 Finally{\em   , we provide improved approximation results for the maximum variance embedding problem for general graphs, by replacing the optimal orthogonal projection (PCA) with a randomized projection approach .
<meaning-changed>  Finally{\em   , we provide improved approximation results for the maximum variance embedding problem for general graphs, by replacing the optimal orthogonal projection (PCA) with a randomized projection approach .
 Finally{\em problem. For trees , we provide improved approximation results for the maximum variance embedding problem for general graphs, by replacing the optimal orthogonal projection (PCA) with a randomized projection approach .