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DATA >AFFILIATIONS

PURPOSE Create a network from affiliation data.

DESCRIPTION Converts an m´n matrix to an m´m or n´n by forming AA'  or A'A using two different types of binary multiplication. Given a binary incidence matrix A where the rows represent actors and the columns events, then the matrix AA' gives the number of events in which actors simultaneously attended.  Hence AA' (i,j) is the number of events attended by both actor i and actor j.  The matrix A'A gives the number of events simultaneously attended by a pair of actors.  Hence A'A(i,j) is the number of actors who attended both event i and event j. If the data is valued there are two options. The cross product (or co-occurrence method) constructs the standard matrix product as in the binary case. The minimum method takes taking the minimum of the two values in the sums instead of the products. Hence if row i was (5,6,0,1) and row j was (4,2,4,0) then AA'(i,j) is 5*4+6*2+0*4+1*0=32 for the cross product and min(5,4)+min(6,2)+min(0,4)+min(1,0)=6 for the minimum method. These produce the same answers for binary data.
 
  The routine also allows for the final matrix to be normalized to accommodate the different sizes of the events. Consider two actors i and j and let X be the product of the number events they both attended and the number of events they both did not attend, let Y be the product of the number events i attended and j did not with the number of events j attended and i did not. If X=Y the normalized entry is 0.5 otherwise it is (X-SQRT(XY))/(X-Y).

PARAMETERS
Input dataset:
Name of file containing 2-mode dataset. Data type: Matrix

Which mode: (Default = Row).
Choices are:

Row 
Represents row by row matrix of overlaps, i.e. forms AA'

Column
Represents column by column matrix of overlaps, i.e. forms A'A.

Method:
Choices are:
 
Cross-Products (co-occurrence)
Uses standard matrix multiplication.

Minimums (for valued data)
Uses matrix multiplication in which the binary operation of multiplication is replaced by taking the minimum.

Normalization:
Selecting none gives the raw products. Bonacich '72 normalization gives the values as described in the description above. 

Output dataset: (Default = 'Affiliations').
Name of file which contains new matrix.


LOG FILE New matrix.

TIMING O(N^2).

COMMENTS None. 

REFERENCES Bonacich P. (1972) 'Techniques for analyzing overlapping memberships' Sociological Methodology 176-185 Jossey-Bass.