# A Cross-Platform Personalized Recommender System for Connecting E-Commerce and Social Network
## 4 Evaluation and Analysis
### The Construction of User Interest Profiles
#### 4.4.1 The Process of Building User Interest Profiles  
Here, we choose one user as an example. Considering the fact that the user's interests may change as time goes by, we separate the user's microblogs \(M\) into five groups \(\left(M_{\Delta t_{0}},M_{\Delta t_{1}},M_{\Delta t_{2}},M_{\Delta t_{3}},M_{ \Delta t_{4}}\right)\), so that each group contains microblogs that the user released during \(\Delta t\) (six months). Then, we train MTDM using \(M_{\Delta t_{0}},M_{\Delta t_{1}},M_{\Delta t_{2}},M_{\Delta t_{3}},M_{\Delta t _{4}}\), respectively. The user interest vector \(P_{\Delta t_{i}}\) at different times is shown in Table 7.  
We can observe from Table 7 that \(P_{\Delta t_{i}}\) are different from each other. \(P_{\Delta t_{0}}\) shows that, in last six months, the user mainly focused on Car, Mobile and Soccer, while \(P_{\Delta t_{1}}\) shows that the user was interested in Shopping, Mobile, Technology, Soccer and News. This phenomenon demonstrates that user interests as detected using microblogs, which reflect \begin{table}
\begin{tabular}{c l l l} \hline \hline \(M_{\Delta t_{i}}\) & **Topics** & **Keyword in Topic** & \(P_{\Delta t_{i}}\) \\ \hline \multirow{6}{*}{\(M_{\Delta t_{0}}\)} & Topic 1 & (Mata 0.015) & \\ \cline{2-4}  & Topic 2 & (Toyota 0.019) & \\ \cline{2-4}  & Topic 3 & (Mobile 0.011) & (Mobile, 0.011), (Fuel tank, \\ \cline{2-4}  & Topic 4 & (Fuel tank 0.012) & 0.012), (Sichuan, 0.026) \\ \cline{2-4}  & Topic 5 & (Sichuan 0.026) & \\ \hline \multirow{6}{*}{\(M_{\Delta t_{1}}\)} & Topic 1 & (Shopping 0.015) & \\ \cline{2-4}  & Topic 2 & (Boom 0.010) & \{(Shopping, 0.015), (News, 0.010), (Mobile, 0.069), (Technology, 0.008), (Soccer, 0.012)\} \\ \cline{2-4}  & Topic 5 & (Soccer 0.012) & \\ \hline \multirow{6}{*}{\(M_{\Delta t_{2}}\)} & Topic 1 & (Environment 0.011) & \\ \cline{2-4}  & Topic 2 & (Mobile 0.018) & \{(Environment, 0.011), (Mobile, 0.018), (Technology, 0.006), (Car, 0.013), (Huawei, 0.022)\} \\ \cline{2-4}  & Topic 4 & (Driver 0.013) & \\ \cline{2-4}  & Topic 5 & (Huawei 0.022) & \\ \hline \multirow{6}{*}{\(M_{\Delta t_{3}}\)} & Topic 1 & (Mobile 0.017) & \\ \cline{2-4}  & Topic 2 & (Environment 0.017) & \{(Mobile, 0.017), (Environment, 0.017), (Meizu, 0.019), (Website, 0.009), (Soccer, 0.007)\} \\ \cline{2-4}  & Topic 3 & (Meizu 0.019) & (Meizu, 0.019), (Website, 0.009), (Soccer, 0.007)\} \\ \cline{2-4}  & Topic 4 & (Website 0.009) & 0.009), (Soccer, 0.007)\} \\ \cline{2-4}  & Topic 5 & (Soccer fan 0.007) & \\ \hline \multirow{6}{*}{\(M_{\Delta t_{4}}\)} & Topic 1 & (Japan 0.013) & \{(Japan, 0.013), (Mobile, 0.030), (Company, 0.014), (Word Cup Soccer 0.035), (News, 0.007)\} \\ \cline{2-4}  & Topic 2 & (Soccer fan 0.007) & \\ \cline{1-1} \cline{2-4}  & Topic 3 & (Company 0.014) & 0.030), (Company, 0.014), (Soccer, 0.035), (News, 0.007)\} \\ \cline{1-1} \cline{2-4}  & Topic 4 & (World Cup Soccer 0.035) & (Soccer, 0.035), (News, 0.007)\} \\ \cline{1-1} \cline{2-4}  & Topic 5 & (Soccer fan 0.007) & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Examples of profiles building process. actual user preferences, would change over different time periods. This indirectly shows the necessity of distinguishing stable interest profiles and temporal interest profiles. The interest profiles \(P_{u_{M}}\) in a user \(u\)'s microblogs can be obtained by  
\[f(t)=(1+\lambda t)e^{-\lambda t} \tag{15}\]  
\[P_{u_{M}}=\sum_{i=0}^{n}P_{\lambda t_{i}}f(t_{i}) \tag{16}\]  
Here the value of \(\lambda\) we choose is 1; therefore, \(f(t_{0})=f(0)=1\), \(f(t_{1})=f(1)=0.772\), \(f(t_{2})=f(2)=0.434\), \(f(t_{3})=f(3)=0.231\), \(f(t_{4})=f(4)=0.107\). The user's \(P_{u_{M}}\) that we obtain is {(Soccer, 0.0296), (Mobile, 0.0259), (Car, 0.0246), (Shopping, 0.0116), (Huawei, 0.009548), (Technology, 0.0088), (Environment, 0.0087), (News, 0.0085), (Meizu, 0.0044), (Website, 0.0021), (Japan, 0.0014), (Company, 0.0015)).