# Unsupervised Cyclic Siamese Networks Automating Cell Imagery Analysis
## 3 Methodology
### Architecture and Learning Scheme
#### 3.3.2 Learning Scheme
Examples of translated images and a pipeline of their generation can be seen in Figure 4. Cycled images also generate reconstruction losses, which are defined as  
\[REC\text{-}T_{loss}(x,t)=C_{\mathrm{Rec}}^{n\rightarrow\mathfrak{s}}\cdot \mathrm{Rec}(x_{n\rightarrow\mathfrak{s}},y_{n\rightarrow\mathfrak{s}})+C_{ \mathrm{Rec}}^{s\rightarrow\mathfrak{n}}\cdot\mathrm{Rec}(x_{s\rightarrow \mathfrak{n}},y_{s\rightarrow\mathfrak{n}}) \tag{2}\]  
These images do not exactly resemble natural images and are distinguishable from them by the human eye, but they are actually close enough in their relevant characteristics to natural images that when designing the learning scheme in the way described below, they are not distinguished as fake natural images by the architecture, a beneficial circumstance that allows the simulation of labeled natural data and shared representations, which becomes more clear when taking a look at the UMAP of the internal representation later in Section 4.3. This process also leads us to translated natural images, for which the label is known, and therefore allows for the generation of the regression loss \(\mathrm{Reg}(x_{\mathfrak{s}\rightarrow\mathfrak{n}},I)\
eq 0\). This way, we can train the full regression pipeline for natural data, without any labeled natural data at all. Henceforth, we refer to this process as translation learning. Furthermore, we can translate the same images again, leading to two new types of images yet again \(t\in\{x_{\mathfrak{s}\rightarrow\mathfrak{n}\rightarrow\mathfrak{s}},x_{ \mathfrak{n}\rightarrow\mathfrak{s}\rightarrow\mathfrak{n}}\}\), which should appear near-identical to the original reconstruction \(y\). We first designed this difference to be a loss as well, but we later omitted this training step for hyperparameter optimization, as it did not improving the accuracy on cell counts significantly while adding another step of the more demanding image backpropagation to the pipeline. However, we still create these bilateral translations for specialized top-performing models (see Table 2) and for reasons mentioned below. Since the cycling of data through the different types is what allows the architecture to perform a regression task on unlabeled natural data, we call it Siamese-Cycle-VAE or SC-VAE for short, and variants with enabled bilateral learning cycles will be called SC-VAE-B from here on. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **MAE (Syn) \(\downarrow\)** & **MRE (Syn) \(\downarrow\)** & **Acc. (Syn) \(\uparrow\)** & **MAE (Stat) \(\downarrow\)** & **MRE (Stat) \(\downarrow\)** & **Acc. (Stat) \(\uparrow\)** \\ \hline \multicolumn{7}{c}{PC (phase-contrast microscopy)} \\ \hline EfficientNet (ss) & 4.987 & 79.4\% & 5.0\% & 1.67 & 25.12\% & 23.4\% \\ BiT (ss) & N/A & N/A & N/A & 2.32 & 29.7\% & 25.4\% \\ Twin-VAE (ss) & **0.09** & 0.68\% & 68.2\% & 0.60 & 5.92\% & 57.8\% \\ Transfer Twin-VAE (ss) & 0.15 & 0.43\% & 85.0\% & 0.66 & 6.46\% & 53.7\% \\ Dual Transfer Twin-VAE (ss) & 0.12 & **0.43\%** & **85.0\%** & 0.58 & 5.56\% & 58.7\% \\ Watershed (_u_) & 0.94 & 18.0\% & 24.0\% & 1.66 & 29.0\% & 23.1\% \\ C-VAE (_u_) & 0.24 & 2.65\% & 54.2\% & 1.03 & 19.1\% & 28.9\% \\ S-VAE (_u_) & **0.09** & 0.53\% & 76.3\% & 2.64 & 41.2\% & 11.6\% \\ SC-VAE (_u_) & 0.11 & 0.83\% & 66.1\% & 0.49 & 5.16\% & 61.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation of all baselines and SC-VAE on the data sets Nat-PC, Nat-BF, Syn-PC and Syn-BF. For each method and data set, we report the mean absolute (MAE), the mean relative error (MRE), and the accuracy. Ultimately, only performance on natural data (Nat) is important, but we also report the performance on synthetic data (Syn) to provide further context. We use an upward arrow \(\uparrow\) to indicate that higher is better; a downward arrow \(\downarrow\) means lower is better. The best results achieved per category are marked in bold, (_ss_) denotes a semi-supervised method, (_u_) an unsupervised method.