Nonnegativity based matrix factorization is usually powerful for learning the parts-based “shallow” representation, however it fails to discover deep hidden information within both the basis concept and representation spaces. In this paper, we therefore propose a new dual-constrained deep semi-supervised coupled factorization network (DS²CF-Net) for learning hierarchical representations. DS²CF-Net is formulated as the joint partial-label and structure-constrained deep factorization network using multi-layers of linear transformations, which coupled updates the basic concepts and new representations in each layer. An error correction mechanism with feature fusion strategy is also integrated between consecutive layers to improve the representation ability of features. To improve the discriminating abilities of both representation and coefficients in feature space, we clearly consider how to enrich the prior knowledge by the coefficients-based label prediction, and incorporate the enriched prior knowledge as the additional label and structure constraints. To be specific, the label constraint enables the intra-class samples to have the same coordinate in the feature space, while the structure constraint forces the coefficients in each layer to be block-diagonal so that the enriched prior knowledge are more accurate. Besides, we integrate the adaptive dual-graph learning to retain the locality structures of both the data manifold and feature manifold in each layer. Finally, a fine-tuning process is performed to refine the structure-constrained matrix and data weight matrix in each layer using the predicted labels for more accurate representations. Extensive simulations on public databases show that our method can obtain state-of-the-art performance.

基于非负的矩阵分解对于学习基于部分的“浅”表示通常很有效，但是它无法在基础概念和表示空间中发现深层隐藏信息。因此，在本文中，我们提出了一种新的双约束深度半监督耦合分解网络（DS ² CF-Net），用于学习分层表示。DS ²CF-Net 被制定为使用多层线性变换的联合部分标签和结构约束的深度分解网络，它耦合更新了每一层的基本概念和新表示。连续层之间还集成了具有特征融合策略的纠错机制，以提高特征的表示能力。为了提高特征空间中表示和系数的区分能力，我们清楚地考虑了如何通过基于系数的标签预测来丰富先验知识，并将丰富的先验知识作为附加标签和结构约束。具体来说，标签约束使类内样本在特征空间中具有相同的坐标，而结构约束迫使每一层中的系数为块对角线，从而使丰富的先验知识更加准确。此外，我们集成了自适应双图学习以保留每一层中数据流形和特征流形的局部结构。最后，执行微调过程以使用预测标签细化每一层中的结构约束矩阵和数据权重矩阵，以获得更准确的表示。对公共数据库的大量模拟表明，我们的方法可以获得最先进的性能。执行微调过程以使用预测标签细化每一层中的结构约束矩阵和数据权重矩阵以获得更准确的表示。对公共数据库的大量模拟表明，我们的方法可以获得最先进的性能。执行微调过程以使用预测标签细化每一层中的结构约束矩阵和数据权重矩阵以获得更准确的表示。对公共数据库的大量模拟表明，我们的方法可以获得最先进的性能。