In this article, a new method, called FWP, is proposed for clustering longitudinal curves. In the proposed method, clusters of mean functions are identified through a weighted concave pairwise fusion method. The EM algorithm and the alternating direction method of multiplier algorithm are combined to estimate the group structure, mean functions and the principal components simultaneously. The proposed method also allows to incorporate the prior neighborhood information to have more meaningful groups by adding pairwise weights in the pairwise penalties. In the simulation study, the performance of the proposed method is compared to some existing clustering methods in terms of the accuracy for estimating the number of subgroups and mean functions. The results suggest that ignoring covariance structure will have a great effect on the performance of estimating the number of groups and estimating accuracy. The effect of including pairwise weights is also explored in a spatial lattice setting to take consideration of the spatial information. The results show that incorporating spatial weights will improve the performance. A real example is used to illustrate the proposed method.

翻译：本文提出了一种名为FWP的新方法，用于纵向曲线的聚类。在该方法中，通过加权凹型成对融合方法识别均值函数的聚类结构。为了同时估计群组结构、均值函数及主成分，本文结合了EM算法与交替方向乘子法。所提方法还允许在成对惩罚项中引入先验邻域信息权重，从而形成更具意义的群组。在模拟研究中，从估计子群数量与均值函数的准确性角度，将所提方法与现有聚类方法进行了比较。结果表明，忽略协方差结构将显著影响群组数量估计与估计精度。本文还在空间格点设置中探讨了加入成对权重的影响，以考虑空间信息。结果显示，引入空间权重能够提升性能。通过一个实际案例对所提方法进行了说明。