Maximum Likelihood Solution to the Parafac Model

Mayekawa, Shin-ichi

doi:10.2333/bhmk.14.21_45

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…It is important to note that (48) differs from (14) because in the former, covariances among different occasions and among specific factors are not considered. Mayekawa (1987) extends the Parafac2 model by introducing the variances of the specific factors and providing the ML estimation. About the structural approach, it is worth mentioning the work of Stegeman & Lam (2014), where an estimation procedure, based on minimum rank FA, for the structural Parafac model in (14) is proposed under the assumption of uncorrelated specific factors.…”

Section: Related Modelsmentioning

confidence: 99%

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Factor Uniqueness of the Structural Parafac Model

2020

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Factor analysis is a well-known method for describing the covariance structure among a set of manifest variables through a limited number of unobserved factors. When the observed variables are collected at various occasions on the same statistical units, the data have a three-way structure and standard factor analysis may fail. To overcome these limitations, three-way models, such as the Parafac model, can be adopted. It is often seen as an extension of principal component analysis able to discover unique latent components. The structural version, i.e., as a reparameterization of the covariance matrix, has been also formulated but rarely investigated. In this article, such a formulation is studied by discussing under what conditions factor uniqueness is preserved. It is shown that, under mild conditions, such a property holds even if the specific factors are assumed to be within-variable, or within-occasion, correlated and the model is modified to become scale invariant.

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Section: Related Modelsmentioning

confidence: 99%

Section: Related Modelsmentioning

confidence: 99%

Factor Uniqueness of the Structural Parafac Model

2020

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“…To our knowledge this particular unsupervised model and estimation approach, which provides a generative model for the sampled mode, is novel. Related maximumlikelihood based CP factorizations have been proposed by [23] and [32], and there is a large body of work on Bayesian models for the CP and other multiway factorizations (see, e.g., [13] and [35]).…”

Section: Special Casesmentioning

confidence: 99%

Supervised multiway factorization

Lock¹,

Li²

2018

Electron. J. Statist.

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We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order array. Such data are increasingly encountered in biomedical research and other fields. We use a novel likelihood-based latent variable representation of the CP factorization, in which the latent variables are informed by additional covariates. We give conditions for identifiability, and develop an EM algorithm for simultaneous estimation of all model parameters. SupCP can be used for dimension reduction, capturing latent structures that are more accurate and interpretable due to covariate supervision. Moreover, SupCP specifies a full probability distribution for a multiway data observation with given covariate values, which can be used for predictive modeling. We conduct comprehensive simulations to evaluate the SupCP algorithm. We apply it to a facial image database with facial descriptors (e.g., smiling / not smiling) as covariates, and to a study of amino acid fluorescence. Software is available at https://github.com/lockEF/SupCP.

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An Overview of Three-way Analysis and Some Recent Developments

Kiers

1998

Studies in Classification, Data Analysis, and Knowledge Organization

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Maximum Likelihood Solution to the Parafac Model

Cited by 4 publications

References 13 publications

Factor Uniqueness of the Structural Parafac Model

Factor Uniqueness of the Structural Parafac Model

Supervised multiway factorization

An Overview of Three-way Analysis and Some Recent Developments

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