PST (International Patent)

PST – Pick and Squash Tracking  (International Patent)

PST is an evolutionary algorithm for multi dimensional scaling:

given N points and their distances in a K dimensional space, find the distribution of these points in a P dimensional space with P<<K, so that we minimize the “difference” between the original distances and those in the projected space.

This algorithm is also able to estimate the position of a “hidden point” in the space P in order to decrease the difference between the matrices of distances of the space K and P:

After that the PST algorithm has reached up its local maximum, we can try to reduce further the Error, adding a Hidden Unit of L-dimension: moving into the L-dimension space the position of this Hidden Unit, the Pst can still try to minimize further the Error Function. At this point, the Pst algorithm has to create another evolutionary algorithm, working in parallel to the first one, to move the Hidden Unit into the L-dimensional space and to decide which couples of points have to pass trough it to be connected.

Patent

[1] Pick & Squash Tracking An Algorithm for projecting information data belonging to a multidimensional space into a space having less dimensions a method for the cognitive analysis of multidimensional information data based on the said algorithm and a program comprising the said algorithm stored on a recordable support. Applicant Semeion Research Centre Inventor P.M.Buscema. International Patent: Application n. PCT/EP2004/051190 deposited 06-22-2004. USA Patent US 7,792,869 B2 Sep. 7, 2010.

References

[1] P.M. Buscema, E. Grossi, M. Breda, T. Jefferson
“Outbreaks source: A new mathematical approach to identify their possible location”
in Physica A 388 (2009), 47364762.

[2] P.M. Buscema, S. Terzi
A new Evolutionary Approach to topographic mapping
Proceedings of the 7th WSEAS International Conference on Evolutionary Computing Cavtat, Croatia, June 12-14, 2006, pp. 12-19.

[3] P.M.Buscema, S.Terzi
“PST : An Evolutionary Approach to the Problem of Multi Dimensional Scaling”
In WSEAS Transactions on information science and applications, Issue 9, Volume 3, Sept 2006, pp. 1704-1710.