Artificial intelligence · University
PCA, variance and dimensionality reduction · revision notes
Principal component analysis finds orthogonal directions of high variance in centred data under its standard formulation.
Key ideas and conditions
Purpose
Principal component analysis finds orthogonal directions of high variance in centred data under its standard formulation.
Computation
Principal directions can be obtained from covariance eigenvectors or a singular-value decomposition of centred data.
Variance
Explained-variance ratios summarize variance captured, not predictive accuracy or importance to every task.
Scale
PCA is sensitive to units and scaling. High variance can reflect nuisance variation, and low-variance directions can still be useful for prediction.
Explain without looking
- How are distinct principal directions chosen in the standard Euclidean formulation?
- Why should PCA be fit on training data rather than the combined train and test data in a strict evaluation?
Further reading and review references
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