Zhejiang Provincial Key Laboratory of Service Robot, College of Computer Science, Zhejiang University, Zhejiang 310027, China.
IEEE Trans Image Process. 2011 May;20(5):1327-36. doi: 10.1109/TIP.2010.2090535. Epub 2010 Nov 1.
Sparse coding has received an increasing amount of interest in recent years. It is an unsupervised learning algorithm, which finds a basis set capturing high-level semantics in the data and learns sparse coordinates in terms of the basis set. Originally applied to modeling the human visual cortex, sparse coding has been shown useful for many applications. However, most of the existing approaches to sparse coding fail to consider the geometrical structure of the data space. In many real applications, the data is more likely to reside on a low-dimensional submanifold embedded in the high-dimensional ambient space. It has been shown that the geometrical information of the data is important for discrimination. In this paper, we propose a graph based algorithm, called graph regularized sparse coding, to learn the sparse representations that explicitly take into account the local manifold structure of the data. By using graph Laplacian as a smooth operator, the obtained sparse representations vary smoothly along the geodesics of the data manifold. The extensive experimental results on image classification and clustering have demonstrated the effectiveness of our proposed algorithm.
近年来，稀疏编码受到了越来越多的关注。它是一种无监督学习算法，旨在从数据中找到一组基，以捕捉数据中的高层语义，并根据基学习稀疏坐标。最初应用于模拟人类视觉皮层，稀疏编码已被证明对许多应用有用。然而，大多数现有的稀疏编码方法都没有考虑数据空间的几何结构。在许多实际应用中，数据更有可能位于高维环境空间中嵌入的低维子流形上。已经表明，数据的几何信息对于判别很重要。在本文中，我们提出了一种基于图的算法，称为图正则化稀疏编码，用于学习稀疏表示，这些稀疏表示明确考虑了数据的局部流形结构。通过使用图拉普拉斯作为平滑算子，得到的稀疏表示沿着数据流形的测地线平滑变化。在图像分类和聚类的广泛实验结果表明了我们提出的算法的有效性。
