用自编码器实现可参数化且可逆的降维，支持新数据嵌入与生成。
Evaluating Autoencoders for Parametric and Invertible Multidimensional Projections
- 设计定制损失函数的自编码器，学习2D嵌入与原空间逆映射。
- 在四个不同维度和复杂度的数据集上，投影平滑性优于前馈网络。
- 适合需要可逆降维与灵活控制平滑度的研究者使用。
近年来，神经网络被用于构建参数化且可逆的多维数据投影。参数化投影允许在不重新计算整体投影的情况下嵌入未见数据，而可逆投影则支持生成新数据点。然而，这些特性尚未在任意投影方法中同时探索。本文评估了三种自编码器（AE）架构，用于创建参数化且可逆的投影。基于给定投影，训练AE学习映射至2D空间及反向映射回原始空间。我们在四个维度和模式复杂度各异的数据集上，采用t-SNE进行定量与定性比较。结果表明，带有定制损失函数的自编码器能生成比前馈网络更平滑的参数化与逆向投影，同时使用户可控制平滑程度的强弱。
原文摘要 · Abstract (English)
Recently, neural networks have gained attention for creating parametric and invertible multidimensional data projections. Parametric projections allow for embedding previously unseen data without recomputing the projection as a whole, while invertible projections enable the generation of new data points. However, these properties have never been explored simultaneously for arbitrary projection methods. We evaluate three autoencoder (AE) architectures for creating parametric and invertible projections. Based on a given projection, we train AEs to learn a mapping into 2D space and an inverse mapping into the original space. We perform a quantitative and qualitative comparison on four datasets of varying dimensionality and pattern complexity using t-SNE. Our results indicate that AEs with a customized loss function can create smoother parametric and inverse projections than feed-forward neural networks while giving users control over the strength of the smoothing effect.
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