{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T08:54:00Z","timestamp":1761814440993,"version":"build-2065373602"},"reference-count":34,"publisher":"PeerJ","license":[{"start":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T00:00:00Z","timestamp":1761782400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>\n                    Unsupervised clustering algorithms have been extensively applied in various research fields. In cluster analysis, determining the best cluster number\n                    <jats:italic>k<\/jats:italic>\n                    is significant. At present, many cluster validity indices (CVIs) have been proposed, including the Calinski-Harabaz index, silhouette index, and Dunn index. However, these CVIs are not effective in determining\n                    <jats:italic>k<\/jats:italic>\n                    for ring, semi-ring, and manifold data sets. We propose MPV (minimum distance and peak variation), a density-peak-based method for automated\n                    <jats:italic>k<\/jats:italic>\n                    detection. It constructs a separation measure through a dual mechanism: (1) distances between density peaks and (2) minimum distances between clusters, while using the maximum intra-cluster minimum distance to model compactness. The optimal for ring, semi-ring, and flow datasets is determined by detecting the largest change in the separation measure sequence. Experiments on 28 synthetic and real-world datasets demonstrate MPV\u2019s accuracy in determining\n                    <jats:italic>k<\/jats:italic>\n                    for complex structures.\n                  <\/jats:p>","DOI":"10.7717\/peerj-cs.3315","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T08:50:48Z","timestamp":1761814248000},"page":"e3315","source":"Crossref","is-referenced-by-count":0,"title":["MPV: a density-peak-based method for automated cluster number 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