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Modern Geomatics Technologies and Applications

3.3 Stability of cluster centres
Given the random nature of clustering methods, the question is: to what extent the clustering results are stable. To
investigate this, each of the clustering algorithms was run 4 times and its accuracy was calculated at each run. Table 3 and 4
show the stability of the clustering methods to cover 90% and 60% of the results of the test. In this Table, the stability value
represents the difference between the minimum and maximum RMSE values calculated for each clustering method in 9 and
25 cluster modes. To obtain these figures, the clustering techniques were run three times to see if their results change over
different runs or not. In this experiment, K=9 was considered, as it gives results more similar to those obtained in empirical
methods. Also, RMSE1, RMSE2 and RMSE3 show the accuracy of the techniques in each run.
As can be seen, the RMSE value shown for the clustering algorithms Average linkage, Complete linkage, Single linkage,
SOM, Dbscan, Mean shift, Gclust, and Optics are all equal to zero. This means that these methods have a high degree of
stability, i.e. at each execution of the program has achieved exactly the same results. In contrast, the stability figure for other
methods is not zero. Among the remaining methods, the K-Means and FCM methods are more stable. It should be noted that
zero stability does not necessarily mean that the clustering algorithm is better than the other techniques. For example, even
though Single Linkage or Dbscan methods have high stability, their accuracy is lower compared to the other methods.
Meanwhile, the Average Linkage, SOM, and FCM methods, in addition to having high stability, have good accuracy too. An
example of the instability of the genetic algorithm is shown in Fig. 13. Generally, the Average Linkage, FCM, and SOM
methods provide the best results from all points of view, i.e. accuracy, stability, and distribution.

4. Conclusion
In this paper, the effectiveness of various clustering techniques in selecting optimum locations for control points was
evaluated. The tests were carried out in an area of 400m-by-400m with 72 control points and 9 check points, all measured
using an accurate GPS. Then the area was imaged using a DJI Phantom 4 Pro. Using the clustering techniques, the area was
divided into 5, 9, and 25 sections. Then using control points closest to the section centres the accuracy of the photogrammetric
model was evaluated. The results showed that the Average Link, SOM and FCM perform better than the other clustering
techniques, from the consistency and accuracy points of view. It is interesting to note that points selected using these three
techniques give accuracies even better than those obtained using empirical grid-based methods.

5. References

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photogrammetric block. Int. Archives of the Photogrammetry, Remote Sensing and Spatial

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[6] Gindraux, S., Boesch, R., & Farinotti, D., 2017. Accuracy assessment of digital surface models from unmanned aerial
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