Fig. 4

Performance comparison between the proposed splitting functions and existing ones. (a), (b) and (c-d) respectively correspond to the splitting functions \(w_e(\mathcal {S})=\gamma _e(\mathcal {S})\cdot \gamma _e(e\setminus \mathcal {S})\), \(w_e(\mathcal {S})=\min \{\gamma _e(\mathcal {S}),\gamma _e(e\setminus \mathcal {S})\}\) and \(w_e(\mathcal {S})=\min \{\gamma _e(\mathcal {S}),\gamma _e(e\setminus \mathcal {S}),\beta \gamma _e(e)\}\). We fix \(\beta =0.15\) in (c) and fix \(\alpha =1\) in (d). The red curves (cardinality-based) and the green curve (all-or-nothing) respectively correspond to the cases when \(\alpha =0\) and when \(\beta\) is small enough (\(\beta =10^{-3.5}\) here). For the blue curves (EDVWs-based), a 5-fold cross-validation is adopted in (a–c) to search the optimal \(\alpha\) and in (d) to search the optimal \(\beta\)