# Manifold Alignment with Label Information

arXiv: https://arxiv.org/abs/2210.12774 · HTML: https://mlsanity.com/paper/2210.12774/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [A Brief Review of Domain Adaptation](https://mlsanity.com/paper/2010.03978/) (2020)
- [MAGAN: Aligning Biological Manifolds](https://mlsanity.com/paper/1803.00385/) (2018)
- [Kernel Manifold Alignment](https://mlsanity.com/paper/1504.02338/) (2015)
- [Geometry-Based Data Generation](https://mlsanity.com/paper/1802.04927/) (2018)
- [Diffusion Transport Alignment](https://mlsanity.com/paper/2206.07305/) (2022)
- [MultiView Diffusion Maps](https://mlsanity.com/paper/1508.05550/) (2015)
- [Semisupervised Manifold Alignment of Multimodal Remote Sensing Images](https://mlsanity.com/paper/2104.07803/) (2021)

## Built on by (most cited first, 5 of 5)

- [Graph Integration for Diffusion-Based Manifold Alignment](https://mlsanity.com/paper/2410.22978/) (2024)
- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)
- [Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders](https://mlsanity.com/paper/2509.22913/) (2025)
- [Boosting Hyperspectral Image Classification with Gate-Shift-Fuse Mechanisms in a Novel CNN-Transformer Approach](https://mlsanity.com/paper/2406.14120/) (2024)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

Multi-domain data is becoming increasingly common and presents both challenges and opportunities in the data science community. The integration of distinct data-views can be used for exploratory data analysis, and benefit downstream analysis including machine learning related tasks. With this in mind, we present a novel manifold alignment method called MALI (Manifold alignment with label information) that learns a correspondence between two distinct domains. MALI can be considered as belonging to a middle ground between the more commonly addressed semi-supervised manifold alignment problem with some known correspondences between the two domains, and the purely unsupervised case, where no known correspondences are provided. To do this, MALI learns the manifold structure in both domains via a diffusion process and then leverages discrete class labels to guide the alignment. By aligning two distinct domains, MALI recovers a pairing and a common representation that reveals related samples in both domains. Additionally, MALI can be used for the transfer learning problem known as domain adaptation. We show that MALI outperforms the current state-of-the-art manifold alignment methods across multiple datasets.