MAPCLUS - A MATHEMATICAL-PROGRAMMING APPROACH TO FITTING THE ADCLUS MODEL
MAPCLUS - A MATHEMATICAL-PROGRAMMING APPROACH TO FITTING THE ADCLUS MODEL
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DOI：
10.1007/bf02294077
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发表时间：
1980-01-01
期刊：
影响因子：
3
通讯作者：
CARROLL, JD
中科院分区：
文献类型：
--
作者：
ARABIE, P;CARROLL, JD
本文提出了一种新的算法MAPCLUS（Mathematical Programming CLUStering）来拟合Shepard-Arabie ADCLUS（for Additive CLUStering）模型。MAPCLUS利用交替最小二乘法结合基于罚函数方法的数学规划优化过程，对定义聚类成员资格的参数施加离散（0，1）约束。这个过程是由几个其他的数值技术（特别是一个基于启发式的组合优化过程）的补充，以提供一个有效的通用计算机实现的算法，获得ADCLUS表示。MAPCLUS说明与应用程序的谢泼德和阿拉比使用旧的ADCLUS程序给出的例子之一。MAPCLUS解决方案使用一半的集群来实现几乎相同的拟合优度。最后，我们考虑扩展本方法，以拟合ADCLUS模型的三向推广，称为INDCLUS（INdividual Differences CLUStering）。
We present a new algorithm, MAPCLUS (MAthematical Programming CLUStering), for fitting the Shepard-Arabie ADCLUS (for ADditive CLUStering) model. MAPCLUS utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach, to impose discrete (0,1) constraints on parameters defining cluster membership. This procedure is supplemented by several other numerical techniques (notably a heuristically based combinatorial optimization procedure) to provide an efficient general-purpose computer implemented algorithm for obtaining ADCLUS representations. MAPCLUS is illustrated with an application to one of the examples given by Shepard and Arabie using the older ADCLUS procedure. The MAPCLUS solution uses half as many clusters to achieve nearly the same level of goodness-of-fit. Finally, we consider an extension of the present approach to fitting a three-way generalization of the ADCLUS model, called INDCLUS (INdividual Differences CLUStering).