# A Review on Clustering Techniques: Creating Better User Experience for Online Roadshow
## 3 Discussion
### Similarity Measure  
Similarity measure refers to a function that measures the similarity between two data points. A similarity measure is used to cluster similar data points into the same clusters, while dissimilar data points are placed into different clusters. Choosing a suitable and accurate similarity measure is subjective in clustering. There are many similarity measures that are used by different researchers. The usage frequency of similarity measure among the four categories of clustering techniques is displayed in Table 2.  
_Euclidian distance_ is shown with a frequency of 16, as the most commonly applied similarity measure in web usage mining. _Euclidean distance_ is used widely because it is calculated based on the Cartesian coordinates and well understood by many. However, _Euclidean distance_ has the drawback of significantly amplifying the effect of outliers by squaring the distances. The second most commonly used similarity measure is _cosine similarity_. [PERSON] et al. [28] claimed that the _cosine similarity_ is more suitable than the _Euclidean distance_ because the _Euclidean distance_ might intercept the magnitude of data points to be equal distance for all the dimensions. On contrary, _cosine similarity_ works better in high-dimensional data [66]. When the data points of the weblog are plotted on a multi-dimensional space, the _cosine similarity_ can capture the angle of the data points rather than their magnitude. Some other similarity measures that are not frequently used in web usage mining are _Manhattan distance_, _Hamming distance_, _Jaccard similarity_, and _fuzzy similarity_. Instead of squaring the distances as in _Euclidean distance_, _Manhattan distance_ is the sum of absolute differences between the data points across all dimensions. It is not frequently used as it is sensitive to outliers. _Hamming distance_ is commonly used as the similarity measure only when it needs to be applied in information theory to detect and correct errors in \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Clustering Technique** & **Similarity Measure** & **Evaluation Metric** & **Functional Purpose** \\ \hline Improved & & & Precision [39; 40], & \\ _CHAMELEON_ & - & Recall [39; 40], & Page categorization [39], & Web personalization [40]. \\  & & & F-measure [40], & \\ \hline Bisecting _k-means_ & Cosine similarity [66]. & Accuracy [41; 42], & User group discovery [41], & \\  & & Classified AP (CAP) \({}^{\star}\)[66]. & Web queries categorization [66], & Intrusion detection [42]. \\ \hline _DBSCAN_ & Euclidean distance [45] & DB index [45], C index [31]. & User group discovery [44; 45]. \\ \hline Improved _DBSCAN_ & SSM \({}^{\star}\)[67]. & & V-measure [49], & \\  & & Intra-cluster distance [49], & User group discovery [49; 67], & \\  & & Accuracy [47; 48], & Page categorization [48], & \\  & & Recall [47], F-measure [47], & Web personalization [47]. & \\ \hline  & & & Error rate [68; 69], & User group categorization [52], \\  & & Accuracy [54; 61; 68; 70], & Page recommendation [53; 70], & \\  & & SSE [55], MAE [70], & Web personalization [68]. & \\ FCM & Euclidean distance [52; 53; 61; 68], & Inter-cluster distance [53], & User group discovery [54; 55; 69], & \\  & Manhattan distance [53]. & Intra-cluster distance [53], & Improvement of PageRank & \\  & & Recall [68], & algorithm \({}^{\star}\)[61], & Improvement of Kohonen \\  & & F-measure [68], \(\mathbf{S}_{\text{new}}\)\({}^{\star}\)[60]. & & clustering \({}^{\star}\)[60]. \\ \hline  & & Rand index [59], SSE [59], & \\  & & Error rate [57], & & \\ Improved _FCM_ & Euclidean distance [57], & Precision [58], & User group discovery [56; 57; 59], & Web queries categorization [58]. \\  & & Cosine similarity [58]. & & \\  & & F-measure [58], & & \\  & & Accuracy [58]. & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._bits. [PERSON] et al. [30] compared the usage of _Cosine similarity_ and _Hamming similarity_ as the distance measure in _k-medoids_ clustering.