A regularization technique that penalizes the L1 norm (that is the sum of the absolute values of the model coefficients).

It can be seen as a Convex relaxation of the hard problem of Sparsity-based regularization.

It can also be seen, when applied to feature selection in the principal components basis as s a filter where we include those features which correlate best with the output, basically.

When used in a least-squares problem, the method is called Lasso