Principal component directions and scores
Definition taught in Principal component analysis, part of Statistical learning
Principal component directions and scores
| Type | Definition |
| Taught in | Principal component analysis |
| Part | Statistical learning |
| Questions using it | 2 |
The first principal component direction is the unit vector \mathbf{a}_1\in\mathbb{R}^p along which the sample variance of the data is largest. The first principal component scores are the projections of the observations onto \mathbf{a}_1, the dot products \mathbf{a}_1^\top\mathbf{x}_i. The second principal component direction \mathbf{a}_2 is the unit vector orthogonal to \mathbf{a}_1 along which the sample variance is largest subject to that constraint. The third is orthogonal to the first two, and so on until p directions, and the p corresponding sets of scores, are defined.
Used in
- Taught in Principal component analysis, where the derivation and examples are.
- Also used in Covariance and the multivariate normal
- Questions that use it (2) — A two-variable analysis · LDA and principal components
- All 7 questions on Principal component analysis
See also
Principal component directions · Eigenvalues and eigenvectors · Singular value decomposition · Variance · Scaling · Principal components by Lagrange multipliers · Reconstruction from principal components · Choosing the number of principal components