Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply being low-rank or sparse. Fully extracting and exploiting hidden structure information in the data is always desirable and favorable. To reveal more underlying effective manifold structure, in this paper, we explicitly model the data relation. Specifically, we propose a structure learning framework that retains the pairwise similarities between the data points. Rather than just trying to reconstruct the original data based on self-expression, we also manage to reconstruct the kernel matrix, which functions as similarity preserving. Consequently, this technique is particularly suitable for the class of learning problems that are sensitive to sample similarity, e.g., clustering and semisupervised classification. To take advantage of representation power of deep neural network, a deep auto-encoder architecture is further designed to implement our model. Extensive experiments on benchmark data sets demonstrate that our proposed framework can consistently and significantly improve performance on both evaluation tasks. We conclude that the quality of structure learning can be enhanced if similarity information is incorporated.

依靠底层的低维数据结构，低等级和稀疏建模方法已在广泛的应用中取得了巨大的成功。但是，在许多应用程序中，数据可以显示的结构不仅仅是简单的低秩或稀疏。完全提取和利用数据中的隐藏结构信息始终是理想和有利的。为了揭示更多潜在的有效流形结构，在本文中，我们对数据关系进行了显式建模。具体来说，我们提出了一种结构学习框架，该框架保留了数据点之间的成对相似性。我们不仅尝试基于自我表达来重建原始数据，还设法重建内核矩阵，该矩阵起到相似性保留的作用。所以，该技术特别适合对样本相似性敏感的一类学习问题，例如聚类和半监督分类。为了利用深度神经网络的表示能力，进一步设计了深度自动编码器体系结构来实现我们的模型。在基准数据集上进行的大量实验表明，我们提出的框架可以一致且显着地提高两项评估任务的性能。我们得出结论，如果纳入相似性信息，则可以提高结构学习的质量。在基准数据集上进行的大量实验表明，我们提出的框架可以一致且显着地提高两项评估任务的性能。我们得出结论，如果纳入相似性信息，则可以提高结构学习的质量。在基准数据集上进行的大量实验表明，我们提出的框架可以一致且显着地提高两项评估任务的性能。我们得出结论，如果纳入相似性信息，则可以提高结构学习的质量。