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Cluster Validation Based on Fisher’s Linear Discriminant Analysis

Author

Listed:
  • Fabian Kächele

    (Institute for Operations Research, Analytics & Statistics, Karlsruhe Institute of Technology)

  • Nora Schneider

    (Institute for Operations Research, Analytics & Statistics, Karlsruhe Institute of Technology)

Abstract

Cluster analysis aims to find meaningful groups, called clusters, in data. The objects within a cluster should be similar to each other and dissimilar to objects from other clusters. The fundamental question arising is whether found clusters are “valid clusters” or not. Existing cluster validity indices are computation-intensive, make assumptions about the underlying cluster structure, or cannot detect the absence of clusters. Thus, we present a new cluster validation framework to assess the validity of a clustering and determine the underlying number of clusters $$k^*$$ k ∗ . Within the framework, we introduce a new merge criterion analyzing the data in a one-dimensional projection, which maximizes the ratio of between-cluster- variance to within-cluster-variance in the clusters. Nonetheless, other local methods can be applied as a merge criterion within the framework. Experiments on synthetic and real-world data sets show promising results for both the overall framework and the introduced merge criterion.

Suggested Citation

  • Fabian Kächele & Nora Schneider, 2025. "Cluster Validation Based on Fisher’s Linear Discriminant Analysis," Journal of Classification, Springer;The Classification Society, vol. 42(1), pages 54-71, March.
    • Handle: RePEc:spr:jclass:v:42:y:2025:i:1:d:10.1007_s00357-024-09481-3
    DOI: 10.1007/s00357-024-09481-3
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    References listed on IDEAS

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    1. Julian Rossbroich & Jeffrey Durieux & Tom F. Wilderjans, 2022. "Model Selection Strategies for Determining the Optimal Number of Overlapping Clusters in Additive Overlapping Partitional Clustering," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 264-301, July.
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