Cluster analysis two: Dbscan algorithm

I. Basic CONCEPTS

Dbscan algorithm

• Core object (a): If the density of a point reaches the threshold set by the algorithm, it is the core point (that is, the number of points within the R neighborhood is not less than minpts)
• Distance threshold for Neighborhood: Set radius r
• Direct density up to: If a point p in the R neighborhood of point Q and Q is the core point, then the p-q is direct density ( core object, in the neighborhood )
• Density up to: if there is a sequence of points q0, q1....qk, to any qi-qi-1 is direct density can reach, it is said from the q0 to qk density can be reached, which is actually direct density can reach the transmission ( direct density can reach )
• Density connection: If from a core point p, point Q and point k are density can be reached, then the point Q and point K is density connected
• Boundary Point (B, C): A non-core point belonging to a class that cannot be developed offline
• Noise Point (N): A point that does not belong to any one of the clusters, from any core point is a density unreachable

Two. Basic process

Algorithm flow: (data set, radius, density threshold)

• Mark all objects as not visited
• Randomly select an object that has not been accessed P, Mark p for the visited
• If a neighborhood of P has at least minpts objects

1. Create a new cluster C and add p to C
2. A collection of objects in a field that makes N p
3. For each point in N: If P is not visited, Mark P is already visited. And if P's neighborhood has at least minpts objects, add these objects to n; If P is not a member of any cluster, add p to C

• Otherwise mark P for noise
• Until there are no objects marked as not visited

Parameter selection:

• Radius: can be set according to K Distance: To find the mutation point K distance

  K Distance: p={p (i) for a given dataset, i=0,1,... n}, calculated point P (i) to a subset of Set D
  Distance between the distances, in order from small to large, d (k) is called K-distance.

• minpts:k-distance from the value of K, generally take smaller, multiple attempts

Three. Pros and cons

Advantage

• You do not need to specify the number of clusters
• You can find clusters of any shape
• Good at finding outliers.
• Only two parameters

Disadvantage

• High-dimensional data can be difficult to do (dimensionality reduction)
• The parameters are difficult to select, but the effect on the results is very large
• Sklearn is slow (data reduction strategy)

Cluster analysis two: Dbscan algorithm