Cobweb (clustering)

COBWEB is an incremental system for hierarchical conceptual clustering.

COBWEB incrementally organizes observations into a classification tree. Each node in a classification tree represents a class (concept) and is labeled by a probabilistic concept that summarizes the attribute-value distributions of objects classified under the node. This classification tree can be used to predict missing attributes or the class of a new object.

There are four basic operations COBWEB employs in building the classification tree. Which operation is selected depends on the category utility of the classification achieved by applying it. The operations are:

• Merging Two Nodes
  Merging two nodes means replacing them by a node whose children is the union of the original nodes' sets of children and which summarizes the attribute-value distributions of all objects classified under them.

• Splitting a node
  A node is split by replacing it with its children.

• Inserting a new node
  A node is created corresponding to the object being inserted into the tree.

• Passing an object down the hierarchy
  Effectively calling the COBWEB algorithm on the object and the subtree rooted in the node.

The COBWEB Algorithm

Algorithm COBWEB
  COBWEB(root, record):
  Input: A COBWEB node root, an instance to insert record
  if root has no children then
    children := {copy(root)}
    newcategory(record) \\ adds child with record’s feature values.
    insert(record, root) \\ update root’s statistics
  else
    insert(record, root)
    for child in root’s children do
      calculate Category Utility for insert(record, child),
      set best1, best2 children w. best CU.
    end for
    if newcategory(record) yields best CU then
      newcategory(record)
    else if merge(best1, best2) yields best CU then
      merge(best1, best2)
      COBWEB(root, record)
    else if split(best1) yields best CU then
      split(best1)
      COBWEB(root, record)
    else
      COBWEB(best1, record)
    end if
  end

• "←" is a loose shorthand for "changes to". For instance, "largest ← item" means that the value of largest changes to the value of item.
• "return" terminates the algorithm and outputs the value that follows.

References

• Fisher, Douglas H. (July 1987). "Improving inference through conceptual clustering". Proceedings of the 1987 AAAI Conferences. AAAI Conference. Seattle Washington. pp. 461–465. 

• Fisher, Douglas H. (1987). "Knowledge acquisition via incremental conceptual clustering". Machine Learning 2 (2): 139–172. doi:10.1007/BF00114265. http://www.springerlink.com/content/qj16212n7537n6p3/fulltext.pdf.