# Boundary Matching and Interior Connectivity-Based Cluster Validity Analysis
## 3 Materials and Methods
### Clustering Evaluation Based on Boundary and Interior Points
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset and** & \multicolumn{2}{c}{**DB**} & \multicolumn{2}{c}{**DC**} & \multicolumn{2}{c}{**GS**} & \multicolumn{2}{c}{**CVIBI**} \\ \cline{2-9}
**Algorithm** & **DPC** & **C-Means** & **DPC** & **C-Means** & **DPC** & **C-Means** & **DPC** & **C-Means** \\ \hline _Set_ 1 & 4 & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) \\ _Set_ 2 & 2 & 3 & 7\(\surd\) & 3 & 7\(\surd\) & 5\(\surd\) & 7\(\surd\) & 5\(\surd\) \\ _Set_ 3 & 2 & 4 & 5\(\surd\) & 4 & 5\(\surd\) & 5\(\surd\) & 5\(\surd\) & 5\(\surd\) \\ _Set_ 4 & 2 & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) & 3\(\surd\) & 5\(\surd\) \\ _Set_ 5 & 4\(\surd\) & 5\(\surd\) & 4\(\surd\) & 5\(\surd\) & 4\(\surd\) & 5\(\surd\) & 4\(\surd\) & 5\(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation of clustering results by CVIBI, DB, DC and GS for 15 datasets. Figure 16: Tests of CVIBI on CT images with DPC. Q.L. and M.D.M. ; writing--original draft preparation, Q.L. ; writing--review and editing, M.D. and J.L. ; visualization, Y.W. ; supervision, S.Y. ; project administration, S.Y. ; funding acquisition, S.Y. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 61573251 and 61973232. The authors declare no conflict of interest. ## References

* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Measurement data classification optimization based on a novel evolutionary kernel clustering algorithm for multi-target tracking. _IEEE Sens. J._**2018**, _18_, 3722-3733. [CrossRef]
* [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] Energy efficient clustering algorithm for multi-hop wireless sensor network using type-2 fuzzy logic. _IEEE Sens. J._**2017**, _17_, 4492-4499. [CrossRef]
* [PERSON] and [PERSON] (2019) [PERSON]; [PERSON] [PERSON] A new image segmentation method using clustering and region merging techniques. In _Applications of Artificial Intelligence Techniques in Engineering_; Springer: Singapore, 2019; pp. 603-614. * [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] I-nice: A new approach for identifying the number of clusters and initial cluster centres. _Inf. Sci._**2018**, _466_, 129-151. [CrossRef]
* [PERSON] and [PERSON] (2008) [PERSON]; [PERSON] A cluster validity measure with a hybrid parameter search method for the support vector clustering algorithm. _Pattern Recognit._**2008**, _41_, 506-520. [CrossRef]
* [PERSON] and [PERSON] (1979) [PERSON]; [PERSON] A cluster separation measure. _IEEE Trans. Pattern Anal. Mach. Intell._**1979**, 224-227. [CrossRef]
* [PERSON] et al. (2001) [PERSON]; [PERSON]; [PERSON] Estimating the number of clusters in a data set via the gap statistic. _J. R. Stat. Soc. Ser. B (Stat. Methodol. )_**2001**, _63_, 411-423. [CrossRef]
* [PERSON] and [PERSON] (1991) [PERSON]; [PERSON] A validity measure for fuzzy clustering. _IEEE Trans. Pattern Anal. Mach. Intell._**1991**, _13_, 841-847. [CrossRef]
* [PERSON] et al. (2016) [PERSON]; [PERSON]; [PERSON] Improved bayesian information criterion for mixture model selection. _Pattern Recognit. Lett._**2016**, _69_, 22-27. [CrossRef]
* [PERSON] and [PERSON] (1998) [PERSON]; [PERSON] Detecting features in spatial point processes with clutter via model-based clustering. _J. Am. Stat. Assoc._**1998**, _93_, 294-302. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON] Bayesian cluster enumeration criterion for unsupervised learning. _IEEE Trans. Signal Process._**2018**, _66_, 5392-5406. [CrossRef]
* [PERSON] et al. (2013) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON] An extensive comparative study of cluster validity indices. _Pattern Recognit._**2013**, _46_, 243-256. [CrossRef]
* [PERSON] et al. (2019) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] An unsupervised and robust validity index for clustering analysis. _Soft Comput._**2019**, _23_, 10303-10319.