Non-negative matrix factorisation
Topic of Principal component analysis, part of Statistical learning
Non-negative matrix factorisation
| Type | Topic |
| Taught in | Principal component analysis |
| Part | Statistical learning |
Approximating a non-negative data matrix by the product of two low-rank non-negative matrices, so that components add up parts rather than cancel. It is named in the course as an alternative to principal components.
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
Principal component directions and scores · Principal component directions · Scaling · Principal components by Lagrange multipliers · Reconstruction from principal components · Choosing the number of principal components · How many components, on a correlation with no response · Singular value decomposition