PCA

PCA finds the principal components of a multi-channel Signal over its window — the directions in channel space along which the data actually varies.

Scores is the data expressed in the new basis, with components labelled by how much they explain ("PC1 (61 %)"). Basis is the orthonormal loadings as a matrix (rows are components, columns are channels — the change-of-basis matrix). Explained gives the variance fractions and Dominant the first component's loadings.

Two details make it usable live rather than only in a notebook. Signs and the order of near-equal components are held steady between frames, so the picture does not flip every time two components swap by a hair. And Standardize uses the correlation matrix instead of the covariance matrix, so channels with big units do not dominate simply for being big.

• Reduce many channels to a few — Sixteen EEG electrodes become three scores that carry most of the movement.
• A cleaner control signal — PC1 of a multi-channel sensor is usually steadier than any single channel.
• See the structure — Plot the Basis as a heatmap: which channels load onto which component.
• 3D from many dimensions — The first three scores into Plot 3D's Scatter or a point cloud.
• Detect a change of regime — When Explained shifts, the shape of the data has changed.

• Standardize whenever the channels have different units or wildly different scales. Otherwise the biggest unit wins.
• Components are only meaningful while the window's statistics are stable; a very short window gives a jittery basis.
• The sign of a component is arbitrary in principle — here it is stabilised, so treat a sudden flip as a real change.
• Explained falling off slowly means the data genuinely is high-dimensional; do not force it into three.
• For separating mixed sources rather than finding variance directions, ICA is the right tool.