cw changes [ci skip]

Author: marscher

notebooks/02-dimension-reduction-and-discretization.ipynb

@@ -131,7 +131,9 @@
    "source": [
     "Have you noticed how the $k$-means centers follow the density of the data points while the regspace centers are spread uniformly over the whole area? \n",
     "\n",
-    "If your are only interested in well sampled states, you should use a density based method to discretize. If exploring new states is one of your objectives, it might be of advantage to place states also in rarely observed regions. The latter is especially useful in adaptive sampling approaches, because in the initial phase you want to explore the phase space as much as possible. The downside of placing states in areas of low density is that we will have poor statistics on these states. Another advantage of regular space clustering is, that is very fast in comparison to $k$-means, namely regspace clustering runs in linear time, while $k$-means is super polynomial in time.\n",
+    "If your are only interested in well sampled states, you should use a density based method to discretize. If exploring new states is one of your objectives, it might be of advantage to place states also in rarely observed regions. The latter is especially useful in adaptive sampling approaches, because in the initial phase you want to explore the phase space as much as possible. The downside of placing states in areas of low density is that we will have poor statistics on these states. \n",
+    "\n",
+    "Another advantage of regular space clustering is that is very fast in comparison to $k$-means: regspace clustering runs in linear time while $k$-means is superpolynomial in time.\n",
     "\n",
     "For very large datasets we also offer a mini batch version of $k$-means, which has the same semantics as the original method, but trains the centers on subsets of your data. This tutorial does not cover this case, but you should keep in mind, that $k$-means requires your low dimensional space to fit into your main memory.\n",
     "\n",