# Comparison of Machine Learning Methods in Stochastic Skin Optical Model Inversion
## 1 Introduction  
Skin related diseases such as skin cancer are common [1], and non-invasive methods for diagnosing them are needed. According to [PERSON] et al. [2], the melanoma incidence is increasing. The incidence between 2009-2016 was 491.1 cases per hundred thousand people, which is nearly 64% more compared to the time period of 1999-2008. The difference in incidence at an older age is even starker, as the incidence nearly doubled from 1278.1 to 2424.9 in people older than 70 years old [2]. The cost of the melanoma for the society has the same trend and early detection and accurate treatment lowers these costs and improves the life expectancy of the patients. Hyperspectral imaging is one way for the early detection and guidance for the treatment. Skin physical parameter retrieval with hyperspectral camera or spectrometer and machine learning (ML) provide a non-invasive method of measuring the chromophore concentrations and other parameters in the skin [3]. One hinderance to developing ML models for clinical use is that the needed training datasets are large and difficult to produce. The ethical standards of using human testing make it hard to obtain data, and there needs to be a team of medical staff in addition to computer science specialists for the work. One way to avoid some of these pitfalls is to use mathematical modeling to produce training data for ML algorithms. In this study, we use the stochastic model, which is partially of our own design. In our previous research [4; 5], we have used convolutional neural networks (CNN) for stochastic model inversion. In [4], we used CNN in inverting the stochastic model for leaf optical properties (SLOP) [6], which was the inspiration for the stochastic model used in this study. We found the inversion successful. In [5], we compared the invertibility and usefulness in the physical parameterretrieval from the stochastic model used in this study and a Kubelka-Munk model [7] by inversion with CNN. It has since occurred to us that it would be useful to verify the applicability of the CNN networks in model inversion by comparing it to other ML algorithms. The ML algorithms have been compared multiple times in different hyperspectral imaging scenarios. For example, one study compared ML algorithms in assessing strawberry foliage Anthracnose disease stage classification [8]. They compared spectral angle mapper, stepwise discriminant analysis, and their own spectral index they call simple slope measure. These algorithms did not show good performance in the task, with classification accuracy just breaking 80%. Another study found a least mean squares classifier to perform best in classifying a small batch of lamb muscles compared to six other machine learning algorithms including support vector machine (SVM) approaches, simple neural networks, nearest neighbor algorithm, and linear discriminator analysis [9]. The algorithms were also tested using principal component analysis (PCA) for dimensionality reduction in training and testing data. They found no statistical differences in the classification results between using PCA for the data or not. [PERSON] et al. [10] have written a survey on machine learning methods in hyperspectral remote sensing tasks. The retrieval of (bio)physical or (bio)chemical parameters from the hyperspectral images was one of the tasks, and they found three articles where SVMs were used in retrieval, five articles that used latent linear models such as PCA, four that used ensemble learning, and five that used Gaussian processes. Surprisingly, they found no articles where deep learning was used in retrieval. In the articles [8; 9; 10], the distinction to our work is that they do not apply mathematical modeling prior to applying machine learning. In contrast, the following articles by [PERSON] et al. and [PERSON] et al. are similar to our work, only employing different mathematical and machine learning models [11; 12; 13]. [PERSON] et al.