Subspaces Indexing Model on Grassmann Manifold for Image Search
Subspaces Indexing Model on Grassmann Manifold for Image Search
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DOI：
10.1109/tip.2011.2114354
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发表时间：
2011-09
影响因子：
10.6
通讯作者：
Xinchao Wang;Zhu Li;D. Tao
中科院分区：
文献类型：
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作者：
Xinchao Wang;Zhu Li;D. Tao
传统的线性子空间学习方法，如主成分分析（PCA），线性判别分析（LDA），从整个数据集导出子空间。这些方法都有局限性，因为它们是线性的，而我们试图建模的数据分布通常是非线性的。此外，这些算法未能纳入本地变化的内在样本分布流形。因此，这些算法在大规模数据集上是无效的。这些方法的核版本可以在一定程度上缓解问题，但当数据集很大时，计算涉及N × N的特征/QP问题时，面临着严重的计算挑战。当N很大时，内核版本在计算上是不实用的。为了解决上述问题，提高识别/搜索性能，特别是在大规模的图像数据集，我们提出了一种新的局部子空间索引模型的图像搜索称为格拉斯曼流形上的子空间索引模型（SIM-GM）。SIM-GM将全局空间划分为具有层次结构的局部补丁;因此，全局模型由分段线性局部子空间模型近似。通过进一步应用格拉斯曼流形距离，SIM-GM能够将本地化模型组织成索引结构的层次结构，并允许快速查询选择用于分类的最佳模型。我们提出的SIM-GM具有许多优点：1）它能够有效地处理大量的训练样本; 2）它是一种查询驱动的方法，即，它能够返回一个有效的局部空间模型，从而显著提高识别性能; 3）它是一个通用的框架，可以集成多种学习算法。理论分析和大量的实验结果证实了该模型的有效性。
Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribution we are trying to model is typically nonlinear. Moreover, these algorithms fail to incorporate local variations of the intrinsic sample distribution manifold. Therefore, these algorithms are ineffective when applied on large scale datasets. Kernel versions of these approaches can alleviate the problem to certain degree but face a serious computational challenge when data set is large, where the computing involves Eigen/QP problems of size N × N. When N is large, kernel versions are not computationally practical. To tackle the aforementioned problems and improve recognition/searching performance, especially on large scale image datasets, we propose a novel local subspace indexing model for image search termed Subspace Indexing Model on Grassmann Manifold (SIM-GM). SIM-GM partitions the global space into local patches with a hierarchical structure; the global model is, therefore, approximated by piece-wise linear local subspace models. By further applying the Grassmann manifold distance, SIM-GM is able to organize localized models into a hierarchy of indexed structure, and allow fast query selection of the optimal ones for classification. Our proposed SIM-GM enjoys a number of merits: 1) it is able to deal with a large number of training samples efficiently; 2) it is a query-driven approach, i.e., it is able to return an effective local space model, so the recognition performance could be significantly improved; 3) it is a common framework, which can incorporate many learning algorithms. Theoretical analysis and extensive experimental results confirm the validity of this model.