The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Three‐mode principal components analysis: Choosing the numbers of components and sensitivity to local optima
Abstract
A method that indicates the numbers of components to use in fitting the three‐mode principal components analysis (3MPCA) model is proposed. This method, called DIFFIT, aims to find an optimal balance between the fit of solutions for the 3MPCA model and the numbers of components. The achievement of DIFFIT is compared with that of two other methods, both based on two‐way PCAs, by means of a simulation study. It was found that DIFFIT performed considerably better than the other methods in indicating the numbers of components. The 3MPCA model can be estimated by the TUCKALS3 algorithm, which is an alternating least squares algorithm. In a study of how sensitive TUCKALS3 is at hitting local optima, it was found that, if the numbers of components are specified correctly, TUCKALS3 never hits a local optimum. The occurrence of local optima increased as the difference between the numbers of underlying components and the numbers of components as estimated by TUCKALS3 increased. Rationally initiated TUCKALS3 runs hit local optima less often than randomly initiated runs.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
The application of electronic computers to factor analysis
Kaiser, H. F. (1960) · Educational and Psychological Measurement · doi:10.1177/001316446002000116 · Cited by 12,459
Determining the number of components from the matrix of partial correlations
Velicer, W. F. (1976) · Psychometrika · doi:10.1007/bf02293557 · Cited by 2,438
Cited by
Unsupervised Multiway Data Analysis: A Literature Survey
Acar, E., & Yener, B. (2009) · IEEE Transactions on Knowledge and Data Engineering · doi:10.1109/tkde.2008.112 · Cited by 434
Metadata
- Authors
- Timmerman, M. E., & Kiers, H. A. L.
- Venue
- British Journal of Mathematical and Statistical Psychology
- Publisher
- Wiley
- Published
- 2000-05
- Volume
- 53
- Issue
- 1
- Pages
- 1-16
- ISSN
- 0007-1102 (ISSN-L)
- 2044-8317
- OpenAlex
- W2135307683
- Cited by
- 185
- References
- 2
- FWCI
- 1.20
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Three‐mode principal components analysis: Choosing the numbers of components and sensitivity to local optima. https://app.cochat.ai/papers/10.1348/000711000159132
- The paper
- Timmerman, M. E., & Kiers, H. A. L. (2000). Three‐mode principal components analysis: Choosing the numbers of components and sensitivity to local optima. British Journal of Mathematical and Statistical Psychology. https://doi.org/10.1348/000711000159132
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
