Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent space. We use a local distance preserving loss that is based on the continuous k-nearest neighbours graph which is known to capture topological features at all scales simultaneously. To improve training performance, we formulate learning as a constraint optimisation problem with local distance preservation as the main objective and reconstruction accuracy as a constraint. We generalise this approach to hierarchical variational auto-encoders thus learning generative models with geometrically consistent latent and data spaces. Our method provides state-of-the-art performance across several standard datasets and evaluation metrics.

翻译：保持数据相似的自动编码模型是典型的代言学习工具。 在本文中, 我们引入了几个自动编码模型, 在绘制数据空间到潜空时保持本地距离。 我们使用基于连续 K 近邻图的本地远程保存损失模型, 该图可以同时捕捉所有尺度的地貌特征。 为了提高培训绩效, 我们将学习作为一种制约性优化问题, 将本地远程保存作为主要目标, 重建准确性作为制约。 我们将这一方法推广到等级变异自动编码器, 从而学习具有几何一致的潜值和数据空间的基因模型。 我们的方法提供了多个标准数据集和评估指标的最新性能 。