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Manifold clustering optimized by adaptive aggregation strategy

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Abstract

Different from general spherical datasets, manifold datasets have a more complex spatial manifold structure, which makes it difficult to distinguish sample points on different manifold structures by Euclidean distance. Although the density peak clustering (DPC, two parameters: the cut-off ratio \(\mathrm{dc}\) and the number of class centers \(C\)) algorithm can search for density peaks quickly and assign sample points, it cannot identify clusters effectively with complex manifold structures due to the sample similarity measurement only based on Euclidean distance. To solve these problems, this paper proposes a Manifold Clustering optimized by Adaptive Aggregation Strategy (MC-AAS, two parameters: the number of nearest neighbors \(k\) and the threshold ratio of core points \(p\)). Firstly, it introduces a novel manifold similarity measurement based on the shared nearest neighbors and redefines the local density of sample points by summing the manifold similarity. Secondly, the core points are determined by the statistical characteristics of local density, and the local sub-clusters of manifold structural datasets are obtained by means of the nearest neighbor connection of the core points. And then, the initial clusters are merged on the basis of the statistical test of boundary density and the silhouette coefficient of adjacent subclass to realize the identification of manifold structural datasets. Finally, based on three evaluation metrics: Adjusted Mutual Information, Adjusted Rand Index and Fowlkes-Mallows Index, we conduct extensive experiments on synthetic datasets and real-world datasets. The experimental results indicate that, compared with current methods, the MC-AAS algorithm achieves a better clustering effect in identifying complex manifold datasets and has better robustness.

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Notes

  1. https://docs.scipy.org/doc/scipy-1.0.0/reference/generated/scipy.cluster.hierarchy.linkage.html.

  2. https://scikit-learn.org/dev/modules/generated/sklearn.metrics.silhouette_samples.html.

  3. https://scikit-learn.org/dev/modules/generated/sklearn.metrics.silhouette_score.html.

  4. https://scikit-learn.org/stable/modules/generated/sklearn.metrics.adjusted_mutual_info_score.html.

  5. https://scikit-learn.org/stable/modules/generated/sklearn.metrics.adjusted_rand_score.html.

  6. https://scikit-learn.org/stable/modules/generated/sklearn.metrics.fowlkes_mallows_score.html.

  7. https://scikit-learn.org/dev/modules/generated/sklearn.cluster.AffinityPropagation.html.

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Funding

This work is supported by the National Key Research and Development Program of China (No.2021YFC3300602).

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Authors and Affiliations

  1. School of Computer Engineering and Science, Shanghai University, Shanghai, 200444, China

    Yunong Zhang & Xiao Wei

  2. Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, 233000, Anhui, China

    Chunzhong Li

Authors
  1. Yunong Zhang
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  2. Xiao Wei
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  3. Chunzhong Li
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Contributions

YZ Conceptualization, Methodology, Code, Writing—original draft. XW Supervision, Writing—review and editing, Funding acquisition. CL Supervision, Writing—review and editing. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Xiao Wei.

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Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Not Applicable.

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Not Applicable.

Availability of data and material

The experimental datasets include two major categories in this paper, six two-dimensional manifold datasets are artificially constructed, and the other six real datasets come from the UCI Machine Learning Repository. These datasets are available upon request to the corresponding author.

Code availability

The python code written to get the simulation results is available upon request to the corresponding author.

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Zhang, Y., Wei, X. & Li, C. Manifold clustering optimized by adaptive aggregation strategy. Knowl Inf Syst 65, 379–408 (2023). https://doi.org/10.1007/s10115-022-01769-3

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