A new method for clustering functional data is proposed via information maximization. The proposed method learns a probabilistic classifier in an unsupervised manner so that mutual information (or squared loss mutual information) between data points and cluster assignments is maximized. A notable advantage of this proposed method is that it only involves continuous optimization of model parameters, which is simpler than discrete optimization of cluster assignments and avoids the disadvantages of generative models. Unlike some existing methods, the proposed method does not require estimating the probability densities of Karhunen-Lo`eve expansion scores under different clusters and also does not require the common eigenfunction assumption. The empirical performance and the applications of the proposed methods are demonstrated by simulation studies and real data analyses. In addition, the proposed method allows for out-of-sample clustering, and its effect is comparable with that of some supervised classifiers.
翻译:通过信息最大化,提出了将功能数据分组的新方法;拟议方法以未受监督的方式学习了一种概率分类法,以便数据点和组群任务之间的相互信息(或平损相互信息)最大化;这一拟议方法的一个显著优点是,它仅涉及连续优化模型参数,这比分散地优化集束任务并避免基因化模型的不利之处更为简单;与某些现行方法不同,拟议方法并不要求估计不同组群下Karhunen-Lo`eve扩展分的概率密度,也不要求通用的机能假设;模拟研究和真实数据分析表明了所提议方法的经验性表现和应用;此外,拟议方法允许外合成群集,其效果与某些受监督的分类师相似。