学习等距分离图
Learning Isometric Separation Maps
摘要：
最大方差展开（MVU）及其变体在低维空间中嵌入数据流形方面非常成功，经常揭示真正的内在维度。在本文中，我们将展示如何将监督类信息纳入MVU类方法，而不会破坏其凸性。我们称之为这种方法的等距分离图，我们表明，由此产生的内核矩阵可以用作一个二进制/多类支持向量机的半监督（转导）框架中的方法。我们还表明，该方法总是找到一个核矩阵，线性分离的训练数据，而不投影在无限维空间。在传统的支持向量机中，我们选择一个核，并希望数据在核空间中成为线性可分的。在本文中，我们展示了如何超平面可以选择ad-hoc和内核的训练，使数据始终是线性可分的。与大间隔SVM的比较显示出相当的性能。
英文摘要：
Maximum Variance Unfolding (MVU) and its variants have been very successful in embedding data-manifolds in lower dimensional spaces, often revealing the true intrinsic dimension. In this paper we show how to also incorporate supervised class information into an MVU-like method without breaking its convexity. We call this method the Isometric Separation Map and we show that the resulting kernel matrix can be used as a binary/multiclass Support Vector Machine-like method in a semi-supervised (transductive) framework. We also show that the method always finds a kernel matrix that linearly separates the training data exactly without projecting them in infinite dimensional spaces. In traditional SVMs we choose a kernel and hope that the data become linearly separable in the kernel space. In this paper we show how the hyperplane can be chosen ad-hoc and the kernel is trained so that data are always linearly separable. Comparisons with Large Margin SVMs show comparable performance.
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