Cluster Algorithms

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Cluster Algorithms

• Sep 12th 2006

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Goal of Clustering

• To group similar board games.
• Hundreds of board games are compared and grouped
  into clusters such that they are close enough to
  be converted from one board game to another.

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Clustering Types

• Exclusive Clustering
• Eg K means
• Overlapping Clustering
• Eg Fuzzy C-means
• Hierarchical Clustering
• Eg Hierarchical clustering
• Probabilistic Clustering
• Eg Mixture of Gaussians

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K-means Clustering Algorithm

• The algorithm is composed of the following steps
• Start with K board games that are the amongst the
  board games that are being clustered. These board
  games represent the initial group centroids.
• Assign each board game to the group that has the
  closest centroid.
• When all objects have been assigned, recalculate
  the positions of the K centroids.
• Repeat Steps 2 and 3 until the centroids no
  longer move. This produces a separation of the
  objects into groups from which the metric to be
  minimized can be calculated.

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Fuzzy C-Means Clustering

• This algorithm is based upon iterative
  optimization of the objective function, with
  update of membership and cluster centers.
• This is based upon initial membership matrix for
  each item in a cluster.
• Center of clusters are calculated based upon the
  membership function.
• Once the centers are determined the membership
  matrix is updated
• When the difference between two sequential
  membership matrix is less than the initial
  termination criterion the algorithm is stopped.
  Otherwise step 2 and 3 are repeated.

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Hierarchical Clustering Algorithms

• With a defined NN distance matrix for N board
  games the following steps results into a
  hierarchical cluster
• Start by assigning each item to a cluster, so
  that if you have N items, you now have N
  clusters, each containing just one item.
• Now start merging closest pair of clusters so
  that the at merger we have one less cluster.
• Compute distances between the new cluster and
  each of the old clusters.
• Repeat steps 2 and 3 until all items are
  clustered into a single cluster of size N. ()
• Once the hierarchical tree is formed, it is
  possible to derive k clusters from this tree by
  cutting the k-1 longest link.

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Reference

• A Tutorial on Clustering Algorithms
• http//www.elet.polimi.it/upload/matteucc/Clusteri
  ng/tutorial_html/index.html
• Clustering Analysis
• http//www.statsoft.com/textbook/stcluan.html