欧几里德距离差异和绝对曼哈顿距离差异的总和:用于小型数据表的多标准决策工具
1Plasma Chemistry Research Group, Institute of Materials and Environmental Chemistry, HUN-REN Research Centre for Natural Sciences, Institute of Excellence, Hungarian Academy of Sciences, Budapest, Hungary.
这项研究引入了新的算法,即欧几里德距离差异总和 (DnE) 和绝对曼哈顿距离差异总和 (DnM),将排名差异总和 (SRD) 扩展到非排名数据. 这些方法提供了优越的歧视和复杂的模式,用于集群和决策.
科学领域:
- 多标准决策 (MCDM) 是指多标准的决策.
- 数据分析 数据分析
- 统计建模 统计建模
背景情况:
- 排名转换方法,如排名差异总和 (SRD),可能导致信息丢失.
- 现有的算法仅限于排名环境,因此对于非排名数据需要新的方法.
研究的目的:
- 将排名差异总和 (SRD) 算法扩展到非排名环境中.
- 开发新的不相似性测量和验证技术,以克服等级转换中的信息丢失.
主要方法:
- 开发了新的不相似度措施:欧几里德距离差异总和 (DnE) 和绝对曼哈顿距离差异总和 (DnM).
- 利用对向量比较,确定一个黄金标准,并结合随机化和威尔科克森测试进行验证.
- 应用了欧几里德和曼哈顿距离,以及变量分析 (ANOVA),用于16个不同的数据集 (3-80列,5-8行).
主要成果:
- DnE和DnM表现出优越的区分能力,提供比SRD更复杂的排名和分组模式.
- 虽然随机化测试的灵敏度有所不同 (SRD > DnE > DnM),但DnE和DnM提供了不同的集群模式.
- 尽管随机分布中的小扭曲,但DnE和DnM允许可靠地确定I型错误概率.
结论:
- DnE和DnM是有效的不相似性测量,集群工具和MCDM技术,用于非排名环境.
- 这些新方法保留了SRD的优点 (简单性,通用性),同时扩大了适用性.
- DnE和DnM为ANOVA和Wilcoxon等统计测试提供了通用尺度,增强了数据分析能力.
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