A new distance with derivative information for functional k-means clustering algorithm

•Define a novel distance used to measure the similarity among functional samples.•Present the optimal representation of cluster centroids for the functional k-means clustering algorithm based on the new distance.•Experimental results show the effectiveness, robustness and convergence of the function...

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Veröffentlicht in:Information sciences Jg. 463-464; S. 166 - 185
Hauptverfasser: Meng, Yinfeng, Liang, Jiye, Cao, Fuyuan, He, Yijun
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.10.2018
Schlagworte:
Cluster centroid
Derivative information
Functional data
Functional k-means clustering algorithm
Variational theory
Variational theory
Functional data
Functional k-means clustering algorithm
Cluster centroid
Derivative information
ISSN:0020-0255, 1872-6291
Online-Zugang:Volltext
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Zusammenfassung:•Define a novel distance used to measure the similarity among functional samples.•Present the optimal representation of cluster centroids for the functional k-means clustering algorithm based on the new distance.•Experimental results show the effectiveness, robustness and convergence of the functional k-means clustering algorithm based on the new distance. The functional k-means clustering algorithm is a widely used method for clustering functional data. However, with this algorithm, the derivative information is not further considered in calculating the similarity between two functional samples. In fact, the derivative information is very important for catching the trend characteristic differences among functional data. In this paper, we define a novel distance used to measure the similarity among functional samples by adding their derivative information. Furthermore, in theory, we construct cluster centroids that can minimize the objective function of the functional k-means clustering algorithm based on the proposed distance. After preprocessing functional data using three types of common basis representation techniques, we compare the clustering performance of the functional k-means clustering algorithms based on four different similarity metrics. The experiments on six data sets with class labels show the effectiveness and robustness of the functional k-means clustering algorithm with the defined distance statistically. In addition, the experimental results on three real-life data sets verify the convergence and practicability of the functional k-means clustering algorithm with the defined distance.
ISSN:0020-0255
1872-6291
DOI:10.1016/j.ins.2018.06.035