IEEE Trans Image Process. 2015 Dec;24(12):4918-33. doi: 10.1109/TIP.2015.2472277. Epub 2015 Aug 24.
Low-rank representation (LRR) has received considerable attention in subspace segmentation due to its effectiveness in exploring low-dimensional subspace structures embedded in data. To preserve the intrinsic geometrical structure of data, a graph regularizer has been introduced into LRR framework for learning the locality and similarity information within data. However, it is often the case that not only the high-dimensional data reside on a non-linear low-dimensional manifold in the ambient space, but also their features lie on a manifold in feature space. In this paper, we propose a dual graph regularized LRR model (DGLRR) by enforcing preservation of geometric information in both the ambient space and the feature space. The proposed method aims for simultaneously considering the geometric structures of the data manifold and the feature manifold. Furthermore, we extend the DGLRR model to include non-negative constraint, leading to a parts-based representation of data. Experiments are conducted on several image data sets to demonstrate that the proposed method outperforms the state-of-the-art approaches in image clustering.
低秩表示（LRR）因其在探索数据中嵌入的低维子空间结构方面的有效性，在子空间分割中受到了相当多的关注。为了保持数据的内在几何结构，在 LRR 框架中引入了图正则化器来学习数据中的局部和相似信息。然而，通常情况下，不仅高维数据位于环境空间中的非线性低维流形上，而且它们的特征也位于特征空间中的流形上。在本文中，我们通过在环境空间和特征空间中都保持几何信息的方式，提出了一种对偶图正则化 LRR 模型（DGLRR）。所提出的方法旨在同时考虑数据流形和特征流形的几何结构。此外，我们将 DGLRR 模型扩展到包括非负约束，从而实现数据的基于部分的表示。在几个图像数据集上进行的实验表明，所提出的方法在图像聚类方面优于最先进的方法。
