# Rough IPFCM Clustering Algorithm and Its Application on Smart Phones with Euclidean Distance
## 2 Proposed Rough Interval Possibilistic Fuzzy C-Means Clustering Algorithm with Euclidean Distance
The initial state for the proposed mobile RIPFCM approach is shown in Figure 16b, and the final results are shown in Figure 16c for **Case 4** with noise and outliers. ++

Finally, Table 1 shows the comparisons of RMSE under four cases with different approaches. The validity of the results for the proposed method were verified. From the simulation results, Tables 1 and 2 show that the proposed RIPFCM clustering algorithm has better performance than the IPFCM and IFCM clustering algorithm for the SID clustering with noise, outliers, and overlapping problems. At the same time, this also shows the expansion of smart phones' computing power and a possible future application in new symbolic data analysis. Hence, the proposed method was also implemented on a smart phone and extended the application of the smart phone in machine learning, fuzzy clustering, and non-single-valued data analysis. In order to establish the number of clusters to be used in each case, we used the IFCM clustering method for different numbers of clusters. Then, we used the most suitable results to test the proposed method in order to enhance the accuracy of the performance. ## 4 Conclusions

The new RIPFCM clustering algorithm with Euclidean distance is based on the integration of the rough set and the IPFCM clustering algorithm; it was applied to the analysis of SID as developed in this paper. The proposed new RIPFCM clustering algorithm not only can efficiently handle the overlapping partition problem but also shows better performance than the IPFCM clustering algorithm in the handing of noise problems for SID. In addition, we also combined the rough set to reduce the iteration number and increase the convergence of the IPFCM clustering algorithm. At the same time, the proposed new method also was implemented on a smart phone to address SID. This implementation showed the expansion of smart phones' computing power. Consequently, the proposed new method extended the application of smart phones in machine learning, fuzzy clustering, and non-single-valued data analysis and its future application in new SDA. Because the proposed method has more parameters, it has better accuracy performance with RMSE. However, its limitation is that it requires adjustment of the additional parameters, and thus the calculation speed of the proposed method will be slower. Conceptualization, S.-C.C. and J.-T.J.; data curation, C.-M.C. and C.-C.C. ; methodology, C.-M.C., S.-C.C. and J.-T.J.; software, C.-M.C. and S.-C.C. ; supervision, J.-T.J.; validation, C.-C.C. ; visualization, C.-M.C. and S.-C.C. ; writing--original draft, S.-C.C. and J.-T.J. All authors have read and agreed to the published version of the manuscript. This work was supported by the National Science Council Under Grant MOST 110-2221-E-150-040. The authors declare no conflict of interest. ## Abbreviations \begin{table}
\begin{tabular}{c c c c} \hline \hline
**RMSE** & **IFCM**[9] & **IPFCM**[13] & **Proposed Method** \\ \hline RMSE of Case 1a & 2.9519 & 1.4371 & 1.0590 \\ \hline RMSE of Case 1b & 4.0212 & 1.1363 & 0.7626 \\ \hline RMSE of Case 2a & 6.3297 & 4.7523 & 1.5127 \\ \hline RMSE of Case 2b & 10.2120 & 4.6490 & 1.1871 \\ \hline RMSE of Case 3a & 1.6043 & 1.3731 & 1.0983 \\ \hline RMSE of Case 3b & — & 1.0457 & 1.0457 \\ \hline RMSE of Case 4 & — & 1.8449 & 1.3827 \\ \hline \multicolumn{4}{l}{— means poor convergence.} \\ \end{tabular}
\end{table} 
Table 2: Comparison of RMSE under four cases with different approaches. ## References

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