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**NETWORK>2****-MODE NETWORKS >2-MODE FACTIONS**

**PURPOSE **Uses a genetic algorithm to simultaneously cluster rows and columns of a 2-mode matrix.

**DESCRIPTION **Clusters rows and columns of a 2-mode matrix X by finding a pair of corresponding 2-class partitions such that if row i and column j are in corresponding classes, then we expect xij to be a large value. In contrast, if i and j are not in corresponding classes, then we expect xij to be small. The fit is simply the correlation between the data matrix and an idealized structure matrix in which there are large values within classes and small values between classes.

**PARAMETERS**

**Input dataset:**

** **Name of file containing two-mode network to be analyzed. Data type: Matrix.

**Row Partition: **(Default = 'rowfactionspart')

Name of output file which contains a cluster indicator vector for the row partition. This vector has the form (k1,k2,...ki...) where ki assigns vertex i to cluster ki and ki is either 1 or 2. This vector is not displayed at output.

** Column Partition: **(Default = 'colfactionspart')

Name of output file which contains a cluster indicator vector for the column partition. This vector has the form (k1,k2,...ki...) where ki assigns vertex i to cluster ki and ki is either 1 or 2. This vector is not displayed at output.

**LOG FILE **The starting and the final correlation of the ideal structure and the permuted incidence matrix . A blocked incidence matrix dividing the rows and columns independently into two clusters each.

**TIMING **O(N^2) per iteration. ** **

**COMMENTS** Care should be taken when using this routine.

The algorithm seeks to find the maxima of the cost function. Even if successful this result may still be a low value in which case the partition may not have found cohesive clusters.

In addition there may be a number of alternative partitions which also produce the maximum value; the algorithm does not search for additional solutions. Finally it is possible that the routine terminates at a local maxima and does not locate the desired global maxima.

To test the robustness of the solution the algorithm should be run a number of times from different starting configurations. If there is good agreement between these results then this is a sign that there is a clear split of the data into subgroups.

** **See Factions.

**REFERENCES **Borgatti SP and Everett M G (1997) Network analysis of 2-mode data. Social Networks 19 243-269.