# DLME: Deep Local-flatness Manifold Embedding

arXiv: https://arxiv.org/abs/2207.03160 · HTML: https://mlsanity.com/paper/2207.03160/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 7 Jul 2022.

## Builds on (most cited first, 14 of 14)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Parametric UMAP embeddings for representation and semi-supervised learning](https://mlsanity.com/paper/2009.12981/) (2020)
- [Online Deep Clustering for Unsupervised Representation Learning](https://mlsanity.com/paper/2006.10645/) (2020)
- [Deep Comprehensive Correlation Mining for Image Clustering](https://mlsanity.com/paper/1904.06925/) (2019)
- [Deep Discriminative Clustering Analysis](https://mlsanity.com/paper/1905.01681/) (2019)
- [Clustering by Maximizing Mutual Information Across Views](https://mlsanity.com/paper/2107.11635/) (2021)
- [Boosting Discriminative Visual Representation Learning with Scenario-Agnostic Mixup](https://mlsanity.com/paper/2111.15454/) (2021)
- [Extendable and invertible manifold learning with geometry regularized autoencoders](https://mlsanity.com/paper/2007.07142/) (2020)
- [Harnessing Hard Mixed Samples with Decoupled Regularizer](https://mlsanity.com/paper/2203.10761/) (2022)

## Built on by (most cited first, 16 of 16)

- [MogaNet: Multi-order Gated Aggregation Network](https://mlsanity.com/paper/2211.03295/) (2022)
- [Boosting Novel Category Discovery Over Domains with Soft Contrastive Learning and All-in-One Classifier](https://mlsanity.com/paper/2211.11262/) (2022)
- [Unsupervised visualization of image datasets using contrastive learning](https://mlsanity.com/paper/2210.09879/) (2022)
- [EVNet: An Explainable Deep Network for Dimension Reduction](https://mlsanity.com/paper/2211.15478/) (2022)
- [DiffAug: Enhance Unsupervised Contrastive Learning with Domain-Knowledge-Free Diffusion-based Data Augmentation](https://mlsanity.com/paper/2309.07909/) (2023)
- [UDRN: Unified Dimensional Reduction Neural Network for Feature Selection and Feature Projection](https://mlsanity.com/paper/2207.03809/) (2022)
- [SparseSwin: Swin Transformer with Sparse Transformer Block](https://mlsanity.com/paper/2309.05224/) (2023)
- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [PhyloGen: Language Model-Enhanced Phylogenetic Inference via Graph Structure Generation](https://mlsanity.com/paper/2412.18827/) (2024)
- [Adaptive Self-Distillation for Minimizing Client Drift in Heterogeneous Federated Learning](https://mlsanity.com/paper/2305.19600/) (2023)
- [Leader-Follower Neural Networks with Local Error Signals Inspired by Complex Collectives](https://mlsanity.com/paper/2310.07885/) (2023)
- [Deep Manifold Graph Auto-Encoder for Attributed Graph Embedding](https://mlsanity.com/paper/2401.06727/) (2024)
- [Deep Manifold Transformation for Protein Representation Learning](https://mlsanity.com/paper/2402.09416/) (2024)
- [Deep Multi-Manifold Transformation Based Multivariate Time Series Fault Detection](https://mlsanity.com/paper/2405.16258/) (2024)
- [Robust Network Learning via Inverse Scale Variational Sparsification](https://mlsanity.com/paper/2409.18419/) (2024)
- [PCaM: A Progressive Focus Attention-Based Information Fusion Method for Improving Vision Transformer Domain Adaptation](https://mlsanity.com/paper/2506.17232/) (2025)

## Abstract (arXiv)

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.