Grassmann Manifold Optimization for Fast $L_1$-Norm Principal Component Analysis
Grassmann Manifold Optimization for Fast $L_1$-Norm Principal Component Analysis
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DOI：
10.1109/lsp.2018.2886742
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发表时间：
2019-02
影响因子：
3.9
通讯作者：
Breton L. Minnehan;A. Savakis
中科院分区：
文献类型：
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作者：
Breton L. Minnehan;A. Savakis
在这封信中，我们提出了一个快速格拉斯曼流形优化方法的$L_1$-范数为基础的主成分分析（GM-$L_1$-PCA）。我们的方法是一个两步迭代的成本最小化和流形收缩技术，有效地同时找到所有的主成分。我们进行复杂性分析，并表明GM-$L_1$-PCA实现了显着减少处理时间，同时获得可比或更好的结果，目前国家的最先进的$L_1$-PCA方法。我们进一步证明了改进的GM-$L_1$-PCA技术的$L_2$-PCA的数据集上的面部图像损坏与离群数据点。我们的实验表明，GM-$L_1$-PCA的计算效率更高，并且产生的结果比以前的方法具有更低的重投影误差。此外，我们的方法的处理时间相对独立于数据集大小，非常适合当今常见的各种大数据问题。
In this letter, we propose a fast Grassmann manifold optimization method for $L_1$-norm based principal component analysis (GM-$L_1$-PCA). Our approach is a two-step iterative cost-minimization and manifold retraction technique that efficiently finds all principal components simultaneously. We perform complexity analysis and show that GM-$L_1$-PCA achieves a significant reduction in processing time while obtaining comparable or better results to current state-of-the-art $L_1$-PCA methods. We further demonstrate the improvement of GM-$L_1$-PCA technique over $L_2$-PCA on a dataset of facial imagery corrupted with outlying data points. Our experiments show that GM-$L_1$-PCA is computationally more efficient and produces results with lower reprojection error than previous methods. Furthermore, the processing time of our approach is relatively independent of dataset size and well suited for various big-data problems commonly encountered today.