A Semi-Supervised Approach to Bearing Fault Diagnosis under Variable Conditions towards Imbalanced Unlabeled Data

. 2018 Jun 29;18(7):2097. doi: 10.3390/s18072097

Algorithm 1. Greedy Gradient Max-Cut

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Input: the graph $G_{A} = {X, A}$ and labeled vertex $X_{l}$ and label $Y$ ;
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Initialization:
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Construct the initial cut ${S_{j}}$ by the initial labeled vertex $X_{l}$ :

$S_{j} = {x_{i} | y_{i j} = 1}, j = 1, 2, \dots, c$
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Unlabeled vertex set $X_{u} = X X_{l}$ ;
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repeat
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for all $j = 0$ to $| X_{u} |$ do
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calculate the connectivity:

$c_{i j} = \sum_{k = 1}^{n} λ_{k} a_{i k} y_{k j}, x_{i} \in X_{u}, j = 1, \dots, c$
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End for
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Update the cut ${S_{j}}$ by placing the vertex xi* to the Sj* subset:

$(i^{*}, j^{*}) = \arg \min_{i, j, x_{i} \in X_{u}} c_{i j}$
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Add xi to $X_{l} : X_{l} \leftarrow X_{l} + x_{i} ；$
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Delete xi from $X_{u} : X_{u} \leftarrow X_{u} - x_{i};$
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Until $X_{u} = \emptyset$
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Output: the final cut and the corresponding labeled subsets $S_{j}, j = 1, 2, \dots, c$ Sj, j = 1, 2,…, c