A Framework of Joint Graph Embedding and Sparse Regression for Dimensionality Reduction
A Framework of Joint Graph Embedding and Sparse Regression for Dimensionality Reduction
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DOI：
10.1109/tip.2015.2405474
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发表时间：
2015-02
影响因子：
10.6
通讯作者：
Xiaoshuang Shi;Zhenhua Guo;Zhihui Lai;Yujiu Yang;Z. Bao;D. Zhang
中科院分区：
文献类型：
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作者：
Xiaoshuang Shi;Zhenhua Guo;Zhihui Lai;Yujiu Yang;Z. Bao;D. Zhang
在过去的几十年里，人们开发了大量的降维算法。尽管这些算法的动机不同，但它们可以用一个称为图嵌入的共同框架来解释。为了挖掘数据的显著特征，提出了一些基于图嵌入的稀疏回归算法。然而，问题是这些算法包括两个独立的步骤：(1)嵌入学习和(2)稀疏回归。因此，它们的性能在很大程度上取决于构造图的有效性。本文提出了一种将图嵌入和稀疏回归的目标函数相结合的框架，使嵌入学习和稀疏回归能够共同实现和优化，而不是简单地使用图谱进行稀疏回归。通过提出的框架，可以统一有监督、半监督和无监督学习算法。此外，我们还分析了所提出框架的两种优化问题。通过对该框架采用1,2范数正则化，该框架可以同时进行特征选择和子空间学习。在7个标准数据库上的实验表明，联合图嵌入和稀疏回归方法可以显著提高识别性能，并始终优于稀疏回归方法。
Over the past few decades, a large number of algorithms have been developed for dimensionality reduction. Despite the different motivations of these algorithms, they can be interpreted by a common framework known as graph embedding. In order to explore the significant features of data, some sparse regression algorithms have been proposed based on graph embedding. However, the problem is that these algorithms include two separate steps: (1) embedding learning and (2) sparse regression. Thus their performance is largely determined by the effectiveness of the constructed graph. In this paper, we present a framework by combining the objective functions of graph embedding and sparse regression so that embedding learning and sparse regression can be jointly implemented and optimized, instead of simply using the graph spectral for sparse regression. By the proposed framework, supervised, semisupervised, and unsupervised learning algorithms could be unified. Furthermore, we analyze two situations of the optimization problem for the proposed framework. By adopting an ℓ2,1-norm regularization for the proposed framework, it can perform feature selection and subspace learning simultaneously. Experiments on seven standard databases demonstrate that joint graph embedding and sparse regression method can significantly improve the recognition performance and consistently outperform the sparse regression method.