Functional Autoencoders for Functional Data Representation Learning
Functional Autoencoders for Functional Data Representation Learning
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DOI：
10.1137/1.9781611976700.75
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Tsung-Yu Hsieh;Yiwei Sun;Suhang Wang;Vasant G Honavar
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文献类型：
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作者：
Tsung-Yu Hsieh;Yiwei Sun;Suhang Wang;Vasant G Honavar
在许多实际应用中，例如监测个人健康、气候、大脑活动、环境暴露等，感兴趣的数据在连续体（例如时间）中平稳变化，从而产生多维功能数据。解决功能数据的聚类、分类和回归问题需要有效的方法来学习功能数据的紧凑表示。从功能数据中学习表示的现有方法，例如功能主成分分析，通常仅限于学习从数据空间到表示空间的线性映射。然而，在许多应用中，这样的线性方法是不够的。因此，我们研究了学习函数数据的非线性表示的新问题。具体来说，我们提出了功能自编码器，它推广了神经网络自编码器，以学习功能数据的非线性表示。我们从第一性原理推导出一种基于函数梯度的自编码器训练算法。我们提出的实验结果表明，功能自编码器优于最先进的基线方法。
In many real-world applications, e.g., monitoring of individual health, climate, brain activity, environmental exposures, among others, the data of interest change smoothly over a continuum , e.g., time, yielding multi-dimensional functional data . Solving clustering, classi-fication, and regression problems with functional data calls for effective methods for learning compact representations of functional data. Existing methods for representation learning from functional data, e.g., functional principal component analysis, are generally limited to learning linear mappings from the data space to the representation space. However, in many applications, such linear methods do not suffice. Hence, we study the novel problem of learning non-linear representations of functional data. Specifically, we propose functional autoencoders, which generalize neural network autoencoders so as to learn non-linear representations of functional data. We derive from first principles, a functional gradient based algorithm for training functional autoencoders. We present results of experiments which demonstrate that the functional autoencoders outperform the state-of-the-art baseline methods.