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Week 2 Summary: Physics of data formation

Cross-Book Summary

1. Signal Formation & Noise

Measurement Mapping: Signal = physical state convolved with instrument PSF.
Stochastics: Data is a stochastic process.
Noise as Prior: Noise distributions reveal detector physics.

2. Dimension Reduction & Structure

Dimensionality Curse: High dimension, low intrinsic rank.
SVD vs. PCA: PCA uses covariance; SVD factorizes matrix efficiently.
Principal Variations: Top singular vectors capture main physical phenomena.
Reduced Order Modeling: PCA scores map to processing parameters.

90-Minute Lecture Strategy

Part 1: Measurement Chain

Signal formation process.
Resolution and Contrast.
Nyquist-Shannon sampling limit.

Part 2: Statistical Foundations

Variance, Covariance, Correlation.
Covariance Matrix geometry.
Noise distributions.

Part 3: Dimension Reduction

Finding natural coordinates.
PCA steps: Center, Covariance, Eigen-decomposition.
SVD mechanics.
Scree Plots and explained variance.

Part 4: Materials Case Studies

Spectral Denoising with PCA.
Time-series Compression.
Microstructure Eigen-modes.

Part 5: Physics-ML Integration

PCA as physical mode finder.
Non-linear limits of PCA.
Fourier periodicity exercise.

Quarto Website Update (Summary)

Summary for ML-PC Week 2:

Connects physical data acquisition to mathematical representation.
Analyzes signal formation, resolution, and noise as priors.
Introduces PCA and SVD for low-dimensional structure discovery.
Demonstrates dimensionality reduction in high-dimensional datasets.