The graph-based semisupervised label propagation (LP) algorithm has delivered impressive classification results. However, the estimated soft labels typically contain mixed signs and noise, which cause inaccurate predictions due to the lack of suitable constraints. Moreover, the available methods typically calculate the weights and estimate the labels in the original input space, which typically contains noise and corruption. Thus, the encoded similarities and manifold smoothness may be inaccurate for label estimation. In this article, we present effective schemes for resolving these issues and propose a novel and robust semisupervised classification algorithm, namely the triple matrix recovery-based robust auto-weighted label propagation framework (ALP-TMR). Our ALP-TMR introduces a TMR mechanism to remove noise or mixed signs from the estimated soft labels and improve the robustness to noise and outliers in the steps of assigning weights and predicting the labels simultaneously. Our method can jointly recover the underlying clean data, clean labels, and clean weighting spaces by decomposing the original data, predicted soft labels, or weights into a clean part plus an error part by fitting noise. In addition, ALP-TMR integrates the auto-weighting process by minimizing the reconstruction errors over the recovered clean data and clean soft labels, which can encode the weights more accurately to improve both data representation and classification. By classifying samples in the recovered clean label and weight spaces, one can potentially improve the label prediction results. Extensive simulations verified the effectivenss of our ALP-TMR.

中文翻译：

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基于稳健的基于三矩阵恢复的自动加权标签传播。

基于图的半监督标签传播（LP）算法提供了令人印象深刻的分类结果。但是，估计的软标签通常包含混合的符号和噪声，由于缺乏适当的约束，它们会导致预测不准确。此外，可用的方法通常计算权重并估计原始输入空间中的标签，而原始输入空间通常包含噪声和损坏。因此，编码的相似度和歧管平滑度对于标签估计可能是不准确的。在本文中，我们提出了解决这些问题的有效方案，并提出了一种新颖且健壮的半监督分类算法，即基于三重矩阵恢复的健壮自动加权标签传播框架（ALP-TMR）。我们的ALP-TMR引入了TMR机制，可在分配权重和同时预测标签的步骤中从估计的软标签中去除噪声或混合符号，并提高对噪声和异常值的鲁棒性。我们的方法可以通过将原始数据，预测的软标签或权重分解为干净的部分以及通过拟合噪声的错误部分来共同恢复底层的干净数据，干净的标签和干净的加权空间。此外，ALP-TMR通过最大程度地减少恢复的干净数据和干净软标签上的重构误差来集成自动加权过程，从而可以更准确地编码权重，从而改善数据表示和分类。通过对回收的干净标签和重量空间中的样品进行分类，可以潜在地改善标签预测结果。