today we look at a few more alternatives to the submatrix of 1 problem discussed earlier.
one such method is to facilitate merge along vertical and horizontal axis in a way such that contiguous regions of 1s are identified, sized and top left corner identified. then we split the original matrix into 2 power x sub matrices by repeatedly dividing both x and y axis. This works well for cohesive matrices where the 1s are all together as islands. Since each point is counted only once during the merge before being assigned to a group and the results aggregated, this is more efficient than the nested evaluation of each point as a candidate for top left corner. Moreover we keep track of the top left and bottom right corners of each candidate submatrix from the adjoining contiguous overlaps during each merge. each overlap along a merge front determines the span of the submatrix
today we review a new topic called social balance theory from the chapter on network measures. this theory is about friends and enemies relationships abd i had never really paid attention to it so far. it states:
The friend of my friend is my friend, The friend of my enemy is my enemy, The enemy of my enemy is my friend, The enemy of my friend is my enemy.
All this theory states is that the friends or enemy relationships are consistent when the above is followed.
we can represent these relationships in a graph. The friendhip is denoted by positive edges, the enemity by negative edges and a triangle between participants denotes imbalance if the weights around the edges of the triangle taken together is less than zero. this kind of metric can also be explored for graphs that are not triangular in general.
one such method is to facilitate merge along vertical and horizontal axis in a way such that contiguous regions of 1s are identified, sized and top left corner identified. then we split the original matrix into 2 power x sub matrices by repeatedly dividing both x and y axis. This works well for cohesive matrices where the 1s are all together as islands. Since each point is counted only once during the merge before being assigned to a group and the results aggregated, this is more efficient than the nested evaluation of each point as a candidate for top left corner. Moreover we keep track of the top left and bottom right corners of each candidate submatrix from the adjoining contiguous overlaps during each merge. each overlap along a merge front determines the span of the submatrix
today we review a new topic called social balance theory from the chapter on network measures. this theory is about friends and enemies relationships abd i had never really paid attention to it so far. it states:
The friend of my friend is my friend, The friend of my enemy is my enemy, The enemy of my enemy is my friend, The enemy of my friend is my enemy.
All this theory states is that the friends or enemy relationships are consistent when the above is followed.
we can represent these relationships in a graph. The friendhip is denoted by positive edges, the enemity by negative edges and a triangle between participants denotes imbalance if the weights around the edges of the triangle taken together is less than zero. this kind of metric can also be explored for graphs that are not triangular in general.
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