Two-Dimensional PCA with F-Norm Minimization
Two-Dimensional PCA with F-Norm Minimization
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DOI：
10.1609/aaai.v31i1.10798
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发表时间：
2017-02
期刊：
影响因子：
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通讯作者：
Qianqian Wang;Quanxue Gao
中科院分区：
文献类型：
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作者：
Qianqian Wang;Quanxue Gao
二维主成分分析（2DPCA）已广泛应用于人脸图像表示和识别。但它对异常值的存在很敏感。为了缓解这个问题，我们提出了一种新颖的鲁棒2DPCA，即具有F范数最小化的2DPCA（F-2DPCA），它是直观的并且直接从2DPCA导出。在F-2DPCA中，空间维度（属性维度）的距离以F-范数来测量，而不同数据点的求和则使用1-范数。因此，它对于异常值和旋转不变性也具有鲁棒性。为了求解F-2DPCA，我们提出了一种快速迭代算法，该算法在每次迭代中都有一个封闭形式的解，并证明了其收敛性。人脸图像数据库的实验结果说明了其有效性和优势。
Two-dimensional principle component analysis (2DPCA) has been widely used for face image representation and recognition. But it is sensitive to the presence of outliers. To alleviate this problem, we propose a novel robust 2DPCA, namely 2DPCA with F-norm minimization (F-2DPCA), which is intuitive and directly derived from 2DPCA. In F-2DPCA, distance in spatial dimensions (attribute dimensions) is measured in F-norm, while the summation over different data points uses 1-norm. Thus it is robust to outliers and rotational invariant as well. To solve F-2DPCA, we propose a fast iterative algorithm, which has a closed-form solution in each iteration, and prove its convergence. Experimental results on face image databases illustrate its effectiveness and advantages.