Tucker core consistency for validation of restricted Tucker3 models

Area of Science:

• Multivariate data analysis
• Chemometrics
• Biometrics

Background:

• Tucker3 analysis of three-way data arrays is common in chemical and biological systems.
• Restricted Tucker3 models incorporate prior knowledge, often by setting core elements to zero.
• PARAFAC (Parallel Factor Analysis) is a specific case of a restricted Tucker3 model.

Purpose of the Study:

• To extend the core consistency diagnostic to validate constraints in restricted Tucker3 models.
• To introduce a new diagnostic named Tucker core consistency (TuckCorCon).
• To assess the appropriateness of dimensionality and the pattern of nonzero core elements in restricted Tucker3 models.

Main Methods:

• Extension of the core consistency diagnostic for PARAFAC analysis to general restricted Tucker3 models.
• Development and naming of the Tucker core consistency (TuckCorCon) diagnostic.
• Validation using a simulated chemical equilibrium data set and two experimental data sets.

Main Results:

• The TuckCorCon diagnostic effectively evaluates the validity of constraints in restricted Tucker3 models.
• When dimensionality and core pattern are appropriate, TuckCorCon approaches 100%.
• The diagnostic aids in deciding the correct dimensionality and nonzero element patterns for restricted cores.

Conclusions:

• TuckCorCon is a valuable tool for validating restricted Tucker3 models in multivariate data analysis.
• The diagnostic ensures the appropriateness of applied constraints, improving model reliability.
• Applicability demonstrated across simulated and experimental chemical and biological data.