# Comparison of Machine Learning Methods in Stochastic Skin Optical Model Inversion
## 3 Results  
The six inversions had variable success with the simulated data (Figures 3 and 4 and Table 12). The CNN and CNNV2 experiments (Table 12) performed best with correlation coefficients being the highest between 0.93 and 0.96 (mean 0.95) and their RMSE, MSE, and MAE values being lowest 0.09-0.12 (mean 0.11) (RMSE), 0.01-0.02 (mean 0.01) (MSE), and 0.08-0.09 (mean 0.09) (MAE). The performance of the MLP was also good. It outsced CNN in some regression goals by some metrics and was a little poorer in others. Correlation coefficients were between 0.79 and 0.95 (mean 0.91), RMSEs 0.09-0.18 (mean 0.12), MSEs 0.01-0.03 (mean 0.02), and MAEs 0.07-0.14 (mean 0.09). Based on visual interpretation of Figure 4, the second experiment of CNN regressor is the best of the neural network regressors, as the correlation seems to be strongest there.  
In the saliency maps of the CNN and MLP regressors (Figure 3), we see that the CNN experiments had similar areas of interest. The interval between 550 nm and 700 nm seems to be most important in predicting the target variables. In the MLP experiment, the same interval seems to be useful, but additionally it highlights some areas in the ends of the spectrum.  
Lasso and stochastic gradient descent regressors showed similar results. As Figure 4 shows, the correlation is virtually identical, and the points scatter to nearly the same place. In fact, only looking  
at individual points, one can observe some differences between the lasso and SGD regressors. Lasso and SGDR had correlation coefficients between 0.55 and 0.88 (means 0.71 and 0.71, respectively), RMSEs between 0.14 and 0.24 (means 0.20 and 0.20), MSEs between 0.02 and 0.06 (means 0.04 and 0.04), and MAEs between 0.11 and 0.20 (means 0.16 and 0.16).  
Figure 3: The saliency maps of the neural network regressors. (**a**) the first CNN model; (**b**) the second CNN model; (**c**) the MLP model.  
RMSEs between 0.22 and 0.24 (mean 0.23), MSEs between 0.05 and 0.06 (mean 0.05), and MAEs between 0.16 and 0.19 (mean 0.18).  
Overall, the least accurate predictions were for hemoglobin volume fraction and the models were most accurate for dermis thickness prediction. Melanosome volume fraction was relatively easily learned by all regressors, while, in epidermis thickness, there is a clear divide between group of CNN and MLP regressors and other regressors. The neural network models provide accurate responses which seems almost impossible for the other types of models.  
Regarding the test with the measured hyperspectral data in Figure 5, the details of the lesions are most easily visible in the CNN experiments. In MLP, lasso, and LSVR experiments, the epidermis thickness is poorly visible due to noise. Looking at Figure 5, the fourth best model seems to be the SGDR, as the details of the lesions are somewhat visible.  
Figure 5: Comparison of the inversion algorithms used with measured hyperspectral data. Each subfigure represents a target parameter. The colorbar units are arbitrary. (**a**) melanosome volume fraction; (**b**) hemoglobin volume fraction; (**c**) thickness of epidermis; (**d**) thickness of dermis.