The value of supervised dimensionality reduction lies in its ability to uncover meaningful connections between data features and labels. Common dimensionality reduction methods embed a set of fixed, latent points, but are not capable of generalizing to an unseen test set. In this paper, we provide an out-of-sample extension method for the random forest-based supervised dimensionality reduction method, RF-PHATE, combining information learned from the random forest model with the function-learning capabilities of autoencoders. Through quantitative assessment of various autoencoder architectures, we identify that networks that reconstruct random forest proximities are more robust for the embedding extension problem. Furthermore, by leveraging proximity-based prototypes, we achieve a 40% reduction in training time without compromising extension quality. Our method does not require label information for out-of-sample points, thus serving as a semi-supervised method, and can achieve consistent quality using only 10% of the training data.

通过结合随机森林模型和自编码器的功能学习能力，我们为基于随机森林的监督降维方法RF-PHATE提供了一种新的样本外扩展方法，并通过定量评估不同自编码器结构，发现了用于嵌入扩展问题的网络结构，进一步地，通过利用基于邻近性的原型，我们在不降低扩展质量的情况下实现了40%的训练时间的减少。我们的方法不需要样本外样本的标签信息，因此作为半监督方法，并且仅使用10%的训练数据也可以获得一致的质量。

通过自编码器和随机森林相似性提升监督可视化的样本外扩展