「R」NMF rank度量图该怎么看

幕布笔记[1]

• NMF

• W basis
• H coefficients
• Rank选择

• 图

• Sparseness

• 残差和残差平方和自不必说
• dispersion 离差

• In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.[1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. 也就是和方差、标准差类似的概念

• silhouette

• Silhouette refers to a method of interpretation and validation of consistency within clusters of data. The technique provides a succinct graphical representation of how well each object lies within its cluster.[1]
• The silhouette value is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The silhouette ranges from −1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. If most objects have a high value, then the clustering configuration is appropriate. If many points have a low or negative value, then the clustering configuration may have too many or too few clusters.
• The silhouette can be calculated with any distance metric, such as the Euclidean distance or the Manhattan distance.

• cophenetic 同表象相关
  • 描述

http://blog.sciencenet.cn/home.php?mod=space&uid=3406804&do=blog&quickforward=1&id=1175517[2]

• 选择Rank方法汇总
  • 选择cophenetic correlation coefficient 开始下降的最小Rank值
  • 选择cophenetic随rank值变化曲线中最大变动的前一个点
  • 选择RSS出现一个拐点（inflection point）

• 选择观测数据残差减少大于随机数据残差减少的最小Rank

更新：没用一个完全确定的方法可以自动确定数目，一般同时根据聚类的可重复性和残差进行判断。

参考资料

[1]

幕布笔记: https://mubu.com/doc/C4gVcgp-G0

[2]

http://blog.sciencenet.cn/home.php?mod=space&uid=3406804&do=blog&quickforward=1&id=1175517: http://blog.sciencenet.cn/home.php?mod=space&uid=3406804&do=blog&quickforward=1&id=1175517