论文标题
DLME:深层局部载流层嵌入
DLME: Deep Local-flatness Manifold Embedding
论文作者
论文摘要
多种学习(ML)旨在从高维数据中寻求低维的嵌入。这个问题在现实世界中的数据集上是具有挑战性的,尤其是在采样不足的数据中,我们发现在这种情况下,以前的方法的性能很差。通常,ML方法首先将输入数据转换为低维嵌入空间,以维护数据的几何结构,然后在其中执行下游任务。在以前的步骤中,不足采样数据的局部连通性和后期步骤中不适当的优化目标导致了两个问题:结构变形和无限制的嵌入。本文提出了一个新型的ML框架,名为“深层局部流动歧管嵌入(DLME)”来解决这些问题。所提出的DLME通过数据增强来构建语义歧管,并使用基于局部平坦度的假设来克服了结构性失真问题,并通过对歧管的局部平坦度进行了限制。为了克服无限制的嵌入问题,我们设计了一种损失,理论上证明它会根据局部平坦度导致更合适的嵌入。在三种类型的数据集(玩具,生物学和图像)上进行各种下游任务(分类,聚类和可视化)的实验表明,我们所提出的DLME胜过最先进的ML和对比度学习方法。
Manifold learning (ML) aims to seek low-dimensional embedding from high-dimensional data. The problem is challenging on real-world datasets, especially with under-sampling data, and we find that previous methods perform poorly in this case. Generally, ML methods first transform input data into a low-dimensional embedding space to maintain the data's geometric structure and subsequently perform downstream tasks therein. The poor local connectivity of under-sampling data in the former step and inappropriate optimization objectives in the latter step leads to two problems: structural distortion and underconstrained embedding. This paper proposes a novel ML framework named Deep Local-flatness Manifold Embedding (DLME) to solve these problems. The proposed DLME constructs semantic manifolds by data augmentation and overcomes the structural distortion problem using a smoothness constrained based on a local flatness assumption about the manifold. To overcome the underconstrained embedding problem, we design a loss and theoretically demonstrate that it leads to a more suitable embedding based on the local flatness. Experiments on three types of datasets (toy, biological, and image) for various downstream tasks (classification, clustering, and visualization) show that our proposed DLME outperforms state-of-the-art ML and contrastive learning methods.