Hands-On Unsupervised Learning with Python

Sparse PCA and dictionary learning

Standard PCA is generally a dense decomposition; this is to say that the vectors, once transformed, are linear combinations of all of the components with not-null coefficients:

In the previous expression, the coefficients, α_i, are almost always different from zero, so all of the components are involved in the rebuilding process. For dimensionality reduction purposes, this is not an issue, because we are more interested in the variance explained by each component, in order to limit them. However, there are some tasks for which it's helpful to analyze a larger set of building atoms, with the assumption that ...