Partial multi-label learning (PML) aims to learn from the training data where each training example is annotated with a candidate label set, among which only a subset is relevant. Despite the success of existing PML approaches, a major drawback of them lies in lacking of robustness to noisy side information. To tackle this problem, we introduce a novel partial multi-label learning with noisy side information approach, which simultaneously removes noisy outliers from the training instances and trains robust partial multi-label classifier for unlabeled instances prediction. Specifically, we first represent the observed sample set as a feature matrix and then decompose it into an ideal feature matrix and an outlier feature matrix by using the low-rank and sparse decomposition scheme, where the former is constrained to be low rank by considering that the noise-free feature information always lies in a low-dimensional subspace and the latter is assumed to be sparse by considering that the outliers are usually sparse among the observed feature matrix. Secondly, we refine an ideal label confidence matrix from the observed label matrix and use the graph Laplacian regularization to constrain the confidence matrix to keep the intrinsic structure among feature vectors. Thirdly, we constrain the feature mapping matrix to be low rank by utilizing the label correlations. Finally, we obtain both the ideal features and ground-truth labels via minimizing the loss function, where the augmented Lagrange multiplier algorithm and quadratic programming are incorporated to solve the optimization problem. Extensive experiments conducted on ten different data sets demonstrate the effectiveness of our proposed method.

局部多标签学习（PML）旨在从训练数据中学习，其中每个训练示例都用候选标签集进行注释，其中只有一个子集是相关的。尽管现有的PML方法取得了成功，但它们的主要缺点在于缺乏对嘈杂的辅助信息的鲁棒性。为了解决这个问题，我们引入了一种新颖的带有噪声边信息的部分多标签学习方法，该方法同时从训练实例中消除了噪声离群值，并为未标记实例的预测训练了鲁棒的部分多标签分类器。具体来说，我们首先将观察到的样本集表示为特征矩阵，然后使用低秩稀疏分解方案将其分解为理想特征矩阵和离群特征矩阵，其中考虑到无噪声特征信息始终位于低维子空间中，从而将前者约束为低秩，而考虑到观察到的特征矩阵中的离群值通常稀疏，则假定后者稀疏。其次，我们从观察到的标签矩阵中细化一个理想的标签置信矩阵，并使用图拉普拉斯正则化约束该置信矩阵以保持特征向量之间的固有结构。第三，我们利用标签相关性将特征映射矩阵约束为低秩。最后，通过使损失函数最小化，我们同时获得了理想特征和真实标签，其中结合了增强的拉格朗日乘数算法和二次规划来解决优化问题。