Procrustes Cross-Validation of short datasets in PCA context

Area of Science:

• * Statistical modeling and data analysis.
• * Chemometrics and spectral data analysis.

Background:

• * Traditional cross-validation methods, such as leave-one-out cross-validation, can be unsuitable for small datasets where each sample holds significant importance.
• * Removing individual samples in small datasets can lead to a loss of critical information and potentially biased results.

Purpose of the Study:

• * To introduce Procrustes cross-validation as a novel alternative to conventional cross-validation techniques for small datasets.
• * To demonstrate the utility and advantages of Procrustes cross-validation in scenarios with limited sample sizes.

Main Methods:

• * Development and application of Procrustes cross-validation, a technique designed to preserve all samples within the dataset.
• * Validation of the method using two distinct real-world datasets: one with discrete variables (chemical profiles) and another with continuous data (spectra).

Main Results:

• * Procrustes cross-validation effectively handles small datasets without removing samples, preserving data integrity.
• * The method shows advantages in analyzing both discrete chemical profile data and continuous spectral data.
• * Successful implementation in R and Matlab, providing an accessible tool for analysts.

Conclusions:

• * Procrustes cross-validation offers a robust and practical alternative to standard cross-validation for small, sample-critical datasets.
• * The tool is readily usable by analysts across various scientific domains dealing with limited data.
• * This approach enhances the reliability of model evaluation when sample size is a constraint.