Implementation on Cluster Feature Tree

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Implementationon Cluster Feature Tree

• MAIDS group
• NCSA and Dept. of CS
• University of Illinois at Urbana-Champaign
• www.maids.ncsa.uiuc.edu

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CF Tree For Cluster Analysis
Root
Non-leaf node
CF1
CF3
CF2
CF5
child1
child3
child2
child5
Leaf node
Leaf node
CF1
CF2
CF6
prev
next
CF1
CF2
CF4
prev
next
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Cluster Feature Tree

• Built dynamically as new data are inserted
• Used to guide a new insertion into the correct
  cluster
• A height-balanced tree
• With three parameters branching factor B for
  non-leaf node, branching factor L for leaf node,
  and threshold T for diameter (or radius)
• Each non-leaf node contains at most B entries
• Each leaf node contains at most L entries
• Each leaf node has prev and next pointers to
  chain all leaf nodes together
• Diameter (or radius) of all entries in a leaf
  node must be less than T

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Non-leaf Node in CF Tree

• Each entry has a CF vector to store summary
  information
• CF vector is defined as a triple CF (N, LS,
  SS)
• N Number of data points
• LS ?Ni1Xi
• SS ?Ni1Xi2
• CF vector is the sum of all children, and is
  used for computing centroid, radius, diameter and
  distance.
• Each entry has a pointer to its child node.

N, LS, SS
Child
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Leaf Node in CF Tree

• Data structure in each entry of the leaf node
• Data structure in each time slot of the tilted
  time window
• Each entry of the leaf node is a micro-cluster

N, LS, SS (Sum of all time slots in the tilted
time window)
Tilted Time Window
N, LS, SS
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Insert into a CF Tree

• Start from the root, recursively descends the CF
  tree by choosing the closest child node.
• Modify the leaf
• If diameter lt threshold, data is absorbed by the
  leaf.
• If diameter gt threshold, add a new entry to the
  leaf.
• Split the leaf if number of entries in the leaf gt
  L.
• Modify the path to the leaf
• Update the CF info for each non-leaf entry on
  the path.
• Non-leaf node may split as well.
• If the root split, the tree height increases by
  one.

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Delete or Merge Micro-Cluster

• May need to delete or merge micro-clusters to
  free memory space for new micro-clusters.
• Delete any of the current micro-clusters as
  outliers if It is safe.
• Merge clusters if no clusters can be deleted.
• Need modify the path to the leaf after deletion
  and merging.
• Never split a micro-cluster because there is no
  tracking information for individual data point.

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Macro-Cluster Creation

• Modified K-Mean algorithm
• Initialization stage
• Seeds are sampled with probability proportional
  to the number of points in a given micro-cluster
• Partitioning stage
• Distance is computed from seed to the centroid of
  the corresponding micro-cluster
• Seed adjustment stage
• New seed is defined as the weighted centroid of
  the micro-clusters in that partition

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Usage of CF Tree

• Create macro-clusters for user requested time
  horizon using modified K-Mean algorithm
• Find clusters of the network flow between 8AM to
  10AM
• Retrieve all CF vectors of leaf nodes for the
  time slots 8AM 10AM
• Compute macro-clusters
• Evolution analysis of clusters
• Find changes of the network flow from yesterday
  to today
• Retrieve all CF vectors of leaf nodes for
  yesterday and today
• Compute macro-clusters for yesterday and today
• Compare the difference of two sets of
  macro-clusters