Our first model involves two dimensional point data sets. The points will lie in the unit square.
There will be two point sets, corresponding to the ELSs of two key words.
Under the Null hypothesis, the points in each set are uniformly and independently distributed and
the points in one set are independent of the points in the second set.
The Alternative hypothesis states a dependence of the points in the first set with those
of the second set. The Alternative hypothesis states that the points of one set are moved closer
to that of the other set.
One model consistent with the Alternative hypothesis is a constructive probabilistic model.
We generate two random point sets, each having N points, each uniformly distributed in the unit square. Each
point from the second set has a closest point in the first set. The constructive probabilistic
model states that a given fraction f of the points from the second set are going to be moved
closer to their closest points in the first set. Those points chosen will be chosen at random and
their number will satisfy the given fraction f. The movement closer will be in the geodesic
direction. Suppose the distance between point p from the first set to point q of
the second set is d. The new position of the point q will be on its geodesic to point p
at a distance of kd, where k is a uniformly distributed variate on the interval
[0,ad] and where a is a specified fraction in the interval [0,1].
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