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Scatter Balance: An Angle-Based Supervised Dimensionality Reduction

机译：散布平衡：基于角度的有监督维数减少

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摘要

Subspace selection is widely applied in data classification, clustering, and visualization. The samples projected into subspace can be processed efficiently. In this paper, we research the linear discriminant analysis (LDA) and maximum margin criterion (MMC) algorithms intensively and analyze the effects of scatters to subspace selection. Meanwhile, we point out the boundaries of scatters in LDA and MMC algorithms to illustrate the differences and similarities of subspace selection in different circumstances. Besides, the effects of outlier classes on subspace selection are also analyzed. According to the above analysis, we propose a new subspace selection method called angle linear discriminant embedding (ALDE) on the basis of angle measurement. ALDE utilizes the cosine of the angle to get new within-class and between-class scatter matrices and avoids the small sample size problem simultaneously. To deal with high-dimensional data, we extend ALDE to a two-stage ALDE (TS-ALDE). The synthetic data experiments indicate that ALDE can balance the within-class and between-class scatters and be robust to outlier classes. The experimental results based on UCI machine-learning repository and image databases show that TS-ALDE has a lower time complexity than ALDE while processing high-dimensional data.
机译：子空间选择已广泛应用于数据分类，聚类和可视化。投影到子空间中的样本可以得到有效处理。在本文中，我们深入研究了线性判别分析（LDA）和最大余量准则（MMC）算法，并分析了散射对子空间选择的影响。同时，我们指出了LDA算法和MMC算法中散射的边界，以说明在不同情况下子空间选择的异同。此外，还分析了异常类对子空间选择的影响。根据以上分析，我们提出了一种新的基于角度测量的子空间选择方法，称为角度线性判别嵌入（ALDE）。 ALDE利用角度的余弦来获得新的类内和类间散布矩阵，同时避免了样本量小的问题。为了处理高维数据，我们将ALDE扩展为两阶段ALDE（TS-ALDE）。综合数据实验表明，ALDE可以平衡类内和类间散布，并且对异常类具有鲁棒性。基于UCI机器学习存储库和图像数据库的实验结果表明，在处理高维数据时，TS-ALDE的时间复杂度低于ALDE。

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