Geometry Regularized Autoencoders
Geometry Regularized Autoencoders
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DOI：
10.1109/tpami.2022.3222104
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发表时间：
2022-11
影响因子：
23.6
通讯作者：
Andres F. Duque;Sacha Morin;Guy Wolf;Kevin R. Moon
中科院分区：
文献类型：
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作者：
Andres F. Duque;Sacha Morin;Guy Wolf;Kevin R. Moon
数据探索中的一个基本任务是提取低维表示，这些表示捕获数据中的内在几何形状，特别是用于忠实地可视化二维或三维数据。常见的方法使用核方法进行流形学习。然而，这些方法通常仅提供输入数据的嵌入，并且不能自然地扩展到新的数据点。自动编码器在表示学习中也很受欢迎。虽然它们自然地计算可扩展到新数据并且可逆的特征提取器（即，从潜在表示重建原始特征），但与基于内核的流形学习相比，它们通常无法表示内在数据几何形状。我们提出了一种新的方法，通过将几何正则化项的自动编码器的瓶颈集成这两种方法。这种正则化鼓励学习的潜在表示遵循内在的数据几何形状，类似于流形学习算法，同时仍然能够忠实地扩展到新数据并保持可逆性。我们将我们的方法与用于流形学习的自动编码器模型进行比较，以提供定性和定量证据来证明我们在保留内在结构、样本扩展和重建方面的优势。我们的方法很容易实现大数据应用程序，而其他方法在这方面是有限的。
A fundamental task in data exploration is to extract low dimensional representations that capture intrinsic geometry in data, especially for faithfully visualizing data in two or three dimensions. Common approaches use kernel methods for manifold learning. However, these methods typically only provide an embedding of the input data and cannot extend naturally to new data points. Autoencoders have also become popular for representation learning. While they naturally compute feature extractors that are extendable to new data and invertible (i.e., reconstructing original features from latent representation), they often fail at representing the intrinsic data geometry compared to kernel-based manifold learning. We present a new method for integrating both approaches by incorporating a geometric regularization term in the bottleneck of the autoencoder. This regularization encourages the learned latent representation to follow the intrinsic data geometry, similar to manifold learning algorithms, while still enabling faithful extension to new data and preserving invertibility. We compare our approach to autoencoder models for manifold learning to provide qualitative and quantitative evidence of our advantages in preserving intrinsic structure, out of sample extension, and reconstruction. Our method is easily implemented for big-data applications, whereas other methods are limited in this regard.