Archetypes are typical population representatives in an extremal sense, where typicality is understood as the most extreme manifestation of a trait or feature. In linear feature space, archetypes approximate the data convex hull allowing all data points to be expressed as convex mixtures of archetypes. However, it might not always be possible to identify meaningful archetypes in a given feature space. Learning an appropriate feature space and identifying suitable archetypes simultaneously addresses this problem. This paper introduces a generative formulation of the linear archetype model, parameterized by neural networks. By introducing the distance-dependent archetype loss, the linear archetype model can be integrated into the latent space of a variational autoencoder, and an optimal representation with respect to the unknown archetypes can be learned end-to-end. The reformulation of linear Archetypal Analysis as deep variational information bottleneck, allows the incorporation of arbitrarily complex side information during training. Furthermore, an alternative prior, based on a modified Dirichlet distribution, is proposed. The real-world applicability of the proposed method is demonstrated by exploring archetypes of female facial expressions while using multi-rater based emotion scores of these expressions as side information. A second application illustrates the exploration of the chemical space of small organic molecules. In this experiment, it is demonstrated that exchanging the side information but keeping the same set of molecules, e. g. using as side information the heat capacity of each molecule instead of the band gap energy, will result in the identification of different archetypes. As an application, these learned representations of chemical space might reveal distinct starting points for de novo molecular design.

中文翻译：

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通过深度原型分析学习极值表示

原型是极端意义上的典型人口代表，其中典型性被理解为特征或特征的最极端表现。在线性特征空间中，原型近似于数据凸包，允许所有数据点表示为原型的凸混合。然而，在给定的特征空间中识别有意义的原型可能并不总是可能的。学习合适的特征空间和识别合适的原型同时解决了这个问题。本文介绍了由神经网络参数化的线性原型模型的生成公式。通过引入与距离相关的原型损失，线性原型模型可以集成到变分自编码器的潜在空间中，并且可以端到端地学习关于未知原型的最佳表示。线性原型分析作为深度变分信息瓶颈的重新表述，允许在训练期间合并任意复杂的辅助信息。此外，提出了一种基于修正的狄利克雷分布的替代先验。通过探索女性面部表情的原型，同时使用这些表情的基于多评分者的情感分数作为辅助信息，证明了所提出方法的实际适用性。第二个应用说明了对有机小分子化学空间的探索。在这个实验中，证明了交换辅助信息但保持相同的分子集，例如 使用每个分子的热容量而不是带隙能量作为辅助信息，将导致识别不同的原型。作为一种应用，这些化学空间的学习表示可能会揭示从头分子设计的不同起点。