This work was supported by National Natural Science Foundation of China (Grant Nos. 61672049, 61732001).
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Figure 1
Online learning and cold-start performance. (a) MLK; (b) Ep.
Figure 2
Time convergence. (a) MLM; (b) EpEx.
${\rm~RecRating(user).push((user,~item},~T,~l))$; |
${\rm~RecRating(item).push((user,~item},~T,~l))$; |
ConvertRating(user); |
UpdateParameter(user); |
ConvertRating(item); |
UpdateParameter(item); |
$({\rm~user,item}_1,~t_1,~l_1)~\leftarrow~{\rm~RecRating(user).front}()$; |
Update $\phi_{{\rm~user},~j}$ by ( |
${\rm~RecRating(user).pop}()$; |
$({\rm~user,~item}_2,~t_2,~l_2)~\leftarrow~{\rm~RecRating(user).front}()$; |
|
$\tau_{\rm~user}~\leftarrow~t_2$; |
|
$f_{{\rm~user},~t,~j}~\leftarrow~x_{{\rm~user},~t,~j}$; |
|
|
Prepare $E_{{\rm~user},~t,~j}$ by ( |
Initial $\alpha_{\tau_{\rm~user},~j}$ as ( |
Calculate $\alpha_{t,~j}$ by ( |
Initial $\beta_{T,~j}$ as ( |
Calculate $\beta_{t,~i}$ by ( |
Calculate $\gamma_{t,~i}$ and $\xi_{t,~i,~j}$ by ( |
Update $\pi_i$, $A_{i,~j}$, and $p_{j,~k}$ by ( |
| Symbol | Meaning |
| $J$ | Number of user types |
| $K$ | Number of item types |
| $M$ | Max number of recent ratings |
| $\lambda_1$ | Regularization for $\pi$ and $\omega$ |
| $\lambda_2$ | Regularization for $A$ and $B$ |
| $X_{{\rm~user},t}$ | The type ${\rm~user}$ belongs to at time $t$ |
| $Y_{{\rm~item},t}$ | The type item belongs to at time $t$ |
| $R_{{\rm~user,item},t}$ | The rating that ${\rm~user}$ give to item at time $t$ |
| $p_{j,k}$ | Probability that type $j$ user likes type $k$ item |
| $A_{i,j}$ | Jump rate matrix for users |
| $B_{k,m}$ | Jump rate matrix for items |
| $\pi_j$ | Global prior distribution for users |
| $\omega_k$ | Global prior distribution for items |
| $f_{{\rm~user},t,j}$ | Approximation of user variable distribution |
| $g_{{\rm~item},t,k}$ | Approximation of item variable distribution |
| Variable name | Data type | Meaning |
| $\tau_{\rm~user}$ | Number | Time of the first recent rating of ${\rm~user}$ |
| $\tau_{\rm~item}$ | Number | Time of the first recent rating of item |
| $\phi_{{\rm~user},j}$ | Number | Local prior for users |
| $\psi_{{\rm~item},k}$ | Number | Local prior for items |
| $x_{{\rm~user},t,j}$ | Number | $P(X_{{\rm~user},t}=j|{\rm~Rating})$ |
| $y_{{\rm~item},t,k}$ | Number | $P(Y_{{\rm~item},t}=k|{\rm~Rating})$ |
| ${\rm~RecRating(user)}$ | Queue | Recent rating for ${\rm~user}$ |
| ${\rm~RecRating(item)}$ | Queue | Recent rating for item |
$({\rm~user,item}_1,T_1,l_1)~\leftarrow~{\rm~RecRating(user).back}()$; |
$\hat{x}_{{\rm~user},t,j}~\leftarrow~\sum_{i=1}^J~x_{{\rm~user},T_1,i}\exp(A(t-T_1))_{i,j}$; |
$({\rm~user}_2,{\rm~item},T_2,l_2)~\leftarrow~{\rm~RecRating(item).back}()$; |
$\hat{y}_{{\rm~item},t,k}~\leftarrow~\sum_{m=1}^K~y_{{\rm~item},T_2,l}\exp(B(t-T_2))_{m,k}$; |
$\hat{r}_n~\leftarrow~\sum\nolimits_{j~=~1}^J~{\sum\nolimits_{k~=~1}^K~{\hat{x}_{{\rm~user},t,j}~\hat{y}_{{\rm~item},t,k}~\Pr(n-1;N-1,p_{j,k})~}~}~$; |
| Dataset | User | Item | Rating | Density(%) |
| MLK (MovieLens100k) | 944 | 1683 | 100000 | 6.29 |
| MLM (MovieLens1M) | 6040 | 3706 | 1000209 | 4.47 |
| Ep (Epinions) | 2874 | 2624 | 122361 | 1.62 |
| EpEx (Epinions extended) | 11201 | 109520 | 5449415 | 0.44 |
| Setting | Classical | Time-ordered | ||||||
| Dataset | MLK | MLM | Ep | EpEx | MLK | MLM | Ep | EpEx |
| SRec | 0.698 | 0.728 | 0.796 | 0.953 | 0.662 | 0.703 | 0.788 | 0.943 |
| TCARS | 0.783 | 0.951 | 0.702 | 0.746 | 0.940 | |||
| GRU4Rec | 0.652 | 0.654 | 0.715 | 0.936 | 0.613 | 0.622 | 0.705 | 0.939 |
| RRN | 0.665 | 0.730 | 0.740 | 0.938 | 0.684 | 0.702 | 0.734 | 0.936 |
| RT | 0.745 | 0.717 | ||||||
| Setting | Classical | Time-ordered | ||||||
| Dataset | MLK | MLM | Ep | EpEx | MLK | MLM | Ep | EpEx |
| SRec | 0.924 | 0.933 | 0.945 | 0.938 | 0.933 | 0.979 | ||
| TCARS | 0.936 | 0.979 | 0.939 | 0.938 | 0.978 | |||
| GRU4Rec | 0.903 | 0.904 | 0.905 | 0.974 | 0.916 | 0.908 | 0.923 | 0.976 |
| RRN | 0.914 | 0.932 | 0.915 | 0.971 | 0.933 | 0.933 | 0.927 | 0.976 |
| RT | 0.930 | 0.938 | 0.939 | |||||
| Setting | Classical | Time-ordered | ||||||
| Dataset | MLK | MLM | Ep | EpEx | MLK | MLM | Ep | EpEx |
| SRec | 0.855 | 0.897 | 0.919 | 0.850 | 0.872 | 0.897 | ||
| TCARS | 0.854 | 0.880 | 0.955 | 0.794 | 0.876 | 0.831 | 0.964 | |
| GRU4Rec | 0.797 | 0.839 | 0.835 | 0.969 | 0.765 | 0.837 | 0.815 | 0.966 |
| RRN | 0.828 | 0.892 | 0.843 | 0.953 | 0.833 | 0.875 | 0.843 | 0.964 |
| RT | 0.903 | 0.978 | 0.970 | |||||
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