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Nearest‐neighbors medians clustering
Author(s) -
Peña Daniel,
Viladomat Júlia,
Zamar Ruben
Publication year - 2012
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11149
Subject(s) - mathematics , median , uniqueness , partition (number theory) , univariate , cluster analysis , nonparametric statistics , fixed point , sample (material) , algorithm , combinatorics , statistics , mathematical analysis , chemistry , geometry , chromatography , multivariate statistics
We propose a nonparametric cluster algorithm based on local medians. Each observation is substituted by its local median and this new observation moves toward the peaks and away from the valleys of the distribution. The process is repeated until each observation converges to a fixpoint. We obtain a partition of the sample based on the convergence points. Our algorithm determines the number of clusters and the partition of the observations given the proportion α of neighbors. A fast version of the algorithm where only a subset of the observations from the sample is processed is also proposed. A proof of the convergence from each point to its closest fixpoint and the existence and uniqueness of a fixpoint in a neighborhood of each mode is given for the univariate case. © 2012 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2012