Table 3:

Simulation results under the scenarios with the Erdös-Rényi networks and $K=3$. In each cell, we show the median (median absolute deviation) of the CE, PME, TPR and FPR values based on 100 replicates. $\mathrm{C}\mathrm{E}={\left(C_n^2\right)}^{-1}\left|\left\{(i,j):I\left\{\hat{\phi }\left({\mathit{x}}_i\right)=\hat{\phi }\left({\mathit{x}}_j\right)\right\}\ne I\left\{\phi \left({\mathit{x}}_i\right)=\phi \left({\mathit{x}}_j\right)\right\},i<j\right\}\right|,\mathrm{P}\mathrm{M}\mathrm{E}={\sum }_{k=1}^K{∥{\stackrel{\mathbf{ˆ}}{\mathbf{\Omega }}}_k-{\mathbf{\Omega }}_k^0∥}_F/K$, ${\mathrm{T}\mathrm{P}\mathrm{R}=\sum }_{k=1}^K\left[{\sum }_{\ell <j}I\left\{{\omega }_{k,\ell j}^0\ne 0,{\hat{\omega }}_{k,\ell j}\ne 0\right\}/{\sum }_{\ell <j}I\left\{{\omega }_{k,\ell j}^0\ne 0\right\}\right]/K$, and ${\mathrm{F}\mathrm{P}\mathrm{R}=\sum }_{k=1}^K\left[{\sum }_{\ell <j}I\left\{{\omega }_{k,\ell j}^0=0,{\hat{\omega }}_{k,\ell j}\ne 0\right\}/{\sum }_{\ell <j}I\left\{{\omega }_{k,\ell j}^0=0\right\}\right]/K$.

Approach	CE	PME	TPR	FPR
S1 with the balanced design
proposed	$0.002\left(0.002\right)$	$16.805\left(1.169\right)$	$0.988\left(0.004\right)$	$0.040\left(0.001\right)$
SCAN	$0.004\left(0.002\right)$	$26.831\left(1.337\right)$	$0.779\left(0.016\right)$	$0.076\left(0.004\right)$
Tiger	-	$31.927\left(0.190\right)$	$0.797\left(0.015\right)$	$0.176\left(0.005\right)$
True+Tiger	-	$17.662\left(0.593\right)$	$0.918\left(0.008\right)$	$0.073\left(0.001\right)$
True+JGL	-	$18.989\left(0.619\right)$	$0.918\left(0.008\right)$	$0.181\left(0.003\right)$
True+JSEM	-	$17.261\left(0.455\right)$	$0.945\left(0.008\right)$	$0.098\left(0.003\right)$
S2 with the balanced design
proposed	$0.002\left(0.002\right)$	$16.751\left(0.906\right)$	$0.987\left(0.004\right)$	$0.039\left(0.002\right)$
SCAN	$0.004\left(0.002\right)$	$26.975\left(0.412\right)$	$0.772\left(0.007\right)$	$0.076\left(0.001\right)$
Tiger	-	$31.025\left(0.220\right)$	$0.789\left(0.017\right)$	$0.169\left(0.005\right)$
True+Tiger	-	$21.104\left(0.451\right)$	$0.870\left(0.005\right)$	$0.075\left(0.001\right)$
True+JGL	-	$20.795\left(0.460\right)$	$0.901\left(0.020\right)$	$0.184\left(0.021\right)$
True+JSEM	-	$16.403\left(0.586\right)$	$0.965\left(0.009\right)$	$0.087\left(0.002\right)$
S3 with the balanced design
proposed	$0.002\left(0.002\right)$	$14.699\left(0.628\right)$	$0.996\left(0.004\right)$	$0.039\left(0.002\right)$
SCAN	$0.006\left(0.006\right)$	$17.155\left(2.467\right)$	$0.768\left(0.027\right)$	$0.061\left(0.008\right)$
Tiger	-	$20.312\left(0.181\right)$	$0.796\left(0.012\right)$	$0.186\left(0.006\right)$
True+Tiger	-	$17.670\left(0.467\right)$	$0.919\left(0.008\right)$	$0.074\left(0.001\right)$
True+JGL	-	$17.271\left(0.459\right)$	$0.930\left(0.010\right)$	$0.158\left(0.005\right)$
True+JSEM	-	$15.435\left(0.433\right)$	$0.971\left(0.004\right)$	$0.098\left(0.003\right)$
S1 with the imbalanced design
proposed	$0.004\left(0.002\right)$	$16.979\left(1.322\right)$	$0.986\left(0.006\right)$	$0.038\left(0.003\right)$
SCAN	$0.004\left(0.002\right)$	$26.194\left(0.787\right)$	$0.786\left(0.008\right)$	$0.076\left(0.002\right)$
Tiger	-	$31.834\left(0.169\right)$	$0.797\left(0.012\right)$	$0.175\left(0.004\right)$
True+Tiger	-	$18.193\left(0.564\right)$	$0.918\left(0.005\right)$	$0.077\left(0.002\right)$
True+JGL	-	$19.442\left(0.488\right)$	$0.914\left(0.008\right)$	$0.184\left(0.003\right)$
True+JSEM	-	$17.479\left(0.499\right)$	$0.942\left(0.008\right)$	$0.097\left(0.002\right)$
S2 with the imbalanced design
proposed	$0.002\left(0.002\right)$	$18.227\left(1.626\right)$	$0.983\left(0.007\right)$	$0.039\left(0.003\right)$
SCAN	$0.004\left(0.002\right)$	$27.080\left(0.547\right)$	$0.764\left(0.010\right)$	$0.076\left(0.002\right)$
Tiger	-	$31.129\left(0.221\right)$	$0.797\left(0.009\right)$	$0.168\left(0.004\right)$
True+Tiger	-	$21.627\left(0.477\right)$	$0.870\left(0.005\right)$	$0.077\left(0.002\right)$
True+JGL	-	$21.139\left(0.567\right)$	$0.893\left(0.013\right)$	$0.182\left(0.008\right)$
True+JSEM	-	$17.005\left(0.579\right)$	$0.962\left(0.007\right)$	$0.088\left(0.003\right)$
S3 with the imbalanced design
proposed	$0.002\left(0.002\right)$	$14.946\left(0.959\right)$	$0.992\left(0.004\right)$	$0.039\left(0.003\right)$
SCAN	$0.008\left(0.004\right)$	$25.161\left(0.934\right)$	$0.791\left(0.016\right)$	$0.079\left(0.003\right)$
Tiger	-	$32.592\left(0.195\right)$	$0.794\left(0.018\right)$	$0.159\left(0.006\right)$
True+Tiger	-	$18.603\left(0.628\right)$	$0.919\left(0.008\right)$	$0.078\left(0.001\right)$
True+JGL	-	$18.169\left(0.440\right)$	$0.931\left(0.009\right)$	$0.161\left(0.004\right)$
True+JSEM	-	$15.791\left(0.668\right)$	$0.972\left(0.004\right)$	$0.099\left(0.002\right)$