# Efficient Sleep-Wake Cycle Staging via Phase-Amplitude Coupling Pattern Classification
## 3 Results  
### Top Performing MLP Architectures Are Obtained by Using Full or Half of the Comodulogram  
The performance obtained by all the architectures in the first phase of the experiments are depicted in Figure 2. The AUC values are highly constant (with the variability almost always lower than 2%) in protocols 1 and 2 but vary considerably in the extremities in protocols 3 and 4, especially for the REM stage. Moreover, while the first two show an apparently uniform increase in the AUC values with the increase in the number of neurons, protocols 3 and 4 display a bell-shaped curve in this relationship. The maximum AUC values were thus obtained using 6, 6, 35, and 15 neurons in the hidden layer for protocols 1, 2, 3, and 4, respectively. For protocols 3 and 4, the maximum AUC values were extracted within the stable region of the AUC curves. After detecting the best network of the best architecture for each protocol (with the above-mentioned number of neurons in the hidden layer), the ROC curves and final AUC values were computed (Figure 2, bottom row). All of them are clearly above chance (AUC values \(>\) 0.85 always).  
The AUC values encompassing all the stages were 0.884, 0.885, 0.979, and 0.982 for protocols 1 to 4, respectively. The architectures using larger portions of the comodulogram (full or half), and not only pairs of frequency of known neurobiological relevance, performed significantly better for all the stages (Figure 3). Interestingly, while the AUC values for REM were the same (no statistical difference)--and always high--across the different protocols, those for SWS and WK were considerably higher when using more of the comodulogram. Furthermore, for both the SWS and ALL cases, the performances obtained by using the half comodulogram were even significantly superior to the full comodulogram, even with a small difference (SWS 0.971 versus 0.978; ALL: 0.979 versus 0.982). Finally, the AUC values for the REM stage were always considerably higher when compared to those of both SWS and WK, as it can be seen by the blue curves always occupying the top left-most portion of the ROC graphs (Figure 2).  
Figure 3: A comparison of classification performance between the four different protocols of the input data construction for WK (green; **top left**), SWS (red; **top right**), REM (blue; **bottom left**), and ALL (black; **bottom right**). Protocols using more of the comodulogram performed significantly better than those using only well-established frequency pairs described in the literature. Curiously, using only half the comodulogram performed even better than using its entirety, in the cases of SWS and ALL, even though only slightly. Using the one-way ANOVA and post hoc Tukey, the resulting statistics were as follows (mean \(\pm\) s.e.m.): WK) points: 0.823 \(\pm\) 0.001; ranges: 0.819 \(\pm\) 0.001; full: 0.972 \(\pm\) 0.001; and half: 0.974 \(\pm\) 0.001 (difference a-b: \(p\) < 0.0001). SWS) points: 0.841 \(\pm\) 0.001; ranges: 0.851 \(\pm\) 0.001; full: 0.971 \(\pm\) 0.001; and half: 0.978 \(\pm\) 0.001 (differences a-b, -c, -d, b-c, and b-d: \(p\) < 0.0001; difference c-d: \(p\) < 0.001). REM) points: 0.988 \(\pm\) 0.001; ranges: 0.984 \(\pm\) 0.001; full: 0.994 \(\pm\) 0.001; and half: 0.996 \(\pm\) 0.001 (differences a-b, -c, and b-c: \(p\) < 0.0001). ALL) points: 0.884 \(\pm\) 0.001; ranges: 0.885 \(\pm\) 0.001; full: 0.979 \(\pm\) 0.001; and half: 0.982 \(\pm\) 0.001 (differences a-b and a-c: \(p\) < 0.0001; b: \(p\) < 0.0001; and difference b-c: \(p\) < 0.05). The boxplots display the median and 25 th and 75 th percentiles in the main box; the whiskers depict the extremities of the data.