Constrained Concept Factorization (CCF) yields the enhanced representation ability over CF by incorporating label information as additional constraints, but it cannot classify and group unlabeled data appropriately. Minimizing the difference between the original data and its reconstruction directly can enable CCF to model a small noisy perturbation, but is not robust to gross sparse errors. Besides, CCF cannot preserve the manifold structures in new representation space explicitly, especially in an adaptive manner. In this paper, we propose a joint label prediction based Robust Semi-Supervised Adaptive Concept Factorization (RS2ACF) framework. To obtain robust representation, RS2ACF relaxes the factorization to make it simultaneously stable to small entrywise noise and robust to sparse errors. To enrich prior knowledge to enhance the discrimination, RS2ACF clearly uses class information of labeled data and more importantly propagates it to unlabeled data by jointly learning an explicit label indicator for unlabeled data. By the label indicator, RS2ACF can ensure the unlabeled data of the same predicted label to be mapped into the same class in feature space. Besides, RS2ACF incorporates the joint neighborhood reconstruction error over the new representations and predicted labels of both labeled and unlabeled data, so the manifold structures can be preserved explicitly and adaptively in the representation space and label space at the same time. Owing to the adaptive manner, the tricky process of determining the neighborhood size or kernel width can be avoided. Extensive results on public databases verify that our RS2ACF can deliver state-of-the-art data representation, compared with other related methods.

中文翻译：

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基于联合标签预测的鲁棒数据表示的半监督自适应概念分解

约束概念分解 (CCF) 通过将标签信息作为附加约束，产生了优于 CF 的增强表示能力，但它无法对未标记的数据进行适当的分类和分组。最小化原始数据与其直接重建之间的差异可以使 CCF 对小的噪声扰动进行建模，但对粗大的稀疏误差不具有鲁棒性。此外，CCF 不能显式地保留新表示空间中的流形结构，尤其是以自适应方式。在本文中，我们提出了一种基于联合标签预测的鲁棒半监督自适应概念分解（RS2ACF）框架。为了获得鲁棒的表示，RS2ACF 放宽了分解，使其同时对小的入口噪声稳定和对稀疏错误的鲁棒性。为了丰富先验知识以增强辨别力，RS2ACF 清楚地使用标记数据的类信息，更重要的是通过联合学习未标记数据的显式标记指示符将其传播到未标记数据。通过标签指示符，RS2ACF 可以保证相同预测标签的未标记数据映射到特征空间中的同一类。此外，RS2ACF 结合了标记和未标记数据的新表示和预测标签上的联合邻域重建误差，因此流形结构可以同时在表示空间和标签空间中显式和自适应地保留。由于自适应方式，可以避免确定邻域大小或内核宽度的棘手过程。