Hidden Structures in Complex Data
Manifold Learning: Hidden Structures in Complex Data
What if complex data—whether from a camera inside the human body or a scanner observing the human brain—could be translated into an elegant, low-dimensional map that reveals its underlying structure?
In my research, I have explored this question using a powerful mathematical tool known as manifold learning, specifically the technique of Laplacian eigenmaps. Manifold learning enables us to find meaningful patterns in high-dimensional data by uncovering the intrinsic geometry of the system. Rather than focusing on individual measurements, this approach captures the relationships between data points, revealing how complex states evolve in space or time.
In our recent study (Rué-Queralt et al., 2021, Communications Biology), conducted in collaboration with Joan Rué-Queralt, Angus Stevner, Enzo Tagliazucchi, Helmut Laufs, Gustavo Deco, and Morten Kringelbach, we used Laplacian eigenmaps to decode brain states during sleep from fMRI data. By projecting the brain's dynamic activity onto its intrinsic manifold, we could distinguish between different stages of consciousness, from wakefulness to light and deep sleep. This approach revealed a smooth, low-dimensional structure underlying the brain’s transitions through sleep, offering a new lens through which to study the continuity of consciousness.
But my journey with manifolds began far from the brain—in the digestive tract. In earlier work, I applied manifold learning to endoscopic video data to create intuitive maps for navigating and analyzing the interior of the gastrointestinal system. These techniques, developed in collaboration with Nassir Navab, Daniel Mateus, Alexander Meining, and Guang-Zhong Yang, enabled targeted optical biopsies and automated lesion detection by mapping the evolving visual landscape of the endoscopic field (Atasoy et al., IEEE TMI, 2012).
From tracking wave interference patterns to describing tissue surfaces in video data, this work laid the foundation for my later shift to neuroscience. The same mathematics that helps us retarget an optical biopsy site within the oesophagus can help us understand how the brain moves through the geometry underlying different states of consciousness.
Across both domains, the core insight remains the same: beneath apparent complexity lies structure—and manifold learning helps us find it.
• Rué-Queralt, J., Stevner, A., Tagliazucchi, E., Laufs, H., Kringelbach, M. L., Deco, G., & Atasoy, S. (2021). Decoding brain states on the intrinsic manifold of human brain dynamics across wakefulness and sleep. Communications biology, 4(1), 854. doi.org/10.1038/s42003-021-02369-7
• Atasoy, S., Mateus, D., Meining, A., Yang, G. Z., & Navab, N. ( (2012) Endoscopic Video Manifolds for Targeted Optical Biopsy, IEEE Transactions on Medical Imaging, vol. 31, no. 3, pp. 637-653, doi: 10.1109/TMI.2011.2174252..
• Atasoy, S., Mateus, D., Georgiou, A., Navab, N., & Yang, G. Z. (2010, November). Wave interference for pattern description. In Asian Conference on Computer Vision (pp. 41-54). Springer, Berlin, Heidelberg.
• Atasoy, S., Mateus, D., Lallemand, J., Meining, A., Yang, G. Z., & Navab, N. (2010, September). Endoscopic video manifolds. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 437-445). Springer, Berlin, Heidelberg.
• Atasoy, S., Mateus, D., Meining, A., Yang, G. Z., & Navab, N. (2011, September). Targeted optical biopsies for surveillance endoscopies. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 83-90). Springer, Berlin, Heidelberg.
• Atasoy, S., Mateus, D., Georgiou, A., Navab, N., & Yang, G. Z. (2010, November). Wave interference for pattern description. In Asian Conference on Computer Vision (pp. 41-54). Springer, Berlin, Heidelberg.
• Atasoy, S., Mateus, D., Lallemand, J., Meining, A., Yang, G. Z., & Navab, N. (2010, September). Endoscopic video manifolds. In International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 437-445). Springer, Berlin, Heidelberg.
