基于局部和全局映射函数的流形降维空间球形覆盖分类算法∗

摘要

为探索高维数据本质结构和低维表示，并避免一般流形学习中测试数据不能显式降维的不足，提出基于局部和全局映射函数的流形降维空间球形覆盖分类算法。该算法首先抽象融合局部和全局信息映射模型，分别优化局部拉普拉斯矩阵和全局拉普拉斯矩阵，通过对局部和全局拉普拉斯矩阵进行特征值分解，得到训练样本的低维表示。然后借助核映射获取测试样本的低维表示。最后在低维空间建立球形覆盖分类模型，实现目标分类。在MNIST手写体数据集、YaleB和AR人脸数据集上的实验表明文中算法的有效性，证明其在实际应用领域具有一定价值。%To explore the intrinsic structure and the low dimensional representation of high dimensional data and find explicit mapping in some manifold learning algorithms, spherical cover classification algorithm based on manifold dimension reduction space of local and global mapping is proposed. The mapping model combining local information and global information is extracted firstly. The local laplacian matrix and the global laplacian matrix are optimized separately. The low dimensional representation of training data is obtained by eigen-decomposition of the laplacian matrix. Then the low dimensional representation of testing data is obtained by kernel mapping. Finally, the spherical cover classification model in low dimensional space is constructed. Extensive experiments are conducted on MNIST dataset, YaleB face dataset and AR dataset, and the results verify the effectiveness of the proposed algorithm and its value in the application fields.