Broad Learning System (BLS) are widely used in many fields because of its strong feature extraction ability and high computational efficiency. However, the BLS is mainly used in supervised learning, which greatly limits the applicability of the BLS. And the obtained data is less labeled data, but is a large number of unlabeled data. Therefore, the BLS is extended based on the semi-supervised learning of manifold regularization framework to propose a semi-supervised broad learning system (SS-BLS). Firstly, the features are extracted from labeled and unlabeled data by building feature nodes and enhancement nodes. Then the manifold regularization framework is used to construct Laplacian matrix. Next, the feature nodes, enhancement nodes and Laplacian matrix are combined to construct the objective function, which is effectively solved by ridge regression in order to obtain the output coefficients. Finally, the validity of the SS-BLS is verified by three different complex data of G50C, MNIST, and NORB, respectively. The experiment result show that the SS-BLS can achieve higher classification accuracy for different complex data, takes on fast operation speed and strong generalization ability.

中文翻译：

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基于流形正则化和广域网的半监督广域学习系统

广泛的学习系统（BLS）因其强大的特征提取能力和高计算效率而被广泛应用于许多领域。但是，BLS 主要用于监督学习，这极大地限制了 BLS 的适用性。并且得到的数据是较少标注的数据，而是大量的未标注数据。因此，基于流形正则化框架的半监督学习对 BLS 进行了扩展，提出了一种半监督广泛学习系统（SS-BLS）。首先，通过构建特征节点和增强节点，从标记和未标记的数据中提取特征。然后使用流形正则化框架构造拉普拉斯矩阵。接下来，将特征节点、增强节点和拉普拉斯矩阵组合起来构造目标函数，通过岭回归有效地解决了这个问题，以获得输出系数。最后，分别通过 G50C、MNIST 和 NORB 三个不同的复杂数据验证了 SS-BLS 的有效性。实验结果表明，SS-BLS可以对不同的复杂数据实现更高的分类精度，运算速度快，泛化能力强。