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| Content Provider | Springer Nature Link |
|---|---|
| Author | Berge, Jos M. F. |
| Copyright Year | 2010 |
| Abstract | Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by nonsingular transformations. Such transformations have direct applications in Tucker PCA for three-way arrays, where transforming the core array to simplicity is allowed without loss of fit. Simplifying arrays also facilitates the study of array rank. The typical rank of a three-way array is the smallest number of rank-one arrays that have the array as their sum, when the array is generated by random sampling from a continuous distribution. In some applications, the core array of Tucker PCA is constrained to have a vast majority of zero elements. Both simplicity and typical rank results can be applied to distinguish constrained Tucker PCA models from tautologies. An update of typical rank results over the real number field is given in the form of two tables. |
| Starting Page | 3 |
| Ending Page | 12 |
| Page Count | 10 |
| File Format | |
| ISSN | 00333123 |
| Journal | Psychometrika |
| Volume Number | 76 |
| Issue Number | 1 |
| e-ISSN | 18600980 |
| Language | English |
| Publisher | Springer-Verlag |
| Publisher Date | 2011-01-05 |
| Publisher Place | New York |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | tensor decomposition tensor rank typical rank sparse arrays Candecomp Parafac Tucker component analysis Psychometrics Assessment, Testing and Evaluation Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law Statistical Theory and Methods |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Psychology |
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