结合核方法中的样本外和预像问题

P. Arias, G. Randall, G. Sapiro
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引用次数: 75

摘要

核方法在模式识别领域得到了广泛的研究。这些方法隐式地将“核技巧”数据映射到更适合分析的空间中。许多流形学习和降维技术都是简单的核方法,其映射是显式计算的。在这种情况下,与映射相关的两个问题出现了:样本外扩展和图像前计算。在本文中,我们提出了一种新的基于Nystrom公式的样本外扩展的预像方法,展示了这两个问题之间的联系。我们还讨论了特征空间中归一化的重要性,这一点被标准的预图像算法所忽略。作为一个例子,我们将这些思想应用于高斯核,并将我们的方法与其他流行的预图像方法联系起来。最后,我们展示了这些技术在动态形状研究中的应用。
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Connecting the Out-of-Sample and Pre-Image Problems in Kernel Methods
Kernel methods have been widely studied in the field of pattern recognition. These methods implicitly map, "the kernel trick," the data into a space which is more appropriate for analysis. Many manifold learning and dimensionality reduction techniques are simply kernel methods for which the mapping is explicitly computed. In such cases, two problems related with the mapping arise: The out-of-sample extension and the pre-image computation. In this paper we propose a new pre-image method based on the Nystrom formulation for the out-of-sample extension, showing the connections between both problems. We also address the importance of normalization in the feature space, which has been ignored by standard pre-image algorithms. As an example, we apply these ideas to the Gaussian kernel, and relate our approach to other popular pre-image methods. Finally, we show the application of these techniques in the study of dynamic shapes.
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