IEEE Trans Image Process. 2015 Nov;24(11):3717-28. doi: 10.1109/TIP.2015.2441632. Epub 2015 Jun 4.
This paper aims at constructing a good graph to discover the intrinsic data structures under a semisupervised learning setting. First, we propose to build a nonnegative low-rank and sparse (referred to as NNLRS) graph for the given data representation. In particular, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse reconstruction coefficients matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph captures both the global mixture of subspaces structure (by the low-rankness) and the locally linear structure (by the sparseness) of the data, hence it is both generative and discriminative. Second, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph simultaneously within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive NNLRS experiments on three publicly available data sets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semisupervised classification and discriminative analysis, which verifies the effectiveness of our proposed method.
本文旨在构建一个良好的图来发现半监督学习环境下的内在数据结构。首先，我们提出构建一个非负低秩稀疏（简称 NNLRS）图，用于给定的数据表示。具体来说，图中的边的权重是通过寻找一个非负低秩稀疏的重建系数矩阵来获得的，该矩阵表示每个数据样本是其他样本的线性组合。所得到的 NNLRS 图同时捕获了数据的全局混合子空间结构（通过低秩性）和局部线性结构（通过稀疏性），因此它既具有生成性又具有判别性。其次，由于好的特征对于构建好的图非常重要，我们提出在一个框架内同时学习数据嵌入矩阵和构建图，这被称为具有嵌入特征的 NNLRS（简称 NNLRS-EF）。在三个公开可用的数据集中进行的广泛的 NNLRS 实验表明，该方法在半监督分类和判别分析方面都优于最先进的图构建方法，这验证了我们方法的有效性。
