Singular value partitioning
There are three options for Singular Value Partitioning (S.V.P.)
- Entry-focused: The singular value is entirely partitioned into the entry eigenvectors, i.e, alpha = 1, beta = 0. This SVP is needed for accurate comparison among the entries. This is also called row metric preserving, leading to "JK biplot".
- Tester-focused: The singular value is entirely partitioned into the tester eigenvectors, i.e, alpha = 0, beta = 1. This SVP is needed for accurate visualization of the relationship among the testers. This is also called column metric preserving, leading to a "GH biplot".
- Symmetrical: The singular value is symmetrically partitioned into the entry and the tester eigenvectors (alpha = 0.5, beta = 0.5). This SVP is most often used in AMMI analysis and other biplot analysis, but it is not ideal for visualizing either the relationship among entries or that among the testers.
- There are numerous other possible ways to partition the singular values, and their interpretations are not defined.
- All singular value partitioning methods are equally valid in approximating the two-way table and in showing the which-won-where pattern.
Related topics: Singular value decomposition.