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Sparse probabilistic K-means

Author

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  • Jung, Yoon Mo
  • Whang, Joyce Jiyoung
  • Yun, Sangwoon

Abstract

The goal of clustering is to partition a set of data points into groups of similar data points, called clusters. Clustering algorithms can be classified into two categories: hard and soft clustering. Hard clustering assigns each data point to one cluster exclusively. On the other hand, soft clustering allows probabilistic assignments to clusters. In this paper, we propose a new model which combines the benefits of these two models: clarity of hard clustering and probabilistic assignments of soft clustering. Since the majority of data usually have a clear association, only a few points may require a probabilistic interpretation. Thus, we apply the ℓ1 norm constraint to impose sparsity on probabilistic assignments. Moreover, we also incorporate outlier detection in our clustering model to simultaneously detect outliers which can cause serious problems in statistical analyses. To optimize the model, we introduce an alternating minimization method and prove its convergence. Numerical experiments and comparisons with existing models show the soundness and effectiveness of the proposed model.

Suggested Citation

  • Jung, Yoon Mo & Whang, Joyce Jiyoung & Yun, Sangwoon, 2020. "Sparse probabilistic K-means," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    • Handle: RePEc:eee:apmaco:v:382:y:2020:i:c:s0096300320302940
    DOI: 10.1016/j.amc.2020.125328
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    References listed on IDEAS

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    3. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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