  In an ordinary feature selection procedure, a set of important features is
obtained by solving an optimization problem such as the Lasso regression
problem, and we expect that the obtained features explain the data well. In
this study, instead of the single optimal solution, we consider finding a set
of diverse yet nearly optimal solutions. To this end, we formulate the problem
as finding a small number of solutions such that the convex hull of these
solutions approximates the set of nearly optimal solutions. The proposed
algorithm consists of two steps: First, we randomly sample the extreme points
of the set of nearly optimal solutions. Then, we select a small number of
points using a greedy algorithm. The experimental results indicate that the
proposed algorithm can approximate the solution set well. The results also
indicate that we can obtain Lasso solutions with a large diversity.
