Partial Multi-Label Feature Selection via Entropy-Weighted Multi-Scale Neighborhood Granular Label Distribution Learning

. 2026 Apr 9;28(4):422. doi: 10.3390/e28040422

Algorithm 2 PML-FSMNG

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Input: Dataset $X \in R^{n \times d}$ , label distribution matrix $D \in R^{n \times q}$ , parameter $α$ , $β$ , $γ$
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Output: Top ranked features
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Initialize $t \leftarrow 1$ . $W \leftarrow rand (d, q)$ , $b^{⊤} \leftarrow rand (1, q)$ , $S \leftarrow rand (n, n)$ ,
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while not convergence do
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$G_{0}^{(t)} \leftarrow \frac{1}{2} diag (∥ {(X W + 1 b^{⊤} - D)}_{i} ∥_{2}^{- 1})$
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update $b^{(t + 1)}$ by (23)
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$G_{1}^{(t)} \leftarrow \frac{1}{2} diag (∥ W_{i} ∥_{2}^{- 1})$
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$m \leftarrow 1^{⊤} G_{0}^{(t)} 1 + β 1^{⊤} L 1$
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$R \leftarrow I - \frac{1}{m} 1 1^{⊤} (G_{0}^{(t)} + β L)$ , $H \leftarrow I - \frac{1}{m} 1 1^{⊤} G_{0}^{(t)}$
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$E \leftarrow R X$
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update $W^{(t + 1)}$ by (28)
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update $S^{(t + 1)}$ by (32)
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$t \leftarrow t + 1$
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end while
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$W \leftarrow W^{(t)}$
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Rank features with ${∥w_{i .}∥}_{2} (i \in {1, 2, \dots, d})$