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Cluster Algorithms

This document delves into clustering algorithms aimed at grouping similar board games based on their characteristics. It outlines various clustering types such as Exclusive, Overlapping, Hierarchical, and Probabilistic Clustering. Key algorithms discussed include K-means, Fuzzy C-means, and Hierarchical Clustering. Each algorithm's methodology is detailed, showcasing initial centroid selection, iterative grouping, and reassessment of cluster centers until optimal groupings are established. This paper serves as a foundational resource for understanding clustering's role in analyzing board game similarities.

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Cluster Algorithms

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  1. Cluster Algorithms Sep 12th 2006

  2. 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.

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

  4. 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.

  5. 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.

  6. Hierarchical Clustering Algorithms • With a defined N*N 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.

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

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