308. MIT Press, Cambridge, MA, 2006.
- A survey of dimensionality reduction techniques. 03 2014.
- Zhiyong Sun. Cooperative coordination and formation control for multi-agent systems. Springer Theses. Springer, Cham, 2018. Doctoral Thesis accepted by The Australian National University, Canberra, Australia.
- Dimensionality reduction: a comparative review. Tilburg University, TiCC-TR 2009-005, pages 1–35, 2008.
- Visualizing gene interaction graphs with local multidimensional scaling. In Proceedings of the 14th European Symposium on Artificial Neural Networks, pages 557–562, 2006.