Factor analysis
Topic of Principal component analysis, part of Statistical learning
Factor analysis
| Type | Topic |
| Taught in | Principal component analysis |
| Part | Statistical learning |
A probability model that writes the observed variables as linear combinations of a few unobserved factors plus independent variable-specific noise. Unlike principal components it models the covariance, not just the variance directions; the course names it as a relative of PCA and does not develop it.
In Principal component analysis
That value is the smallest residual attainable by any rank-k linear approximation. The leading components are at once the highest-variance coordinates and the best linear summary of the cloud in squared error. A later autoencoder network generalises the second description: a hidden layer smaller than the input tries to reproduce the input after passing through a lower-dimensional representation. Factor analysis and non-negative matrix factorisation are further representations, with different constraints.
Used in
See also
Mean vector and covariance matrix · Variance · Principal component directions and scores · Principal component directions · Scaling · Principal components by Lagrange multipliers · Reconstruction from principal components · Choosing the number of principal components