# Skin Aging Estimation Scheme Based on Lifestyle and Dermoscopy Image Analysis
## 2 Methods
### Skin Aging Estimation Model  
Based on the diverse skin texture features, we first built a skin aging trend model using diverse regression techniques. We considered the polynomial regression and the support vector regression (SVR) for baseline analysis. Polynomial regression is very flexible and useful where a model must be developed empirically. In addition, it provides a good approximation and estimation of the relation between two independent variables. SVR is based on the computation of a linear regression function in a high-dimensional feature space where the input data are mapped via a nonlinear function. SVR has been very popular in the diverse fields such as sequential data prediction, approximation of complex engineering analysis, etc. To find the best polynomial regression, we propose Algorithm 2. ```
Input: observed data \(S\), time sequence \(T\), n-th polynomial regression \(M_{n}\) Output: optimized polynomial regression model \(OM\) for each degree \(n\) \(M_{n}\): = polyfit(\(S\), \(T\), \(n\)) \(D_{n}\): = Minimize(SSE(\(M_{n}\)), RMSE(\(M_{n}\))) if(\(D_{n}<Min(D_{n})\) \(n\)best: = \(n\)  endif endfor OM: = \(M_{n\text{best}}\)  return OM
```  
**Algorithm 2**Finding best polynomial regression model  
Algorithm 2 describes curve fitting steps. For finding the best polynomial, we increased \(n\) and examine the goodness of fit by calculating the sum of squares error (SSE) and adjusting the R-square statistics. SSE indicates a better fit with a value closer to zero. The adjusted R-square statistic is generally the best indicator of the fit quality. For checking the accuracy of the curve fit, we used the confidence bounds on the coefficients. First, given a dataset with \(n\) independent variables and \(m\) observations, the regression model is generally expressed as \(\text{f}(\text{x})=W*X+b\), where \(W\) and  
Figure 2: Examples of skin texture extraction step—**(a)** original image with ROI; **(b)** wrinkle and cell detection; (c) recovered wrinkle width; (d) wrinkle cell gradients. are a vector of coefficients and a vector of independent variables, respectively, and b is the intercept. For selecting the best fitting model, we minimized the SSE. \[\min\sum_{i=1}^{m}\left(y_{i}\ -\hat{y}_{i}\right)^{2}=\min\sum_{i=1}^{m}\left(y_{i }\ -\left(\hat{W}\ast\ X_{i}+\hat{b}\right)\right)^{2} \tag{2}\]  
For generating the estimation baseline, we used the SVM, which includes SVR for prediction and support vector classification (SVC) for classification. SVR differs from polynomial regression in the underlying theoretical settings. To avoid the prediction errors from outliers, we used the kernel functions and parameters to control the prediction errors. Equation (3) indicates how to construct the hyperplane to predict values. \[\min\sum_{i=1}^{m}\left(y_{i}\ -\left(\hat{W}\ast\ X_{i}+\hat{b}\right)\right)^{2 }+C\sum_{j=1}^{n}\left|W_{j}^{2}\right| \tag{3}\]  
Unlike Equation (2), the SVR method has two parameters: C and \(\varepsilon\). Parameter C is introduced to adjust the error sensitivity of the training data in order to avoid over-fitting; setting C to a high value results in fewer prediction errors in the training data. Parameter \(\varepsilon\) is a regularization constant, which controls the flatness of the final model. To determine parameters, we carried out a grid search through a set of parameters, performing cross-validation. Then, we selected the optimal parameters with the best model performance. In order to estimate skin aging associated with lifestyle, we assumed three types of lifestyle changes: 1) current lifestyle will be maintained in the future; 2) current lifestyle will be changed to accelerate the skin aging; and 3) current lifestyle will be changed to maintain the current skin condition. We called them 'normal,' 'negative,' and 'positive,' respectively. Based on this assumption, we defined two classes for skin aging status: 'aging' and'stopping'. The transient pattern of skin texture aging is affected by personal lifestyle.