independent component analysis

**ICA** (Independent Component Analysis) is a **blind source separation technique that decomposes a multivariate signal into statistically independent components** — unlike PCA (which finds uncorrelated components), ICA finds maximally independent sources, revealing the underlying independent physical causes. **How Does ICA Work?** - **Model**: $X = AS$ where $S$ are independent source signals and $A$ is the mixing matrix. - **Objective**: Find the unmixing matrix $W = A^{-1}$ that maximizes the statistical independence of the estimated sources. - **Independence Criteria**: Maximizing non-Gaussianity (kurtosis or negentropy) or minimizing mutual information. - **Algorithms**: FastICA, Infomax, JADE. **Why It Matters** - **Source Separation**: Separates mixed signals into independent physical sources (e.g., separating fault signatures from normal variation). - **Beyond PCA**: PCA gives uncorrelated components; ICA gives truly independent ones — better for identifying root causes. - **Fault Isolation**: Each independent component may correspond to a separate physical mechanism. **ICA** is **finding independent causes in mixed data** — separating overlapping signals to reveal the truly independent sources of variation.