An Algorithm for Euclidean Sum of Squares Classification
An Algorithm for Euclidean Sum of Squares Classification
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欧氏平方和分类算法
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
J. Henderson
中科院分区：
文献类型：
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作者：
A. D. Gordon;J. Henderson
对表面花粉样本进行分析以发现它们自然地分为相似样本的不同组是分类问题的一个例子。在欧几里得分类中，n 个对象的集合可以表示为 p 维欧几里得空间中的 n 个点。平方和准则将 1 到 g 个不相交组中的点的最佳划分定义为使关于 g 个质心的组内总距离平方和最小化的划分。检查对象到 g 组中的所有可能划分通常是不可能的。对为寻求最佳分区而提出的算法的组成进行了严格的审查。该问题用非线性规划术语重新表述，并描述了一种寻求最小平方和的新算法。该算法在分析花粉数据方面的性能与现有的三种算法的性能相比是非常好的。引入了一种高效的混合算法。
A ni analysis of surface pollen samples to discover iJ'they fall naturally in1to distinct groups oJ' simiiilar samiples is an example of a classification problem. In Euclidean classification, a set of n objects can be represented as n points in Euclidean space of p dimensions. The sum oJ'squares criterion defines the optimal partition of the points in1to g disjoint groups to be the partition which mninimzizes the total within-group sumn of squared distances about the g centroids. It is not usually Jeasible to examiine all possible partitions oJ'the objects into g groups. A critical review is mnade of algorithmiis which have been proposedfor seeking optimal partitions. The problem is reformulated itn non-linear programming terms, and a new algorithm for seeking the minimum sumi1 oJ'squares is described. The performance of this algorithm in analyzing the pollen data is Jound to compare vell vith the perJormance of three oJ the existing algorithms. An efficient hybrid algorithmi is introduced.