Two-Stage Regularized Linear Discriminant Analysis for 2-D Data
Two-Stage Regularized Linear Discriminant Analysis for 2-D Data
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DOI：
10.1109/tnnls.2014.2350993
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发表时间：
2015-08
影响因子：
10.4
通讯作者：
Jianhua Zhao;Lei Shi;Ji Zhu
中科院分区：
文献类型：
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作者：
Jianhua Zhao;Lei Shi;Ji Zhu
Fisher线性判别分析（LDA）涉及类内和类间协方差矩阵。对于像图像这样的二维数据，正则化LDA （RLDA）由于对估计的类内矩阵的特征值进行了正则化处理，可以改进LDA算法。然而，它没有考虑特征向量和估计的类间矩阵。为了同时改进这两个矩阵，本文提出了一种新的二维数据的两阶段方法，即双向LDA （BLDA）的第一阶段和RLDA的第二阶段，其中双向LDA和RLDA都基于Fisher准则来处理相关性。BLDA在包含二维数据中固有的行和列相关性的特殊可分离协方差约束下执行LDA。主要的新颖之处在于我们在第一阶段提出了一个简单而有效的统计检验来确定子空间维数。因此，第一阶段在保留数据中重要的判别信息的同时，大幅度地降低了维数。这使得第二阶段能够在更低维的子空间中执行RLDA，从而同时改进两个估计矩阵。在许多二维合成数据集和现实世界数据集上的实验表明，BLDA+RLDA优于几个密切相关的竞争对手。
Fisher linear discriminant analysis (LDA) involves within-class and between-class covariance matrices. For 2-D data such as images, regularized LDA (RLDA) can improve LDA due to the regularized eigenvalues of the estimated within-class matrix. However, it fails to consider the eigenvectors and the estimated between-class matrix. To improve these two matrices simultaneously, we propose in this paper a new two-stage method for 2-D data, namely a bidirectional LDA (BLDA) in the first stage and the RLDA in the second stage, where both BLDA and RLDA are based on the Fisher criterion that tackles correlation. BLDA performs the LDA under special separable covariance constraints that incorporate the row and column correlations inherent in 2-D data. The main novelty is that we propose a simple but effective statistical test to determine the subspace dimensionality in the first stage. As a result, the first stage reduces the dimensionality substantially while keeping the significant discriminant information in the data. This enables the second stage to perform RLDA in a much lower dimensional subspace, and thus improves the two estimated matrices simultaneously. Experiments on a number of 2-D synthetic and real-world data sets show that BLDA+RLDA outperforms several closely related competitors.