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Explanation of the tests:
Two methods were used to optimize the Apollonius results:
1) In the first method (the "manual method") , we used all the circles and then one circle with giving closer results relative to Geo IP was considered to be Apollonius circle.
2) In second method (the "cluster method"), we tried to find out which cluster of circles and for this following approach was used:
1) three circles out of the n (<= 8) circles is closest together. This cluster was determined as follows:
- Let's suppose, we obtained n circles using apollonius. Now, we took each of these n circles and for each
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- circle we calculated the distance s j (where j = 1 .. n) _between it's center and the center of all other _n-1 circles and summed it.
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- We refer to this sum as Sum(
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- s i ). Then we took average of this value, i.e. avg j = Sum(s i ) / n j .
In this way we calculated the average distance value for each of circle and finally one circle with the smallest average value was considered as the Apollonius circle.
For results please see the attachments.
Conclusion:
The cluster based approach takes one circle as apollonius the AP circle and the final coordinates are calculated on the basis of this circle while in the other . The manual approach of using all the circles for calculating latitude and longitude, uses all the circles, so the cluster approach can theoretically (if the Geo IP result is correct) perform equal to the manual approach only in the best case scenario.
However, the main advantage of the cluster based approach is that it does not rely on an a-priori knowledge of the location of the target from Geo IP and instead uses a proper mathematical scheme to select the apollonius circle and doesn't solely rely on Geo IP results. On the other hand, the manual approach relies on the Geo IP results and takes Geo IP results as reference.circles.
In some cases, however, the cluster approach is performing better then than the manual approach which is negating . This appears to negate the fact that the manual approach choses chooses the circle with the minimum error distance. So how can this be? then can the how this could be minimum then 'minimum error distance circle' its because landmarks keep on changing due to which clusters keep on changing so minimum error distance circles keep on changing.
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