Abstract Low-rank representation (LRR), which is a powerful method to find the low-dimensional subspace structure embedded in high-dimensional data spaces, has been used in both unsupervised learning and semi-supervised classification. LRR aims at finding the lowest rank representation that can express each data sample as linear combination of other samples. However, this method doesn’t consider the geometrical structure of the data. Thus the similarity and local structure might be lost in the process of learning. Motivated by this, a novel hierarchical weighted low-rank representation (HWLRR) is proposed in this paper. In the new algorithm, a hierarchical weighted matrix is defined to find more samples that may belong to the same subspace using affinity propagation. By taking advantage of the affinity propagation, our proposed method can preserve both local and global structure of the whole dataset. The experimental results on both unsupervised learning and semi-supervised classification demonstrate the superiority of our proposed method.

中文翻译：

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用于图像聚类和分类的分层加权低秩表示

摘要 低秩表示（LRR）是一种寻找嵌入高维数据空间的低维子空间结构的强大方法，已被用于无监督学习和半监督分类。LRR 旨在找到可以将每个数据样本表示为其他样本的线性组合的最低秩表示。但是，这种方法没有考虑数据的几何结构。因此在学习过程中可能会丢失相似性和局部结构。受此启发，本文提出了一种新颖的分层加权低秩表示（HWLRR）。在新算法中，定义了一个分层加权矩阵，以使用亲和传播找到更多可能属于同一子空间的样本。通过利用亲和传播，我们提出的方法可以保留整个数据集的局部和全局结构。无监督学习和半监督分类的实验结果证明了我们提出的方法的优越性。