BIRCH

1
BIRCH

• An Efficient Data Clustering Method for Very
  Large Databases
• SIGMOD 96

2
Introduction

• Balanced Iterative Reducing and Clustering using
  Hierarchies
• For multi-dimensional dataset
• Minimized I/O cost (linear 1 or 2 scan)
• Full utilization of memory
• Hierarchies ? indexing method

3
Terminology

• Property of a cluster
• Given N d-dimensional data points
• Centroid
• Radius
• Diameter

4
Terminology

• Distance between 2 clusters
• D0 Euclidian distance between centroids
• D1 Manhattan distance between centroids
• D2 average inter-cluster distance
• D3 average intra-cluster distance
• D4 variance increase distance

5
Clustering Feature

• To calculate centroid, radius, diameter, D0, D1,
  D2, D3 and D4, not all points are needed
• 3 values are stored to represent the cluster (CF)
• N number of points in a cluster
• LS linear sum of points in a cluster
• SS square sum of points in a cluster
• CF are additive

6
CF Tree

• Similar to B-tree, R-tree
• Parameter
• B branching factor
• T threshold
• Leaf node contains at most L CF entries, each
  CF should follows DltT or RltT
• Non-leaf node contains at most B CF entries of
  its child
• Each node should fit into 1 page

7
BIRCH

• Phase 1 Scan dataset once, build a CF tree in
  memory
• Phase 2 (Optional) Condense the CF tree to a
  smaller CF tree
• Phase 3 Global Clustering
• Phase 4 (Optional) Clustering Refining (require
  scan of dataset)

8
BIRCH
9
Building CF Tree (Phase 1)

• CF of a data point (3,4) is (1,(3,4),25)
• Insert a point to the tree
• Find the path (based on D0, D1, D2, D3, D4
  between CF of children in a non-leaf node)
• Modify the leaf
• Find closest leaf node entry (based on D0, D1,
  D2, D3, D4 of CF in leaf node)
• Check if it can absorb the new data point
• Modify the path to the leaf
• Splitting if leaf node is full, split into two
  leaf node, add one more entry in parent

10
Building CF Tree (Phase 1)
Sum of CF(N,LS,SS) of all children
Non-leave node
Leave node
CF(N,LS,SS) under condition DltT or RltT
11
Condensing CF Tree (Phase 2)

• Chose a larger T (threshold)
• Consider entries in leaf nodes
• Reinsert CF entries in the new tree
• If new path is before original path, move
  it to new path
• If new path is the same as original path,
  leave it unchanged

12
Global Clustering (Phase 3)

• Consider CF entries in leaf nodes only
• Use centroid as the representative of a cluster
• Perform traditional clustering (e.g.
  agglomerative hierarchy (complete link D2) or
  K-mean or CL)
• Cluster CF instead of data points

13
Cluster Refining (Phase 4)

• Require scan of dataset one more time
• Use clusters found in phase 3 as seeds
• Redistribute data points to their closest seeds
  and form new clusters
• Removal of outliers
• Acquisition of membership information

14
Performance
15
Visualization
16
Conclusion

• A clustering algorithm taking consideration of
  I/O costs, memory limitation
• Utilize local information (each clustering
  decision is made without scanning all data
  points)
• Not every data point is equally important for
  clustering purpose