## 4 Tt-Vfd-Sim
### TT-VFDL-SIM for Classification
We organized representative detailed domains or sensor types, tasks, and data characteristics in the IoT field through existing studies related to multivariate IoT time-series analysis and all IoT time-series datasets in [36; 37]. And the representative datasets in Table 5 that can cover all of them as much as possible are selected. Four streams were selected from each of the original data sources [38; 39; 40], and regression datasets of AIRQUAL, HOMENV, and GASVOLT were constructed by sliding windowing the selected streams into a window of the size described in the Pattern Length column in Table 5. For the two classification datasets, ACCHAR and TRAFFIC, we selected three streams to be used as inputs from the original data sources [41; 42] and constructed patterns of the size specified in the Pattern Length column of Table 5.

We performed necessary preprocessing such as scaling, interpolation, and noise removal for each dataset in Table 5. In particular, each training dataset of ACCHAR and TRAFFIC for the classification target task was reorganized to have equal class distribution. The reason for reorganizing the training datasets of ACCHAR and TRAFFIC into a balanced dataset is to exclude as much as possible the data-driven characteristics that may affect the performance of the target task in addition to the mechanism of each VFDL method. As a result, it was confirmed that precision, recall, sensitivity, specificity, and accuracy had similar distributions of values in all experiments on the classification target task. #### 5.1.2 Target Tasks

We constructed a multivariate target task for the experiment from each dataset in Table 5. AIRQUAL is a dataset that measures the concentration of air pollutants [38]. Based on this, a regression target task was created to predict the concentration of benzene from changes in the concentrations of non-methane hydrocarbon, carbon monoxide, and ozone. HOMENV is a dataset that measures changes in the indoor environment of a home and changes in external weather [39]. We created a regression target task to predict the temperature of the laundry room based on the temperature change in the parents' room and kitchen located on different floors and the external temperature change. GASVOLT is a dataset that monitors the state of a gas chamber [40]. We constructed a regression target task to predict the heater voltage of a gas chamber from three streams of gas concentration changes measured from two different gas sensors. ACCHAR is a human activity recognition (HAR) dataset that classifies four movements including epileptic seizures [41]. The inputs to this classification target task are each X, Y, and Z streams of a 3-axis accelerometer, and the output is an encoded label stream for the four motion classes. TRAFFIC was constructed from the traffic volume dataset [42] measured by loop sensors installed on each road in California. The classification target task predicts encoded labels for 7 days of the week from Monday to Sunday using 3 traffic streams randomly selected in [42] as input. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Task**} & \multirow{2}{*}{**FE**} & \multicolumn{2}{c}{**Pattern Length**} & \multirow{2}{*}{**Train**} & \multirow{2}{*}{**Validation**} & \multirow{2}{*}{**Test**} \\  & & & **Structure** & & **Input** & **Feature** & **Output** & **Size** & **Size** \\ \hline AIRQUAL & Regression & CNN-LSTM & 24 & & 1 & 504 & 72 & 144 \\ \hline HOMENV & Regression & LSTM & 72 & & 1 & 504 & 72 & 144 \\ \hline GASVOLT & Regression & CNN-LSTM & 70 & & 1 & 490 & 70 & 140 \\ \hline ACCHAR & Classification & CNN & 204 & & 4 & 168 & 24 & 83 \\ \hline TRAFFIC & Classification & CNN-LSTM & 144 & & 7 & 294 & 28 & 118 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Datasets used in the experiments. #### 5.1.3 Target Task Models

We constructed three types of multivariate deep learning models as shown in Figure 1 for the target tasks derived from each dataset and used them as target task models for experiments.