More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling

By Joseph B. Kruskal. 1976

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Citations in the corpus

Identifiability of parameters in latent structure models with many observed variables (2008, neutral): “MODELS WITH MANY OBSERVED VARIABLES1 BY ELIZABETH S. ALLMAN2, CATHERINE MATIAS AND JOHN A. RHODES2”
Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder (2016, background): “Identifiability of the diagrams reflects the well-known fact in latent class analysis that a latent class model is identified with at least three independent proxies of the latent factor (Kruskal, 1976; Goodman, 1974; Allman et al., 2009).”
Modeling multi‐way data with linearly dependent loadings (2009, unknown): “see References [22,23]).”
Hyperspectral image noise reduction based on rank-1 tensor decomposition (2013, background): “The development of hyperspectral remote sensing technology makes it possible to provide a large amount of spatial and spectral information for image analysis applications such as classification, unmixing, subpixel mapping, and target detection (Chang, 2003; Landgrebe, 2002).”
Decomposing EEG data into space-time-frequency components using Parallel Factor Analysis (2004, unknown): “On the other hand, it has also been proved that if the data is approximately tri-linear, then the algorithm will show the true underlying phenomena, if the correct number of components is used and if the signal-to-noise ratio is appropriate (Harshman, 1972; Kruskal, 1976, 1997).”
Concurrent EEG/fMRI analysis by multiway Partial Least Squares (2004, methodology): “It has been shown that if the data are approximately trilinear, the correct number of components is used, and the signalto-noise ratio is adequate, then the PARAFAC algorithm will show the true underlying phenomena (Kruskal, 1976, 1977).”
Semi-Parametric Estimation for Conditional Independence Multivariate Finite Mixture Models (2015, unknown): “J. B. Kruskal studied contingency tables in the context of his interest in psychometrics.”
Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects (2015, background): “trices A,B,C need not be full column rank [67], [89] [90, Theorem 2.”
Identifiability of restricted latent class models with binary responses (2016, methodology): “In particular, the work of Allman et al. (2009) is based on the fundamental result of Kruskal’s trilinear decomposition of three-way arrays (Kruskal, 1976, 1977) by ‘unfolding’ a high-way array into a three-way array.”
Nonparametric Identification of Multivariate Mixtures (2010, methodology): “Applying the result of Kruskal’s theorem (Kruskal, 1976, 1977), Allman et al. (2009) approach the problem by finding sufficient conditions in terms of the unobservable component distributions, whereas we approach the problem by finding sufficient conditions in terms of the distribution function of…”