Estimating Mixture of Gaussian Processes by Kernel Smoothing
针对函数型数据存在多个类别时传统方法失效的问题，提出一种结合EM算法、核回归和函数主成分分析的高斯过程混合模型估计方法，并用超市数据验证其有效性。
When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from EM algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.