  Sorted $\ell_1$ Penalized Estimator (SLOPE) is a relatively new convex
regularization method for fitting high-dimensional regression models. SLOPE
allows to reduce the model dimension by shrinking some estimates of the
regression coefficients completely to zero or by equating the absolute values
of some nonzero estimates of these coefficients. This allows to identify
situations where some of~true regression coefficients are equal. In this
article we will introduce the SLOPE pattern, i.e., the set of relations between
the true regression coefficients, which can be identified by SLOPE. We will
also present new results on the strong consistency of SLOPE estimators and
on~the~strong consistency of pattern recovery by~SLOPE when the design matrix
is orthogonal and illustrate advantages of~the~SLOPE clustering in the context
of high frequency signal denoising.
