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Asymmetric Isomap for Dimensionality Reduction and Data Visualization

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Artificial Neural Networks and Machine Learning – ICANN 2024 (ICANN 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15016))

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Abstract

We propose an asymmetric version of the Isomap dimensionality reduction and data visualization approach. Our improvement uses the information on asymmetric input data relationships, and in this way, it determines the input dissimilarities more accurately than original Isomap. We introduce as well the asymmetric coefficients discovering and expressing the asymmetric properties of the input data. These coefficients asymmetrize geodesic distances in Isomap making this method asymmetric. The experiments on two real datasets confirm the effectiveness of our proposal.

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References

  1. Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. Adv. Neural Inf. Process. Syst. 14, 586–691. MIT Press (2001)

    Google Scholar 

  2. Dua, D., Graff, C.: UCI machine learning repository (2019). http://archive.ics.uci.edu/ml

  3. Garzon, M., Yang, C., Venugopal, D., Kumar, N., Jana, K., Deng, L.: Dimensionality Reduction in Data Science. Springer International Publishing (2022). https://doi.org/10.1007/978-3-031-05371-9

  4. Ghojogh, B., Crowley, M., Karray, F., Ghodsi, A.: Elements of Dimensionality Reduction and Manifold Learning. Springer International Publishing (2023). https://doi.org/10.1007/978-3-031-10602-6

  5. Halder, R., Fidkowski, K.J., Maki, K.J.: An adaptive sampling algorithm for reduced-order models using Isomap. Int. J. Numer. Meth. Eng. 125(8), 7427 (2024)

    Article  MathSciNet  Google Scholar 

  6. Hinton, G., Roweis, S.T.: Stochastic neighbor embedding. Adv. Neural. Inf. Process. Syst. 14, 833–840 (2002)

    Google Scholar 

  7. Kohonen, T.: Self-Organizing Maps. Springer (2001). Third Edition https://doi.org/10.1007/978-3-642-56927-2

  8. van der Maaten, L., Hinton, G.E.: Visualizing data using t-SNE. J. Mach. Learn. Res. 9, 2579–2605 (2008)

    Google Scholar 

  9. Martín-Merino, M., Muñoz, A.: Visualizing asymmetric proximities with SOM and MDS models. Neurocomputing 63, 171–192 (2005)

    Article  Google Scholar 

  10. McInnes, L., Healy, J., Melville, J.: UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2020). https://doi.org/10.48550/arXiv.1802.03426

  11. Olszewski, D.: A clustering-based adaptive Neighborhood Retrieval Visualizer. Neural Netw. 140, 247–260 (2021)

    Article  Google Scholar 

  12. Olszewski, D.: Clustering-based adaptive self-organizing map. In: Artificial Intelligence and Soft Computing (ICAISC 2021), Lecture Notes in Computer Science, vol. 12854, pp. 182–192 (2021)

    Google Scholar 

  13. Olszewski, D.: A data-scattering-preserving adaptive self-organizing map. Eng. Appl. Artif. Intell. 105, 104420 (2021)

    Article  Google Scholar 

  14. Olszewski, D.: An asymmetric topology-preserving neighborhood retrieval visualizer. Expert Syst. Appl. 225, 120175 (2023)

    Article  Google Scholar 

  15. Rehman, T.U., Yousaf, M., Jing, L.: A*-FastIsomap: an improved performance of classical Isomap based on A*Search algorithm. Neural Process. Lett. 55, 12719–12736 (2023)

    Article  Google Scholar 

  16. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Google Scholar 

  17. Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319–2323 (2000)

    Article  Google Scholar 

  18. Venna, J., Peltonen, J., Nybo, K., Aidos, H., Kaski, S.: information retrieval perspective to nonlinear dimensionality reduction for data visualization. J. Mach. Learn. Res. 11, 451–490 (2010)

    Google Scholar 

  19. Xiao, L., Chao, S., Zhu, Z., Yang, L.H., Sheng, L.Q., Tao, T.: Three-dimensional aerodynamic shape inverse design based on ISOMAP. Aerosp. Sci. Technol. 139, 108409 (2023)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Warsaw University of Technology, Warsaw, Poland

    Dominik Olszewski

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  1. Dominik Olszewski
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Correspondence to Dominik Olszewski .

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Editors and Affiliations

  1. IDSIA USI-SUPSI, Lugano, Switzerland

    Michael Wand

  2. Comenius University, Bratislava, Slovakia

    Kristína Malinovská

  3. KAUST Center of Generative AI, Thuwal, Saudi Arabia

    Jürgen Schmidhuber

  4. Helmholtz Zentrum München, Neuherberg, Germany

    Igor V. Tetko

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Olszewski, D. (2024). Asymmetric Isomap for Dimensionality Reduction and Data Visualization. In: Wand, M., Malinovská, K., Schmidhuber, J., Tetko, I.V. (eds) Artificial Neural Networks and Machine Learning – ICANN 2024. ICANN 2024. Lecture Notes in Computer Science, vol 15016. Springer, Cham. https://doi.org/10.1007/978-3-031-72332-2_8

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  • DOI: https://doi.org/10.1007/978-3-031-72332-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-72331-5

  • Online ISBN: 978-3-031-72332-2

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