NonuniformGroupSparsePenalty¶
A penalty encouraging group-sparse (few nonzero groups of elements) solutions along one or more axes with non-uniform group sizes, implemented as a proximal operator.
The general use case is to specify an axis along which groups are defined (e.g., feature), and then to supply an array of group membership indices (e.g., [0,0,0,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]) that assignes different features to different groups. The effect is then that only a few groups of elements are active in any given solution. The node supports both the default l1/l2 norm and the more lax l1/linf norm (which leaves the magnitude of elements within an active group less constrained); currently, mixed norms that additionally feature a pointwise sparsity norm are not supported (but can be realized with solvers that support more than one proximal operator). One can also give a comma-separated list of multiple axes (e.g., time,space) to define groups that extend across both axes, but be careful about the order in which the elements appear in the flattened axis. Like all proximal operators, this is normally used as part of the optimization problem formulation given to a (typically convex) solver node. Version 1.0.0
Ports/Properties¶
data¶
Data to process.
step_size¶
Step size.
step_count¶
Current step count for outer solver.
axis¶
Axis along which the elements appear in groups. For example, if this is set to 'feature', then different features can be assigned to different groups, but the result is sparse along all other axes (e.g., channels). You can also give a comma-separated list of multiple axes (e.g., time,space) which are flattened before group indices are taken into consideration.
membership¶
List of group membership indices. Each element is a 0-based integer that indicates the group to which the respective element along the given axis belongs.
norm¶
The norm to use for the group sparsity penalty. The default choice is l1/l2, which is the sum of l2 norms of each group. An alternative choice is l1/linf, which is the sum of the max norms of each group; this penalizes only the largest element in each group, which has the side effect of leaving the other elements in the group unpenalized; as such, the assumption is that if a group is active (nonzero), then any element in the group is equally likely to be active.
group_sparsity¶
Degree of group-wise sparsity in the solution. Larger values will encourage fewer non-zero groups of elements to remain in the solution.
set_breakpoint¶
Set a breakpoint on this node. If this is enabled, your debugger (if one is attached) will trigger a breakpoint.
metadata¶
User-definable meta-data associated with the node. Usually reserved for technical purposes.