Algorithm 2 The framework of Biased Constrained Active Learning

Input: Two heterogeneous social networks: ${\mathcal{G}}^s$ and ${\mathcal{G}}^t$. Two sets of labeled anchor link: The training set ${\mathcal{A}}_t$ and the validation set ${\mathcal{A}}_v$. The query pool $\mathcal{P}$. The max number of queries $n_q$. The potential entropy computation method $H_p$. The threshold adjusting pace ${\Delta }_{\delta }$

Output: The new training set ${\mathcal{A}}_t$ and the new query pool $\mathcal{P}$ 1:Initialize $n\leftarrow 0$, $\delta \leftarrow 0.5$, $H_{old}^{\mathcal{P}}\leftarrow +\infty$, $P_{old}^{+}\leftarrow 0.5$, $d\leftarrow 0.1$ 2:For each a in ${\mathcal{A}}_t$ and $\mathcal{P}$, extract four types of features. 3:while $n<n_q$ do 4:    Train a SVM model $\theta$ on ${\mathcal{A}}_t$ according to the training part in MNA. 5:    For each a in $\mathcal{P}$, use $\theta$ to predict $P_{\theta }(0|a)$ and $P_{\theta }(1|a)$. 6:    $H_{new}^{\mathcal{P}}\leftarrow {\sum }_a^P{H}_B(a)$ 7:    if $H_{new}^{\mathcal{P}}<H_{old}^{\mathcal{P}}$ and $\delta >0$ then $\delta \leftarrow \delta -{\Delta }_{\delta }$ 8:    else if $H_{new}^{\mathcal{P}}\ge H_{old}^{\mathcal{P}}$ then $\delta \leftarrow Max\{P_{old}^{+},\delta +{\Delta }_{\delta }\}$ 9:    end if 10:    Use $\theta$ as the trained classifier in MNA, and use MNA to predict the labels of all links in $\mathcal{P}$, and collect all of the predicted positive links into the set ${\mathcal{A}}_p^{+}$. Then set ${\widehat{\mathcal{A}}}_p^{+}\leftarrow \{a|a\in {\mathcal{A}}_p^{+},P_{\theta }(1|a)\ge \delta \}$. 11:    while ${\widehat{\mathcal{A}}}_p^{+}$ is ∅ do 12:        $\delta \leftarrow \delta -d$, ${\widehat{\mathcal{A}}}_p^{+}\leftarrow \{a|a\in {\mathcal{A}}_p^{+},P_{\theta }(1|a)\ge \delta \}$ 13:        if $\delta <0$ then ${\widehat{\mathcal{A}}}_p^{+}\leftarrow \mathcal{P}$ 14:        end if 15:    end while 16:    ${\mathcal{A}}_p^{+}\leftarrow {\widehat{\mathcal{A}}}_p^{+}$ 17:    if $H_p$ is $H_B$ then 18:        For each a in ${\mathcal{A}}_p^{+}$, compute $H_p(a)$ by Equation (2) 19:    else 20:        Use MNA to predict the labels of all links in ${\mathcal{A}}_v$, and compute $P_{YY}$ and $P_{NY}$ by Equation (4) 21:        For each a in ${\mathcal{A}}_p^{+}$, find $R(a)$ and compute $H_p(a)$ by Equation (5) 22:    end if 23:    Select the link $a_h$ which has the highest $H_p(a)$ in ${\mathcal{A}}_p^{+}$, and identify its real label, and set $P_{old}^{+}\leftarrow P_{\theta }(1|a_h)$ 24:    if the real label of $a_h$ is “negative” then 25:        $a_h\leftarrow 0$, ${\mathcal{A}}_t\leftarrow {\mathcal{A}}_t\cup \{a_h\}$, $\mathcal{P}\leftarrow \mathcal{P}-\{a_h\}$ 26:        $H_{old}^{\mathcal{P}}\leftarrow H_{new}^{\mathcal{P}}-H_B(a_h)$ 27:    else 28:        $a_h\leftarrow 1$ 29:        Find $R(a_h)$ from $\mathcal{P}$. For each $a_r$ in $R(a_h)$, set $a_r\leftarrow 0$ 30:        ${\mathcal{A}}_t\leftarrow {\mathcal{A}}_t\cup \{a_h\}\cup R(a_h)$ ,$\mathcal{P}\leftarrow \mathcal{P}-\{a_h\}-R(a_h)$ 31:        $H_{old}^{\mathcal{P}}\leftarrow H_{new}^{\mathcal{P}}-H_B(a_h)-{\sum }_a^{R(a_h)}{H}_B(a)$ 32:    end if 33:    $n\leftarrow n+1$ 34:end while