# A Review on Clustering Techniques: Creating Better User Experience for Online Roadshow
## 3 Discussion
### Evaluation Metrics
\begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Metrics** & **Equations** \\ \hline DB index [72] & where \(n_{c}\) is the number of clusters, \(i\) and \(j\) are cluster labels, \(\text{diam}(c_{i})\) and \(\text{diam}(c_{j})\) are diameters of clusters, \(\text{d}(c_{i},c_{j})\) is the average distance between the clusters. \\ \hline C index [73] & where \(S\) is the sum of distances over all pairs of objects from the same cluster, \(S_{min}\) is the sum of the of the \(m\) smallest distances out of all pairs of objects, and \(S_{max}\) is the sum of the \(m\) largest distances out of all pairs of objects (let \(m\) be the number of pairs of objects). \\ \hline SSE [74] & where \(n\) is the number of clusters, \(c\) is the number of points, \(x_{i}\) is the data point, and \(\mu_{j}\) is the centroid cluster. \\ \hline V measure [75] & where \(h\) is the homogeneity, \(c\) is the completeness and \(\beta\) is a weight factor that can be adjusted. \\ \hline Dunn index [76] & \(DI=min_{i=1,\ldots,n}\bigg{\{}min_{j=i+1,\ldots,n}\bigg{\{}\frac{dis\big{(}c_{i },c_{j}\big{)}}{max_{w=1,\ldots,diam}\big{(}c_{n}\big{)}}\bigg{\}}\bigg{\}}\) \\  & where \(i\) and \(j\) are the cluster labels, \(k\) is the number of clusters, \(\text{d}iss\Big{(}c_{i},c_{j}\Big{)}\) is the dissimilarity value of cluster \(c_{i}\) and \(c_{j}\), and \(\text{d}iam(c_{m})\) is the diameter/intra-cluster distance of the cluster. \\ \hline Silhouette index [77] & where \(n\) is the total number of points, \(a_{i}\) is the average distance between point \(i\) and all the other points in its own cluster, and \(b_{i}\) is the average distance between point \(i\) and all the other points in other clusters. \\ \hline MAE/Error rate [68] & \(MAE=\frac{\sum_{i=1}^{n}\frac{|P_{i}-q_{i}|}{n}}{n}\) \\ MAE/Error rate [68] & where \(n\) is the total number of points, \(p_{i}\) is the actual cluster label and \(q_{i}\) is the predicted cluster label. \\ \hline Accuracy [78] & where \(\mathit{TP}\) is true positive, \(\mathit{TN}\) is true negative, \(\mathit{FP}\) is false positive, and \(\mathit{FN}\) is false negative. \\ \hline Rand index [74] & \(RI=\frac{\mathit{TP+TN}}{\mathit{TP+TN+TP+FN}}\) \\  & where \(\mathit{TP}\) is true positive, \(\mathit{TN}\) is true negative, \(\mathit{FP}\) is false positive, and \(\mathit{FN}\) is false negative. \\ \hline Jaccard index [78] & \(\mathit{JI}=\frac{\mathit{TP}}{\mathit{TP+FN}+FN}\) \\  & where \(\mathit{TP}\) is true positive, \(\mathit{FP}\) is false positive, and \(\mathit{FN}\) is false negative. \\ \hline Recall [74] & \(Recall=\frac{\mathit{TP}}{\mathit{TP+FN}}\) \\  & where \(\mathit{TP}\) is true positive, and \(\mathit{FN}\) is false negative. \\ \hline Precision [74] & \(Precision=\frac{\mathit{TP}}{\mathit{TP+FP}}\) \\  & where \(\mathit{TP}\) is true positive, and \(\mathit{FP}\) is false positive. \\ \hline F-measure [78] & \(\mathit{Fmeasure}=\frac{(\beta^{2}+1)\times\mathit{P}\times\mathit{R}}{\beta \times\mathit{P}+\mathit{R}}\) \\  & where \(\beta^{2}\) is a weight factor that can be adjusted, \(\mathit{P}\) is the precision value, and \(\mathit{R}\) is the recall value. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation metrics and equations. Based on Table 4, the commonly used internal criteria are _inter-cluster distance_, _intra-cluster distance_, _DB index_, _C index_, and _Sum of Square Error_ (SSE). The _inter-cluster distance_ and _intra-cluster distance_ are usually calculated after the final clustering iteration to determine the cluster validity. If the _inter-cluster distance_ is low and the _intra-cluster distance_ is high, this shows that the clusters are formed well. [PERSON] et al. [63; 67] evaluated the performance of the clusters by calculating the mean and standard deviation of the _intra-cluster distance_ and _inter-cluster distance_ of each distance measure. For _DB index_ and _C index_, a smaller value signifies better clustering quality. _DB index_ and _C index_ attempt to minimize the average of _intra-cluster distance_.