Abstract
In connection with a least-squares solution for fitting one matrix, A , to another, B , under optimal choice of a rigid motion and a dilation, Schönemann and Carroll suggested two measures of fit: a raw measure, e , and a refined similarity measure, e s , which is symmetric. Both measures share the weakness of depending upon the norm of the target matrix, B , e.g. , e ( A , kB ) ≠ e ( A , B ) for k ≠ 1. Therefore, both measures are useless for answering questions of the type: “Does A fit B better than A fits C ?”. In this note two new measures of fit are suggested which do not depend upon the norms of A and B , which are (0, 1)-bounded, and which, therefore, provide meaningful answers for comparative analyses.
Keywords
MathematicsMeasure (data warehouse)Matrix (chemical analysis)Bounded functionAlgorithmCombinatoricsStatisticsComputer scienceMathematical analysis
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Publication Info
- Year
- 1974
- Type
- article
- Volume
- 39
- Issue
- 4
- Pages
- 423-427
- Citations
- 63
- Access
- Closed
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Cite This
James C. Lingoes,
Peter H. Schönemann
(1974).
Alternative Measures of Fit for the Schönemann-Carroll Matrix Fitting Algorithm.
Psychometrika
, 39
(4)
, 423-427.
https://doi.org/10.1007/bf02291666
Identifiers
- DOI
- 10.1007/bf02291666