Supervised multiway factorization.

Area of Science:

• Multivariate statistics
• Machine learning
• Data science

Background:

• Multiway data analysis is crucial in fields like biomedical research.
• Existing methods like supervised singular value decomposition (SupSVD) are limited to vector-valued data.
• Higher-order tensor data requires advanced factorization techniques.

Purpose of the Study:

• To develop a probabilistic PARAFAC/CANDECOMP (CP) factorization incorporating auxiliary covariates, named SupCP.
• To generalize SupSVD for matrix or higher-order tensor data.
• To improve dimension reduction and predictive modeling for complex datasets.

Main Methods:

• Developed a novel likelihood-based latent variable representation for CP factorization.
• Incorporated auxiliary covariates to inform latent variables.
• Derived conditions for model identifiability and an EM algorithm for parameter estimation.

Main Results:

• SupCP enables more accurate and interpretable latent structure discovery through covariate supervision.
• The method provides a full probability distribution for multiway data, facilitating predictive modeling.
• Simulations demonstrated the effectiveness of the SupCP algorithm.

Conclusions:

• SupCP offers a powerful probabilistic framework for analyzing multiway data with covariates.
• The approach enhances understanding of complex data structures in various scientific domains.
• SupCP is applicable to diverse datasets, including facial image analysis and fluorescence studies.