Correlation ≠ Accuracy — Understanding Objective Functions in Materials Data (XRD & Raman)

Описание: In this Crystapedia episode, we explore the subtle but crucial difference between correlation and residuals when analyzing experimental data in materials science — especially in X-ray diffraction (XRD) and Raman spectroscopy.

Many researchers trust correlation as a measure of similarity. But in real-world materials data, correlation can be misleading — two patterns can be highly correlated even when their peaks are misplaced or their baselines are wrong.

We’ll compare the behavior of correlation coefficient and mean squared residual (MSE) using synthetic XRD-like data, showing how each metric influences the fitting outcome under the Levenberg–Marquardt algorithm.

You’ll learn:
—Why correlation can hide systematic fitting errors
—How residuals reveal physical inaccuracies in peak position and intensity
—How to visualize and compare correlation vs MSE in Python
—What happens when the optimizer focuses on the wrong objective

This is the first step toward understanding how objective functions define the truth your optimizer sees — and why this choice matters in every materials experiment.

🎓 Ideal for:
—Materials science students and researchers
—XRD and Raman data analysts
—Python-based experimental data scientists
—Anyone working on curve fitting or signal comparison

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Next episode: Local vs Global Optimization — LM vs DE Compared

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