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中文摘要：
测地距离能在宏观层面上较真实地反映数据中所隐含的几何结构，可基于它的支持向量数据描述（SVDD）无法直接优化．为此，文中提出一种流形分类学习算法的设计框架．用原空间测地距离近似各向同性的特征映射（ISOMAP）降维空间上的欧氏距离，即在隐含ISOMAP降维后空间上执行原学习算法．按照该框架，以SVDD为例发展出嵌入的ISOMAP发现的低维流形的SVDD（mSVDD），从而解决基于测地距离的SVDD的优化问题．USPS手写体数字数据集上的实验表明，mSVDD的单类性能较SVDD有较显著提高．
英文摘要：
Geodesic distance is a good metric to approximate the underlying global geometry. However, support vector data description （SVDD） with geodesic distance cannot be directly optimized. A framework for manifold-based classifier is designed. The Euclid distance in the feature space induced by isometric feature mapping （ISOMAP） dimension reduction is approximated by the geodesic distance in the input space, and implicitly conducts the former learning algorithm （with Euclid distance） after the ISOMAP process. Next, the proposed method is extended to SVDD and a SVDD derivate with ISOMAP manifold embedding （mSVDD） is developed. Experimental results on USPS handwritten digital dataset show that compared with traditional Euclid distance based SVDD, mSVDD significantly increases the performance for one-class classification.
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