Multi-similarity clustering algorithm by ordered pair of normalized real numbers

This paper extends the Fuzzy c-means (FCM) algorithm and proposes the Ordered pair of normalized real numbers clustering (OPNC) algorithm. The OPNC algorithm adopts the paradigm of learning in parallel universes and simultaneously uses multiple similarity measures to convert ordinary data into ordered pairs of normalized real numbers (OPNs). Clustering is performed with OPNs, and OPNs contain different similarity information, so the OPNC algorithm can further improve the clustering performance by combining different similarity measures. Experiments on multiple real datasets and comparisons with other clustering algorithms verified that the OPNC algorithm has excellent performance.