← Back to portfolio

PCA dimensionality reduction

Dataset

Data points (N)200

Clusters3

Cluster spread1.5

Points fall uniformly within ±spread of their cluster centre on every axis. The sliders reshape the current dataset; New data draws fresh centres.

3D view

Rotation speed0.5

Drag the plot to orbit it. Rotation pauses while the pointer is over the plot.

Result

Points0

Dimensions3 → 2

Variance kept–

Power iterations–

Variance kept is the share of the cloud's total variance that survives the drop from three dimensions to two.

How it works

PCA looks for the directions along which the data varies most. It centres the points on their mean, builds the 3 × 3 covariance matrix, then runs power iteration: multiply a random vector by the matrix and normalise, again and again, until it settles on the dominant eigenvector, PC1. Deflation removes that direction so the next pass finds PC2, then PC3. Keeping only the PC1 and PC2 coordinates turns every 3D point into a 2D one while giving up as little variance as possible.

From 3D to 2D

Original datax · y · z

PCA projectionPC1 × PC2

No projection yetIt appears here once PC1 and PC2 are known.

Press Run PCA to find the directions of greatest variance.

Explained variance

PC1–Not found yetkept
PC2–Not found yetkept
PC3–Not found yetdropped

Each eigenvalue divided by their sum: the share of the variance that lies along that component.

Covariance matrix

The diagonal holds the variance of each axis; the other cells show how two axes move together.

Principal axes

Each row is a unit vector. On the 3D plot the axes are drawn in proportion to the standard deviation along them.