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An Effective Partitional Crisp Clustering Method Using Gradient Descent Approach

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  • Soroosh Shalileh

    (Center for Language and Brain, HSE University, Myasnitskaya Ulitsa, 20, 101000 Moscow, Russia
    Vision Modelling Lab, HSE University, Myasnitskaya Ulitsa, 20, 101000 Moscow, Russia)

Abstract

Enhancing the effectiveness of clustering methods has always been of great interest. Therefore, inspired by the success story of the gradient descent approach in supervised learning in the current research, we proposed an effective clustering method using the gradient descent approach. As a supplementary device for further improvements, we implemented our proposed method using an automatic differentiation library to facilitate the users in applying any differentiable distance functions. We empirically validated and compared the performance of our proposed method with four popular and effective clustering methods from the literature on 11 real-world and 720 synthetic datasets. Our experiments proved that our proposed method is valid, and in the majority of the cases, it is more effective than the competitors.

Suggested Citation

  • Soroosh Shalileh, 2023. "An Effective Partitional Crisp Clustering Method Using Gradient Descent Approach," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2617-:d:1166055
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    References listed on IDEAS

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    1. Kim, Jaejik & Billard, L., 2012. "Dissimilarity measures and divisive clustering for symbolic multimodal-valued data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2795-2808.
    2. Kim, Jaejik & Billard, L., 2011. "A polythetic clustering process and cluster validity indexes for histogram-valued objects," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2250-2262, July.
    3. Fionn Murtagh & Pierre Legendre, 2014. "Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion?," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 274-295, October.
    4. Ekaterina Kovaleva & Boris Mirkin, 2015. "Bisecting K-Means and 1D Projection Divisive Clustering: A Unified Framework and Experimental Comparison," Journal of Classification, Springer;The Classification Society, vol. 32(3), pages 414-442, October.
    5. Chavent, Marie & Lechevallier, Yves & Briant, Olivier, 2007. "DIVCLUS-T: A monothetic divisive hierarchical clustering method," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 687-701, October.
    6. Boris Mirkin & Soroosh Shalileh, 2022. "Community Detection in Feature-Rich Networks Using Data Recovery Approach," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 432-462, November.
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