# Semi-Supervised Manifold Alignment Using Parallel Deep Autoencoders
## 5 Experiments and Results
### Cross-Modality Manifold Alignment  
The following pilot case study was included to demonstrate the cross-modality ability of the asymmetric PDAE concept. The 2D-2D kinematics dataset of double pendulum motion as described in Section 5.2.1 was used as dataset \(X\) and image frames of a simulated video of the same motion were used as dataset \(Y\). Dataset \(X\) had 1296 instances, where each instance was a six-dimensional feature vector. Dataset \(Y\) had the same number of instances where each instance was an image with \(128\times 128\) pixels. The datasets were generated and ordered so that each instance \(X_{i}\) of \(X\) had a corresponding instance \(Y_{i}\) in \(Y\) obtained from the same joint angles. In the asymmetric PDAE, the structure of the fully-connected autoencoder was similar to the autoencoder used to align the 2-manifolds described in Section 5.2.2. The structure of the Convolutional Autoencoder (CAE) is given in Table 5. The asymmetric PDAE was trained for 10,000 epochs using the Adam optimiser with a learning rate of 0.0001. Manifold alignment experiments using the asymmetric PDAE were conducted in four different ways, each using a differently-sized correspondence subset for the calculation of \(E_{corr}\). The sizes of the correspondence subsets in the four experiments were 10%, 30%, 50% and 100% of the total number of instances. The results using the four different correspondence subsets are shown in Figure 8. The figures show that the more correspondence pairs were used, the better the alignment could be performed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Noise**} & **MAPA** & **MALG** & **MAGG** & **PDAE** \\ \cline{2-5}  & **feat** & **feat** & **feat** & \\ \hline
0 & 0.106 (0.060) & **0.019 (0.011)** & 0.045 (0.012) & 0.037 (0.020) \\ \hline \multicolumn{5}{c}{Actuator noise} \\ \hline \(\pm 2^{\circ}\) & 0.115 (0.067) & **0.025 (0.011)** & 0.048 (0.015) & 0.029 (0.20) \\ \(\pm 4^{\circ}\) & 0.124 (0.072) & 0.042 (0.021) & 0.058 (0.022) & **0.039 (0.019)** \\ \(\pm 6^{\circ}\) & 0.141 (0.077) & 0.051 (0.025) & 0.075 (0.032) & **0.042 (0.013)** \\ \(\pm 8^{\circ}\) & 0.233 (0.118) & 0.058 (0.033) & 0.082 (0.036) & **0.050 (0.037)** \\ \(\pm 10^{\circ}\) & 0.359 (0.225) & 0.066 (0.030) & 0.090 (0.041) & **0.054 (0.016)** \\ \hline \multicolumn{5}{c}{Coordinate noise} \\ \hline \(\pm 0.2\) & 0.135 (0.078) & 0.032 (0.015) & 0.071 (0.012) & **0.023 (0.012)** \\ \(\pm 0.4\) & 0.151 (0.083) & 0.048 (0.028) & 0.113 (0.042) & **0.024 (0.013)** \\ \(\pm 0.6\) & 0.170 (0.094) & 0.057 (0.033) & 0.158 (0.058) & **0.022 (0.011)** \\ \(\pm 0.8\) & 0.213 (0.121) & 0.072 (0.041) & 0.194 (0.069) & **0.070 (0.033)** \\ \(\pm 1\) & 0.227 (0.122) & 0.083 (0.047) & 0.225 (0.079) & **0.069 (0.033)** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: 3D-3D manifold alignment: Shown is the alignment error \(\Delta\) with the standard deviation for each level of the noise. The lowest \(\Delta\) or closest alignment of each row is highlighted in bold. Figure 8: The figures show cross-modality manifold alignment using the asymmetric PDAE using four versions of the data with different percentages of correspondence pairs (\(10\%,30\%,50\%,100\%\)). The corresponding quantitative alignment errors \(\Delta\) and associated standard deviations \(\sigma\) in parentheses are displayed in the subcaptions next to the correspondence percentage numbers.