The hierarchical clustering algorithm DIANA

Category hierarchical clustering

1. Aggregated hierarchical clustering: from the bottom up; to each object as a cluster, from bottom to top, the similar clusters merged together until combined into a cluster
2. Hierarchical clustering classification: top-down; starting from the cluster containing all points, each split a cluster until the cluster, leaving only a single point

Cohesion between clusters

Single chain:
Definition: two clusters of adjacent as the shortest distance between any two points in the two clusters
formula: dist ({m1, m2} , {m3, m4}) = min (dist {m1, m3}, dist {m1, m4 }, dist {m2, m3}, dist {m2, m4})
features: good art single-stranded non-elliptical processing clusters, but very sensitive to noise and outliers.
Full Chain:
Definition: the proximity of two clusters is the longest distance between any two points in the two clusters
formula: dist ({m1, m2} , {m3, m4}) = max (dist {m1 , m3}, dist {m1, m4}, dist {m2, m3}, dist {m2, m4})
features: good processing chain technology circular cluster, but is less sensitive to noise and outliers.
Group average:
Definition: the proximity of two clusters is the average distance between any two points in the two clusters
formula: dist ({m1, m2} , {m3, m4}) = (dist {m1, m3 } + dist {m1, m4} + dist {m2, m3} + dist {m2, m4}) $\div$ 4

Algorithm idea:

Input: n objects, the number of clusters k termination condition

Output: k clusters, the number of clusters reaches a predetermined termination condition

1. All objects as an initial cluster
2. for(i=1;i≠k;i++) do begin
3. Selected cluster C has a maximum diameter in all clusters
4. Find other points C with the largest average dissimilarity to a point P and P into splinter group, remaining in the old party
5. repeat
6. To find the nearest point of the splinter group old party to a point not greater than the distance from the closest point in the old party and the point is added splinter group
7. until no new node is assigned the old party to spilnter group
8. spilnter group old party and is split into two clusters selected clusters of the new cluster with other clusters set
9. end
   hierarchical clustering algorithm divided generally less use.