## 4 Tt-Vfd-Sim
### TT-VFDL-SIM for Classification
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **FM** \\ **Structure** \\ \end{tabular} } & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{\begin{tabular}{c} **Compression** \\ **Ratio** \\ \end{tabular} } & \multicolumn{3}{c}{**SIM Partial Training (DD) \({}^{*}\)**} & \multicolumn{3}{c}{**Merging Task Training**} & \multicolumn{1}{c}{\begin{tabular}{c} **Best** \\ **Learning** \\ **Rate** \\ \end{tabular} } \\ \cline{3-8}  & & & **MSE** & \(R^{2}\) & **MSE** & \(R^{2}\) & \begin{tabular}{c} **Rest** \\ **Learning** \\ **Rate** \\ \end{tabular} & \begin{tabular}{c} **Optim** \\ **Rate** \\ \end{tabular} \\ \hline \multirow{8}{*}{\begin{tabular}{c} **MFCMLFM** \\ \end{tabular} } & \multirow{2}{*}{AIRQUAL} & **1.20** & **0.00525** & **0.63** & **0.00382** & **0.74** & **0.01** & **DD(D)** \\ \cline{3-8}  & & 2.00 & 0.00730 & 0.50 & **0.00407** & **0.72** & **0.001** & **DD(D)** \\ \cline{3-8}  & & 3.00 & 0.00780 & 0.46 & **0.00404** & **0.73** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & **1.20** & **0.00269** & \(\mathbf{-0.29}\) & **0.00104** & **0.49** & **0.0005** & **DD(R)** \\ \cline{3-8}  & \multirow{2}{*}{HOMENV} & **2.00** & **0.00274** & \(-0.42\) & **0.00161** & **0.21** & **0.01** & **DD(R)** \\ \cline{3-8}  & & 3.00 & 0.00233 & \(-0.23\) & **0.00172** & **0.16** & **0.001** & **DD(D)-Test(R)** \\ \cline{3-8}  & & **1.25** & **0.00620** & **0.57** & **0.00328** & **0.98** & **0.01** & **DD(D)-Test(R)** \\ \cline{3-8}  & & 1.67 & 0.00439 & 0.98 & **0.00390** & **0.98** & **0.01** & **DD(D)** \\ \cline{3-8}  & & 5.00 & 0.00610 & 0.97 & **0.00403** & **0.98** & **0.0005** & **DD(D)** \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} **MLFM** \\ \end{tabular} } & \multirow{2}{*}{AIRQUAL} & **1.20** & **0.00969** & **0.33** & **0.00357** & **0.76** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & 2.00 & 0.00726 & 0.51 & **0.00379** & **0.74** & **0.0005** & **DD(D)-Test(R)** \\ \cline{3-8}  & & 3.00 & 0.00753 & 0.47 & **0.00394** & **0.73** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & **1.20** & **0.00261** & \(\mathbf{-0.27}\) & **0.00100** & **0.51** & **0.01** & **DD(D)-Test(R)** \\ \cline{3-8}  & & 2.00 & 0.00306 & \(-0.57\) & **0.00104** & **0.49** & **0.01** & **DD(D)-Test(R)** \\ \cline{3-8}  & & 3.00 & 0.00246 & \(-0.30\) & **0.00117** & **0.42** & **0.01** & **DD(D)-Test(R)** \\ \cline{3-8}  & & **1.25** & **0.00643** & **0.96** & **0.00398** & **0.98** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & 1.67 & 0.00488 & 0.97 & **0.00402** & **0.98** & **0.01** & **DD(R)** \\ \cline{3-8}  & & 5.00 & 0.00673 & 0.96 & **0.00426** & **0.98** & **0.0005** & **DD(D)** \\ \hline \multirow{8}{*}{
\begin{tabular}{c} **SLFM** \\ \end{tabular} } & \multirow{2}{*}{AIRQUAL} & **1.20** & **0.00780** & **0.46** & **0.00353** & **0.76** & **0.001** & **DD(R)** \\ \cline{3-8}  & & 2.00 & 0.00829 & 0.44 & **0.00367** & **0.75** & **0.001** & **DD(R)** \\ \cline{3-8}  & & 3.00 & 0.00530 & 0.61 & **0.00367** & **0.75** & **0.005** & **DD(R)** \\ \cline{3-8}  & & **1.20** & **0.00255** & \(\mathbf{-0.22}\) & **0.00119** & **0.42** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & 2.00 & 0.00242 & \(-0.26\) & **0.00154** & **0.24** & **0.001** & **DD(R)** \\ \cline{3-8}  & & 3.00 & 0.00271 & \(-0.40\) & **0.00150** & **0.27** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & **1.25** & **0.00509** & **0.97** & **0.00353** & **0.98** & **0.0005** & **DD(R)** \\ \cline{3-8}  & & 1.67 & 0.00561 & 0.97 & **0.00433** & **0.97** & **0.01** & **DD(R)** \\ \cline{3-8}  & & 5.00 & 0.00803 & 0.95 & **0.00460** & **0.97** & **0.01** & **DD(R)** \\ \hline \hline \end{tabular}

* \({}^{*}\)MSE and \(R^{2}\) values of the SIM Partial Training are the averaged values of all guest parties which are participating in the TT-VFDL-SIM (for regression).

\end{table} 
Table 12: Performance of the TT-VFDL-SIM with method option as DD (for regression) under various conditions. option DD was almost always higher than RD.