{
  "id": "2310.12806",
  "version": "v1",
  "published": "2023-10-19T15:01:57.000Z",
  "updated": "2023-10-19T15:01:57.000Z",
  "title": "DCSI -- An improved measure of cluster separability based on separation and connectedness",
  "authors": [
    "Jana Gauss",
    "Fabian Scheipl",
    "Moritz Herrmann"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "Whether class labels in a given data set correspond to meaningful clusters is crucial for the evaluation of clustering algorithms using real-world data sets. This property can be quantified by separability measures. A review of the existing literature shows that neither classification-based complexity measures nor cluster validity indices (CVIs) adequately incorporate the central aspects of separability for density-based clustering: between-class separation and within-class connectedness. A newly developed measure (density cluster separability index, DCSI) aims to quantify these two characteristics and can also be used as a CVI. Extensive experiments on synthetic data indicate that DCSI correlates strongly with the performance of DBSCAN measured via the adjusted rand index (ARI) but lacks robustness when it comes to multi-class data sets with overlapping classes that are ill-suited for density-based hard clustering. Detailed evaluation on frequently used real-world data sets shows that DCSI can correctly identify touching or overlapping classes that do not form meaningful clusters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-19T15:01:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real-world data sets",
      "connectedness",
      "separation",
      "density cluster separability index",
      "meaningful clusters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}