Meinicke Peter, Klanke Stefan, Memisevic Roland, Ritter Helge
P. Meinicke is with the Bioinformatics Department, Faculty of Biology, University of Göttingen, Goldschmidtstr. 1, 37077 Göttingen, Germany.
IEEE Trans Pattern Anal Mach Intell. 2005 Sep;27(9):1379-91. doi: 10.1109/TPAMI.2005.183.
We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the Nadaraya-Watson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides a practical solution to the model selection problem because all parameters can be estimated by leave-one-out cross-validation without additional computational cost. In addition, our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization, beyond classical initializations based on linear PCA. Furthermore, it shows a simple way to fit principal surfaces in general feature spaces, beyond the usual data space setup. The experimental results illustrate these convenient features on simulated and real data.
我们提出了一种基于 Nadaraya-Watson 核回归估计器的无监督公式来学习主曲面的非参数方法。与先前的主曲线和曲面方法相比，新方法具有几个优点：首先，它为模型选择问题提供了一个实际的解决方案，因为所有参数都可以通过留一法交叉验证进行估计，而无需额外的计算成本。此外，我们的方法允许方便地纳入用于参数初始化的非线性谱方法，超越了基于线性主成分分析（PCA）的经典初始化方法。此外，它展示了一种在一般特征空间中拟合主曲面的简单方法，超越了通常的数据空间设置。实验结果在模拟数据和真实数据上展示了这些便利的特性。
