局部保留最大信息差v-支持向量机

Locality-preserved Maximum Information Variance v-support Vector Machine

针对现有模式分类方法不能较好地保持数据空间的局部流形信息或差异信息等问题,提出一种基于流形学习的局部保留最大信息差v-支持向量机(Locality-preserved maximum information variance v-support vector machine,v-LPMIVSVM).对于模式分类问题,v-LPMIVSVM引入局部同类离散度和局部异类离散度概念,分别体现输入空间局部流形结构和局部差异(或判别)信息,通过最小化局部同类离散度和最大化局部异类离散度,优化分类器的投影方向.同时,v-LPMIVSVM采用适于流形数据的测地线距离来度量数据点对间的相似性,以更好地反映流形数据的本质结构.人造和实际数据集实验结果显示所提方法具有良好的泛化性能.

The state-of-the-art pattern classifiers can not efficiently preserve the local geometrical structure or the diversity （or discriminative） information of data points embedded in high-dimensional data space, which is useful for pattern recognition. A novel so-called locality-preserved maximum information variance v-support vector machine （v-LPMIVSVM） algorithm is presented based on manifold learning to address those problems mentioned above. The v-LPMIVSVM in- troduces within-locality homogeneous scatter and within-locality heterogeneous scatter, which respectively denote the within-locality manifold information of data points and the within-locality diversity information of data points, thus constructing an optimal classifier with optimal projection weight vector by minimizing the within-locality homogeneous scatter and simultaneously maximizing the within-locality heterogeneous scatter. Meanwhile, the v-LPMIVSVM adopts geodesic distance metric to measure the distance between data in the manifold space, which can reflect the true geometry of the manifold. Experimental results on artificial and real world problems show the outperformed or comparable effectiveness of v-LPMIVSVM.