# GW-DC: A Deep Clustering Model Leveraging Two-Dimensional Image Transformation and Enhancement
## 3 Experiment and Results  
### Datasets and Evaluation Index  
To verify the performance of the proposed model, six time-series datasets shown in Table 1 were adopted from the UCR time-series website. The length of these datasets ranged from 150 to 15, and the classes of these datasets ranged from 2 to 6. The values of these datasets were normalized using Equation (11) for clustering analysis. The training and test sets of each dataset were provided directly by the UCR time-series website. The specific descriptions of the six datasets are shown in Table 1.  
To evaluate the clustering effect of the proposed GW-DC model, normalized mutual information (NMI) [30] and unsupervised clustering accuracy (ACC) were employed to  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Description** & **Train Size** & **Test Size** & **Length** & **Classes** \\ \hline BME & \begin{tabular}{c} Beef spectrograms, from pure beef and beef \\ adulterated with varying degrees of offal. \\ \end{tabular} & 30 & 150 & 128 & 3 \\ \hline CBF & \begin{tabular}{c} The data for each class is standard normal noise \\ plus different offset terms. \\ \end{tabular} & 30 & 900 & 128 & 3 \\ \hline SmoothSubspace & \begin{tabular}{c} Each time-series contains a continuous subspace \\ spanning 5 continuous timestamps, which is used \\ to test whether smooth subspace can be extracted. \\ \end{tabular} & 150 & 150 & 15 & 3 \\ \hline SonyAIBORobotSurface2 & \begin{tabular}{c} This dataset contains different accelerometers for \\ robot walking in cement or carpet/field. \\ \end{tabular} & 27 & 953 & 65 & 2 \\ \hline SyntheticControl & \
\begin{tabular}{c} Six different categories of control charts, including \\ normal, cyclic, increasing trend, decreasing trend, \\ upward shift, and downward shift. \\ \end{tabular} & 300 & 300 & 60 & 6 \\ \hline UMD &
\begin{tabular}{c} A synthetic dataset with three types: upper, lower, \\ and no bells arising at the initial or final cycle. \\ \end{tabular} & 36 & 144 & 150 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Description of datasets.  
Figure 9: The structure of the proposed DC.  
measure the clustering results. Hence, NMI was selected to measure the similarity in different data distributions, and its calculation formula is  
\[NMI(X;Y)=\frac{2I(X;Y)}{H(X)+H(Y)} \tag{16}\]  
where mutual information \(I(X;Y)\) represents the variation of the clustering information \(X\), given the class information \(Y\). \(H\) represents the entropy, and \(NMI(X;Y)\in[0,1]\). The greater the value of NMI, the greater the correlation between data and classes.  
The mutual information of clustering is  
\[I(X;Y)=\quad\sum_{k}\sum_{b}P(X_{k},Y_{b})\log\frac{P(X_{k},Y_{b})}{P(X_{k})P( Y_{b})} \tag{17}\]  
where \(P(X_{k},Y_{b})\) is the probability that the sample belongs to both class \(X_{k}\) and class \(Y_{b}\). \(P(X_{k})\) represents the probability that the sample belongs to the class \(X_{k}\), and \(P(Y_{b})\) is similar to \(P(X_{k})\). The greater the value of mutual information, the greater the degree of correlation between the data and the category.  
The calculation of ACC is  
\[ACC=\quad\max_{t}\frac{\sum_{i=1}^{n}1\Big{\{}y^{(i)}=t\Big{(}\hat{y}^{(i)} \Big{)}\Big{\}}}{n} \tag{18}\]  
where, \(y^{(i)}\) and \(\hat{y}^{(i)}\) represent the real label and the predicted label of sample \(i\) respectively. \(t\) denotes all possible one-to-one mappings between clusters and labels.