Data Understanding & Preparation

Dimensionality Reduction Lab

Compress correlated high-dimensional measurements into a view you can inspect, while separating mathematically computed PCA from conceptual nonlinear demonstrations.

1 · Dataset 2 · Preprocessing 3 · Feature engineering 4 · Dimensionality reduction 5 · Class imbalance 6 · Data leakage

Lab concept guide

What to observe while you experiment

Dimensionality reduction creates a lower-dimensional representation while preserving a chosen notion of structure. PCA preserves directions of high variance through an orthogonal linear projection; nonlinear embeddings optimise different neighbourhood/geometry objectives and should not be read as literal distances without care.

MechanismFor PCA, centre/scale as appropriate, inspect component directions and explained variance, then project points; treat nonlinear views as exploratory embeddings with method-specific assumptions.

Failure modeInterpreting a 2D embedding as proof of real clusters or applying PCA without considering feature scale and the meaning of variance.

VerificationFor a tiny 2D correlated dataset, verify PCA’s first direction/projection qualitatively or numerically and check how rescaling one feature changes it.

Experiment deliberately

Rescale one feature, rerun PCA and predict the component rotation. Then compare with a nonlinear view and state which distances/neighbourhoods are trustworthy.

Projection Dataset Components Neighbour emphasis 12 StandardiseEqualise feature scales before projection.

Computing projection…

Dimensionality Reduction Lab

What to observe while you experiment

Projection

Variance / structure