BIPLOT GRAPHIC DISPLAY OF MATRICES WITH APPLICATION TO PRINCIPAL COMPONENT ANALYSIS
BIPLOT GRAPHIC DISPLAY OF MATRICES WITH APPLICATION TO PRINCIPAL COMPONENT ANALYSIS
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DOI：
10.1093/biomet/58.3.453
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发表时间：
1971-01-01
期刊：
影响因子：
2.7
通讯作者：
GABRIEL, KR
中科院分区：
文献类型：
--
作者：
GABRIEL, KR
摘要任何秩为2的矩阵都可以显示为双标图，其中每一行都有一个向量，每一列都有一个向量，选择矩阵的任何元素都是对应于其行和列的向量的内积。如果一个矩阵的秩较高，则可以用秩为2的矩阵的双标图近似地显示它，该矩阵近似于原始矩阵。双标图提供了一个有用的数据分析工具，并允许大型数据矩阵的结构的视觉评价。它在主成分分析中尤其具有启发性，其中双标图可以显示单元间的距离，并指示单元的聚类以及显示变量的方差和相关性。
SUMMARYAny matrix of rank two can be displayed as a biplot which consists of a vector for each row and a vector for each column, chosen so that any element of the matrix is exactly the inner product of the vectors corresponding to its row and to its column. If a matrix is of higher rank, one may display it approximately by a biplot of a matrix of rank two which approximates the original matrix. The biplot provides a useful tool of data analysis and allows the visual appraisal of the structure of large data matrices. It is especially revealing in principal component analysis, where the biplot can show inter-unit distances and indicate clustering of units as well as display variances and correlations of the variables.