Functional data clustering using particle swarm optimization

應用粒子群演算法於函數資料之聚類分析

陳人豪(Jen-Hao Chen) ； 洪文良(Wen-Liang Hung)

《智慧科技與應用統計學報》 17卷1期 (2019/07) Pp. 1-16

摘要

To efficiently capture the information of complex data sets, functional data are usually used to model this kind of data. For example, in biology, growth curve data from the Berkeley growth study (Tuddenham and Snyder, 1954) are often used to describe growth patterns. To study the growth patterns, the clusters are used to analyze it. Thus, an efficient clustering algorithm is necessary to categorize the growth curve data. In this paper, we adopt two steps for clustering functional data. The first step is to use three local nonlinear dimensionality reduction methods: locally linear embedding (LLE) (see Roweis and Saul 2000), Laplacian eigenmaps (LE) (see Belkin and Niyogi 2002) and Hessian LLE (HLLE) (see Donoho and Grimes 2003). The second step is to apply the particle swarm optimization (PSO) proposed by Kennedy and Eberhart (1995) to cluster the data into different groups. Comparisons between with the existing methods are made. Some numerical data and real datasets illustrate that the proposed approach performs well according to the correct classification rate criterion.

關鍵字

Clustering ； functional data ； particle swarm optimization ； variance ratio criterion

並列摘要

函數資料常用來描述複雜資料，例如：在生物學中，函數資料可以描述男女的成長曲線。在成長曲線中，發展一個有效率的聚類分析演算法以區別性別特徵是一重要的課題。本文採取兩步驟：非線性維度縮減與群集演算法，提出一有效率的聚類演算法分析函數資料之聚類結構。首先，利用locally linear embedding（LLE）（參閱Roweis與Saul，2000）將維度縮減至有限空間之資料點。其次，利用粒子群演算法（particle swarm optimization）對這些資料點做群集分析。經由數值模擬，所提之方法能夠經由資料的維度縮減與聚類呈現原始函數資料的聚類結構且分類正確率比既有之演算法高。

並列關鍵字

聚類分析 ； 函數資料 ； 粒子群演算法 ； 變異數比值法