基于统计判据的非线性维数约简

现有非线性维数约简算法均需要人工设定适当的邻域点数而（或者邻域半径ε）才能获得合理的嵌入结果．但常用的基于嵌入残差的邻域参数选择方法本质上是循环依赖的，不能有效工作．为实现非线性维数约简算法的定量评价的参数辨识，从讨论优化嵌入的基本判定原则出发，给出了基于空域互信息和正则依赖指数谱的优化嵌入判据实现嵌入质量的定量评价和非线性维数约简算法的非监督参数辨识．仿真实验表明，直观的嵌入质量可被优化嵌入判据有效反映，且由嵌入集拟合恢复原数据集时的拟合精度与优化嵌入判据之间存在显著的正相关．

Nonlinear Dimensionality Reduction Based on Statistical Criterions

Popular nonlinear dimensionality reduction algorithms, e.g. LLE, Isomap and SIE, must configure neighborhood parameters in advance to gain meaningful embedding results. But current criteria of neighborhood parameters selection based on embedding residual are not independent of neighborhood parameters. Therefore it cannot work universally. To improve the availability of nonlinear dimensionality reduction algorithms in the field of self-adaptive manifold learning, the optimal embedding principles are discussed, and criteria of optimal embedding based on spatial mutual information and normalized dependency index spectrum are proposed to quantitatively evaluate embedding quality and achieve unsupervised parameters identifications. Simulation shows that intuitive embedding quality can be effectively indexed by proposed criteria, and there is a remarkably positive correlation between fitting precisions of embedding sets and criteria of optimal embedding.