I have a a set of $12 \times 12$ matrices $B_1, B_2, \dots, B_{30}$. How can I choose a reduced number of vertices $B_j$ where $j$ ranges from $1$ to, say, $5$ or $6$ such that the convex hull of $B_i$ and $B_j$ is similar via some measure (hypervolume or other set difference measure)
My approach
- I transformed the matrices into vectors and formed a two dimensional matrix $A$ of dimension $30 \times 144$. I performed pca on this, obtained a new coordinate transformation for reduced dimension (6), transformed the matrix into 60 x 5 matrix and then used convex hull algorithm; the algorithm because of noise in data produces many vertices in convex hull.
Is there a way to reduce number of vertices of a convex combination of a set. How can I compute the convex hull for noisy data with less number of vertices.