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Joint Exploration of Kernel Functions Potential for Data Representation and Classification: A First Step Toward Interactive Interpretable Dimensionality Reduction

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Abstract

Dimensionality reduction (DR) approaches are often a crucial step in data analysis tasks, particularly for data visualization purposes. DR-based techniques are essentially designed to retain the inherent structure of high-dimensional data in a lower-dimensional space, leading to reduced computational complexity and improved pattern recognition accuracy. Specifically, Kernel Principal Component Analysis (KPCA) is a widely utilized dimensionality reduction technique due to its capability to effectively handle nonlinear data sets. It offers an easily interpretable formulation from both geometric and functional analysis perspectives. However, Kernel PCA relies on free hyperparameters, which are usually tuned in advance. The relationship between these hyperparameters and the structure of the embedded space remains undisclosed. This work presents preliminary steps to explore said relationship by jointly evaluating the data classification and representation abilities. To do so, an interactive visualization framework is introduced. This study highlights the importance of creating interactive interfaces that enable interpretable dimensionality reduction approaches for data visualization and analysis.

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Data availability

The datasets employed in these experiments are not only well-known but are also synthetic, ensuring easy reproducibility.

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Acknowledgements

Authors acknowledge the valuable support given by the SDAS Research Group (https://sdas-group.com/).

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Authors and Affiliations

  1. College of Computing, Mohammed VI Polytechnic University, Lot 660, Hay Moulay Rachid, Ben Guerir, 43150, Morocco

    Yahya Aalaila, Hind Raki, Sami Bamansour, Mouad Elhamdi, Kaoutar Benghzial & Diego H. Peluffo-Ordóñez

  2. Université Jean Monnet, Saint-Étienne, France

    Ismail Bachchar

  3. SDAS Research Group, Ben Guerir, 43150, Morocco

    Yahya Aalaila, Ismail Bachchar, Hind Raki, Sami Bamansour, Mouad Elhamdi, Kaoutar Benghzial, Lorena Guachi-Guachi & Diego H. Peluffo-Ordóñez

  4. Universidad Técnica del Norte, Ibarra, 100105, Ecuador

    MacArthur Ortega-Bustamante

  5. Department of Mechatronics, Universidad Internacional del Ecuador, Av. Simon Bolivar, 170411, Quito, Ecuador

    Lorena Guachi-Guachi

  6. Faculty of Engineering, Corporación Universitaria Autónoma de Nariño, 520001, Pasto, Colombia

    Diego H. Peluffo-Ordóñez

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  1. Yahya Aalaila
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  2. Ismail Bachchar
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  7. MacArthur Ortega-Bustamante
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  8. Lorena Guachi-Guachi
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  9. Diego H. Peluffo-Ordóñez
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Correspondence to Yahya Aalaila.

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This article is part of the topical collection “Emerging Technologies in Applied Informatics” guest edited by Hector Florez and Marcelo Leon.

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Aalaila, Y., Bachchar, I., Raki, H. et al. Joint Exploration of Kernel Functions Potential for Data Representation and Classification: A First Step Toward Interactive Interpretable Dimensionality Reduction. SN COMPUT. SCI. 5, 75 (2024). https://doi.org/10.1007/s42979-023-02405-9

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