# Product Innovation Design Based on Deep Learning and Kansei Engineering
## 3 Empirical Study
### Relationship Model Building  
In this section, we establish a BP network-based relationship model between product parameters and styles. To make the structure of the relationship model easy to design and have good functional performance, a three-layer neural network structure was selected. Specific steps were as follows:  
Figure 4: Sample cutting illustration.  
Figure 5: One of the questionnaires.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Model (\(\mathbf{j_{1}}\))** & **Waist (\(\mathbf{j_{2}}\))** & **Length (\(\mathbf{j_{3}}\))** & **Collar (\(\mathbf{j_{4}}\))** & **Sleeve (\(\mathbf{j_{5}}\))** & **Pocket (\(\mathbf{j_{6}}\))** & **Opening (\(\mathbf{j_{7}}\))** \\ \hline X: 1 & High: 1 & Short: 1 & Collarless: 1 & Set-in: 1 & Patch: 1 & Single breasted: 1 \\ H: 2 & Normal: 2 & Mid: 2 & Stand: 2 & Raglan: 2 & Vertical: 2 & Double breasted: 2 \\ A: 3 & Low: 3 & Long: 3 & Turnover: 3 & Pocket less: 3 & Zipper: 3 \\  & No: 4 & & Lapel: 4 & & & Hidden placket: 4 \\  & & & Hoodie: 5 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Female coat design elements.  
(1) Model Construction  
The structure of BP network is shown in Figure 6. The input layer consists of seven coat parameters \((j_{1},j_{2},j_{3},j_{4},j_{5},j_{6},j_{7})\). Hence, the number of neurons is seven. The output layer is composed of four groups of styles (professional-leisure, vogue-classic, grand-youth, simple-delicate), so the number of neurons is four. The empirical formula for the number of hidden neurons is:  
\[p= \sqrt{n+q}+z \tag{6}\]  
In Equation (6), \(p\), \(n\) and \(q\) are the number of neurons in the hidden, input, and output layers, respectively, and \(z\) is the empirical value (\(1\ \leq\ z\ \leq\ 10\)). Through repeated trials, the number of neurons in the hidden layer is determined.  
(2) Model training and results  
As stated above, we had 100 samples in dataset 4. We used the k-fold cross-validation (CV) method to evaluate our model. First, the sample set was randomly divided into five subsets, each with 20 samples. In these five subsets, each subset was used as the verification set while the remaining four subsets constituted the training sets. The 100 samples and their corresponding style evaluation values (dataset 4) were used to train the BP networks. We repeated trials with different numbers of neurons (\(p\)) in the hidden layer. The comparison results are shown in Table 3.  
As can be seen from Table 3, when \(p=11\), the minimum CV error of 0.324 is obtained. Since Kansei evaluation is a qualitative analysis and the value is a range, our result is satisfactory. The result shows that our relationship model has high reliability for female coat style prediction.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Sample**} & \multicolumn{8}{c}{**CV Error**} \\ \hline
**Training Set** & **Validation Set** & \(p=4\) & \(p=5\) & \(p=6\) & \(p=7\) & \(p=8\) & \(p=9\) & \(p=10\) & \(p=11\) & \(p=12\) & \(p=13\) \\ \hline
2, 3, 4, 5 & 1 & & & & & & & & & \\ \hline
1, 3, 4, 5 & 2 & & & & & & & & & \\ \hline
1, 2, 4, 5 & 3 & & & & & & & & & \\ \hline
1, 2, 3, 4 & 5 & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: K-fold cross-validation (CV) results.  
Figure 6: The structure of back-propagation (BP) neural network relationship model.