# Sales Forecasting for Fashion Products Considering Lost Sales
## 4 Numerical Experiments
### Results and Discussion  
#### 4.5.1 Results for Parameter Estimation  
A total of 20 important features are selected for clustering in the shoe category using the feature selection method in Section 3.3. The runtime of each step is shown in Table 11, and the detailed information on the selected features is given in Table 12 in Appendix A. Then, the silhouette coefficients are computed to determine the best number of clusters. For shoes, the silhouette coefficients of cluster numbers 3 to 5 are 0.2407, 0.1999 and 0.2019. For belts, the silhouette coefficients of cluster numbers 3 to 5 are 0.4240, 0.2938 and 0.3946. As a result, both shoes and belts are divided into three clusters. The statistic characteristics of each cluster are given in Table 3.  
After clustering, GA is used to find the optimal solution for parameters in the TLs model. The results for shoes and belts are listed in Table 4. Each cluster corresponds to a commodity classification in Section 3.1. For shoes, the difference between \(q\) is small, and sales are mainly influenced by \(\alpha\). In the shoe dataset, cluster 3 has the highest \(\alpha\) with 5.0117 and \(q\) with 0.8065. Products in cluster 3 are recognized as major commodities. Similarly, cluster 1 is the targeted commodities and cluster 2 is the common commodities. For belts, cluster 2 is the major commodity because it has the highest \(q\) and \(\alpha\). Cluster 1 is the common commodities, and cluster 3 is the targeted commodities. To conclude, the estimation results demonstrate our model well.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Category**} & \multirow{2}{*}{**Cluster**} & \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**Sample Size**} & \multicolumn{3}{c}{**Sales**} & \multicolumn{3}{c}{**Inventory**} \\ \cline{5-8}  & & & & **Avg** & **Std** & **Avg** & **Std** \\ \hline \multirow{8}{*}{Shoes} & \multirow{4}{*}{Cluster 1} & Total set & 1735 & 48.25 & 41.87 & 62.45 & 53.61 \\  & & Training set & 1128 & 47.97 & 38.87 & 60.97 & 48.99 \\  & & Testing set & 607 & 48.75 & 46.96 & 65.21 & 61.22 \\  & & Total set & 2102 & 44.40 & 36.04 & 56.77 & 46.55 \\  & & Training set & 1863 & 43.89 & 32.24 & 55.81 & 43.94 \\  & & Testing set & 239 & 48.35 & 47.67 & 64.28 & 62.98 \\  & & Total set & 2107 & 35.17 & 28.53 & 44.78 & 36.81 \\  & & Training set & 1465 & 35.91 & 27.80 & 45.35 & 34.66 \\  & & Testing set & 642 & 33.48 & 30.09 & 43.49 & 41.29 \\ \hline \multirow{8}{*}{Bels} & \multirow{4}{*}{Cluster 2} & Total set & 80 & 35.80 & 22.64 & 47.50 & 28.56 \\  & & Training set & 73 & 35.42 & 22.76 & 46.51 & 28.19 \\ \cline{1-1}  & & Testing set & 7 & 39.71 & 22.63 & 57.86 & 32.60 \\ \cline{1-1}  & & Total set & 484 & 36.54 & 24.04 & 46.75 & 29.03 \\ \cline{1-1}  & & Training set & 387 & 34.40 & 21.30 & 44.42 & 25.63 \\ \cline{1-1}  & & Testing set & 97 & 45.06 & 31.50 & 56.08 & 38.59 \\ \cline{1-1}  & & Total set & 304 & 25.90 & 12.16 & 34.91 & 15.50 \\ \cline{1-1}  & & Training set & 282 & 25.70 & 12.10 & 34.72 & 15.42 \\ \cline{1-1}  & & Testing set & 22 & 28.45 & 12.98 & 37.36 & 16.68 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistic characteristics of clusters.