# A Review on Clustering Techniques: Creating Better User Experience for Online Roadshow
## 3 Discussion
### Evaluation Metrics
_SSE_ is not just a metric, but also an objective function that should be optimized when clustering is performed. _SSE_ is the sum of the squared differences between each observation and its mean. As the _SSE_ value decreases, the cluster validity is higher. The least commonly used evaluation metrics are _Silhouette index_ and _Dunn index_. The _Dunn index_ should be maximized to identify clusters that are well separated and compact. _Silhouette index_ computes a width for each point, depending on its membership in any cluster. Similar to the _Dunn index_, a higher _Silhouette index_ indicates an optimal quality of cluster. [PERSON] et al. [60] proposed a new cluster validity index called _Snew_. This new index is defined based on two essential measures, namely intra-cluster property and inter-cluster distance. The minimum value of _Snew_ shows an optimal clustering quality, as it has achieved a small intra-cluster distance and a big inter-cluster distance. This new cluster validity index is introduced since the existing metrics, such as _DB index_ and _Silhouette index_, lack the considerations of data size and distribution. Table 5 shows the evaluation metrics for external criteria. Note that the increase or decrease of the value in different evaluation metric indicates a better performance quality of the clustering technique. The clustering quality displays the performance value of the metrics within the range from 0 to 1 to achieve a good clustering quality. External criteria measure the quality of the clusters based on the ground truth in three ways. The first type is to perform clustering on the weblog and calculate the clustering quality with the actual \begin{table}
\begin{tabular}{c c c c} \hline
**Evaluation Metrics** & **Number of Applications** & **Range** & **Clustering Quality** \\ \hline Intra-cluster distance & 4 & 0 to \(+\infty\) & Distance \(\downarrow\) \\ \hline SSE & 4 & 0 to \(+\infty\) & SSE \(\downarrow\) \\ \hline DB index & 3 & \(-\infty\) to \(+\infty\) & Index \(\downarrow\) \\ \hline C index & 2 & 0 to 1 & Index \(\downarrow\) \\ \hline Inter-cluster distance & 2 & 0 to \(+\infty\) & Distance \(\uparrow\) \\ \hline Dunn index & 1 & 0 to \(+\infty\) & Index \(\uparrow\) \\ \hline Silhouette index & 1 & \(-1\) to \(+1\) & Index \(\uparrow\) \\ \hline (New) Snew & 1 & 0 to \(+\infty\) & Index \(\downarrow\) \\ \hline \end{tabular}
\end{table} 
Table 4: Evaluation metrics for internal criteria. \begin{table}
\begin{tabular}{c c} \hline
**Evaluation Metrics** & **Equations** \\ \hline Purity [78] & \(Purity=\frac{1}{N}\sum\limits_{i=1}^{k}|C_{i}|\frac{1}{|C_{i}|}N_{ij}\) \\  & where \(N\) is the number of points, \(j\) is the cluster label, \(C_{i}\) is a cluster. \\ \hline Entropy [78] & \(Entropy=-\sum\limits_{i=1}^{\zeta}\ P_{ij}\log P_{ij}\) \\  & where \(c\) is the number of clusters, \(P_{ij}\) is the probability of a point in the cluster \(i\) is being classified as class \(j\). \\ \hline R-measure [40] & \(R=\frac{Corage(R)}{|R|}\) \\  & where \(R\) is the points in the clusters. \\ \hline \end{tabular}
\end{table} 
Table 3: _Cont._class label by using any of the evaluation metrics [22; 29; 30; 34; 36; 39; 40; 41; 42; 48; 58; 61; 64; 71]. In the second type, the dataset is first split into training and testing datasets. Clustering will be performed on the training dataset. The testing dataset is used to evaluate the performance of the clustering process [24; 33]. For the third type, clustering is first performed. After that, the result of clustering is trained using a neural network to validate the clusters [7; 68; 69; 23].