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Clustering of Longitudinal Shape Data Sets Using Mixture of Separate or Branching Trajectories

机译:使用单独或分支轨迹的混合物聚集纵向形状数据集

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Several methods have been proposed recently to learn spa-tiotemporal models of shape progression from repeated observations of several subjects over time, i.e. a longitudinal data set. These methods summarize the population by a single common trajectory in a supervised manner. In this paper, we propose to extend such approaches to an unsupervised setting where a longitudinal data set is automatically clustered in different classes without labels. Our method learns for each cluster an average shape trajectory (or representative curve) and its variance in space and time. Representative trajectories are built as the combination of pieces of curves. This mixture model is flexible enough to handle independent trajectories for each cluster as well as fork and merge scenarios. The estimation of such non linear mixture models in high dimension is known to be difficult because of the trapping states effect that hampers the optimisation of cluster assignments during training. We address this issue by using a tempered version of the stochastic EM algorithm. Finally, we apply our algorithm on synthetic data to validate that a tempered scheme achieve better convergence. We show then how the method can be used to test different scenarios of hippocampus atrophy in ageing by using an heteregenous population of normal ageing individuals and mild cognitive impaired subjects.
机译:最近已经提出了几种方法来学习从几次对象的重复观察的形状进展的水疗模型,即纵向数据集。这些方法以监督方式通过单个共同轨迹总结了人口。在本文中,我们建议将这种方法扩展到无监督的设置,其中纵向数据集在没有标签的不同类别中自动聚集在一起。我们的方法学习每个集群的平均形状轨迹(或代表性曲线)及其在空间和时间方差。代表性轨迹是作为曲线碎片的组合构建的。该混合模型足够灵活,可以为每个群集处理独立轨迹以及FORK和合并方案。已知在高尺寸中估计这种非线性混合模型,因为捕获在训练期间的集群分配优化的捕获状态效应难以困难。我们通过使用随机EM算法的钢化版本来解决此问题。最后,我们在合成数据上应用算法以验证回火方案实现更好的收敛。我们展示了通过使用正常老化个体和轻度认知受损受试者的HetereGayous群体来测试该方法如何使用衰老的不同情景。

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