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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.
Geodetic distance can reflect the implied geometry in the data more faithfully on the macroscopic level, which can not be directly optimized based on its support vector data description (SVDD) .Therefore, a design of manifold classification learning algorithm Frame.Using ISOMAP to reduce the Euclidean distance on the space, that is to say, the original learning algorithm is implemented on the reduced ISOMAP space.According to this framework, taking SVDD as an example To develop the SVDD (mSVDD) of low-dimensional manifolds found in the embedded ISOMAP, so as to solve the optimization problem of SVDD based on geodesic distance.Experiments on the USPS handwritten numeral data set show that the single class performance of mSVDD is significantly higher than that of SVDD .