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TRANSFORM > BLOCK

PURPOSE Partition nodes in a data graph into blocks and calculate block densities, sums or other statistics.

DESCRIPTION The adjacency matrix is partitioned into submatrices. The average, sum, maximum, minimum, standard deviation, or sum of squares of each submatrix is then calculated. 
This routine is virtually identical to the Networks>Properties>Density routine, except that it provides more options for aggregating cells within a matrix block.


PARAMETERS
Input dataset:
Name of file containing matrices to be blocked. Data type: Matrix.

Method: (Default = Average)
Choices are

Average -Arithmetic mean of all cells in each submatrix.
Sum -Simple sum of all cells in each submatrix.
Maximum -Largest value of all cells in each submatrix.
Minimum -Smallest value of all cells in each submatrix.
Std Dev -Standard deviation of all cells in each submatrix.
SSQ -Sum of squares of all cells in each submatrix.

Utilize Diagonal values (Default = No)
Whether diagonals are to be included in density calculations.

Row partition/blocking (if any): 
To partition the rows of the data matrix into blocks, specify a blocking vector by giving the dataset name, a dimension and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to sort the rows of the matrix. All rows with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same block of the matrix.  Densities will then be computed separately for each block. The block partitions can also be typed directly into the box by typing in a partition indicator vector. A partition indicator vector has the form (k1,k2,...,ki...) where ki assigns vertex i to group ki.  So that (1 1 2 1 2) assigns vertices 1, 2 and 4 to block 1;  and 3 and 5 to block 2.
  
Column partition/blocking (if any): 
To partition the columns of the data matrix into blocks, specify a blocking vector by giving the dataset name, a dimension and an integer value. For example, to use the second row of a dataset called ATTRIB, enter "ATTRIB ROW 2". The program will then read the second row of ATTRIB and use that information to sort the columns of the data matrix. All columns with identical values on the criterion vector (i.e. the second row of attrib) will be placed in the same block of the matrix.  Densities will then be computed separately for each block.The block partitions can also be typed directly into the box by typing in a partition indicator vector. A partition indicator vector has the form (k1,k2,...,ki...) where ki assigns vertex i to group ki.  So that (1 1 2 1 2) assigns vertices 1, 2 and 4 to block 1;  and 3 and 5 to block 2.


(Output) Reduced image dataset (Default = 'Blocked')
Name of dataset that will contain the reduced block density matrix.
   
(Output) Pre-image dataset (Default= 'PreImage')
Name of dataset that will contain the original data with the rows and columns permuted to form the blocks.

LOG FILE List of block numbers together with their members. The pre-image matrix ie the permuted original data matrix. Blocked matrices. A blank in the matrix indicates that a matrix value (such as the average), was undefined.

TIMING O(N^2)

COMMENTS Users who wish to produce a binary image matrix from the output of this routine can obtain one by using Transform>Dichotomize.

REFERENCES None.