wrds++

README.md

@@ -485,9 +485,9 @@ full cell  ->  mitochondrial intermembrane space
 ```
 the definition for the mitochondrion is fully contained within the melanosome membrane definition and so testing that group should try and account for the mitochondrion. This can be done with the `HierarchicalEnrichment` routine exemplified above. We know that the melanosome membrane is associated with sight and that being diabetic is associated with mitochondrial dysfunction, but also that diabetic retinopathy affects diabetics. We see here that there is a knowledge based genetic connection relating these two spatially distinct regions of the cell.
 
-# [Example 9](https://gist.githubusercontent.com/richardtjornhammar/e84056e0b10f8d550258a1e8944ee375/raw/45fb8322487ff3a384e7f56eb06ac1073aee4da1/example9.py): Impetuous [deterministic DBSCAN](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for dbscan)
+# [Example 9](https://gist.githubusercontent.com/richardtjornhammar/e84056e0b10f8d550258a1e8944ee375/raw/e44e7226b6cb8ca486ff539ccfa775be981a549c/example9.py): Impetuous [deterministic DBSCAN](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for dbscan)
 
-[DBSCAN](https://en.wikipedia.org/wiki/DBSCAN) is a clustering algorithm that can be seen as a way of rejecting points that are positioned in low dense regions of a point cloud. This introduces holes and may result in a larger segment, that would otherwise be connected via a non dense link to become disconnected and form two segments, or clusters, instead. The rejection criterion is simple. The central concern is to evaluate a distance matrix <img src="https://render.githubusercontent.com/render/math?math=A_{ij}">  with an applied cutoff <img src="https://render.githubusercontent.com/render/math?math=\epsilon"> this turns the distances into true or false values depending on if a pair distance between point i and j is within the distance cutoff. This new binary Neighbour matrix <img src="https://render.githubusercontent.com/render/math?math=N_{ij}=A_{ij}<\epsilon"> tells you wether or not two points are neighbours (including itself). The DBSCAN criterion states that a point is not part of any cluster if it has fewer than `minPts` neighbors. Once you've calculated the distance matrix you can immediately evaluate the number of neighbors each point has and the rejection criterion, via <img src="https://render.githubusercontent.com/render/math?math=R_i=(\sum_{j} A_{ij}<\epsilon)-1 < minPts">. If the rejection vector R value of a point is True then all the pairwise distances in the distance matrix of that point is set to a value larger than epsilon. This ensures that a distance matrix search will reject these as Neighbours of any other for the choosen epsilon. By tracing out all points that are neighbors and assessing the [connectivity](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for connectivity) you can find all the clusters.
+[DBSCAN](https://en.wikipedia.org/wiki/DBSCAN) is a clustering algorithm that can be seen as a way of rejecting points, from any cluster, that are positioned in low dense regions of a point cloud. This introduces holes and may result in a larger segment, that would otherwise be connected via a non dense link to become disconnected and form two segments, or clusters. The rejection criterion is simple. The central concern is to evaluate a distance matrix <img src="https://render.githubusercontent.com/render/math?math=A_{ij}">  with an applied cutoff <img src="https://render.githubusercontent.com/render/math?math=\epsilon"> this turns the distances into true or false values depending on if a pair distance between point i and j is within the distance cutoff. This new binary Neighbour matrix <img src="https://render.githubusercontent.com/render/math?math=N_{ij}=A_{ij}<\epsilon"> tells you wether or not two points are neighbours (including itself). The DBSCAN criterion states that a point is not part of any cluster if it has fewer than `minPts` neighbors. Once you've calculated the distance matrix you can immediately evaluate the number of neighbors each point has and the rejection criterion, via <img src="https://render.githubusercontent.com/render/math?math=R_i=(\sum_{j} A_{ij}<\epsilon)-1 < minPts">. If the rejection vector R value of a point is True then all the pairwise distances in the distance matrix of that point is set to a value larger than epsilon. This ensures that a distance matrix search will reject those points as neighbours of any other for the choosen epsilon. By tracing out all points that are neighbors and assessing the [connectivity](https://github.com/richardtjornhammar/impetuous/blob/master/src/impetuous/clustering.py) (search for connectivity) you can find all the clusters.
 
 In this [example](https://gist.githubusercontent.com/richardtjornhammar/e84056e0b10f8d550258a1e8944ee375/raw/e44e7226b6cb8ca486ff539ccfa775be981a549c/example9.py) we do exactly this for two gaussian point clouds. The dbscan search is just a single line `dbscan ( data_frame = point_cloud_df , eps=0.45 , minPts=4 )`, while the last lines are there to plot the [results](https://bl.ocks.org/richardtjornhammar/raw/0cc0ff037e88c76a9d65387155674fd1/?raw=true) ( has [graph revision dates](https://gist.github.com/richardtjornhammar/0cc0ff037e88c76a9d65387155674fd1/revisions) )