Transformation of measurement uncertainties into low-dimensional feature vector space

Area of Science:

• Data Science
• Statistical Modeling
• Geophysics

Background:

• High-resolution datasets require uncertainty quantification for reliable decision-making.
• Dimensionality reduction techniques often neglect the propagation of measurement uncertainty.
• Existing methods lack a unified approach to represent uncertainty in transformed data spaces.

Purpose of the Study:

• To develop a method for mapping measurement uncertainty into low-dimensional spaces.
• To enable statistical inferences from transformed datasets while accounting for uncertainty.
• To provide a versatile tool applicable across various scientific domains.

Main Methods:

• Utilizes approximate Bayesian computation to propagate uncertainty.
• Develops a method independent of feature extraction processes.
• Applies Chebyshev polynomials and principal component analysis for dimensionality reduction.

Main Results:

• Successfully maps measurement uncertainty into equivalent low-dimensional spaces.
• Generates uncertainty distributions for statistical inference without distribution assumptions.
• Demonstrates applicability across structural displacements, soil moisture, and global ocean temperature data.

Conclusions:

• The proposed method offers a robust way to handle uncertainty in dimensionality reduction.
• Enables improved decision-making in model validation, calibration, and condition monitoring.
• Facilitates accurate characterization of phenomena like the El Niño Southern Oscillation.