# Kernel Manifold Alignment

arXiv: https://arxiv.org/abs/1504.02338 · HTML: https://mlsanity.com/paper/1504.02338/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2015.

## Built on by (most cited first, 13 of 13)

- [Recent Advances in Domain Adaptation for the Classification of Remote Sensing Data](https://mlsanity.com/paper/2104.07778/) (2021)
- [Multimodal Remote Sensing Benchmark Datasets for Land Cover Classification with A Shared and Specific Feature Learning Model](https://mlsanity.com/paper/2105.10196/) (2021)
- [Diffusion Transport Alignment](https://mlsanity.com/paper/2206.07305/) (2022)
- [Manifold Alignment with Label Information](https://mlsanity.com/paper/2210.12774/) (2022)
- [Graph Integration for Diffusion-Based Manifold Alignment](https://mlsanity.com/paper/2410.22978/) (2024)
- [Cross-Modal and Multimodal Data Analysis Based on Functional Mapping of Spectral Descriptors and Manifold Regularization](https://mlsanity.com/paper/2105.05631/) (2021)
- [Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets](https://mlsanity.com/paper/2407.01718/) (2024)
- [Random Forest-Supervised Manifold Alignment](https://mlsanity.com/paper/2411.15179/) (2024)
- [Reuse out-of-year data to enhance land cover mapping via feature disentanglement and contrastive learning](https://mlsanity.com/paper/2404.11114/) (2024)
- [Testing using Privileged Information by Adapting Features with Statistical Dependence](https://mlsanity.com/paper/2111.02865/) (2021)
- [Graph Embedding via High Dimensional Model Representation for Hyperspectral Images](https://mlsanity.com/paper/2111.14680/) (2021)
- [Interpretable Hyperspectral AI: When Non-Convex Modeling meets Hyperspectral Remote Sensing](https://mlsanity.com/paper/2103.01449/) (2021)
- [Forest-Guided Semantic Transport for Label-Supervised Manifold Alignment](https://mlsanity.com/paper/2602.00974/) (2026)

## Abstract (arXiv)

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible which allows transfer across-domains and data synthesis. We also present a reduced-rank version for computational efficiency and discuss the generalization performance of KEMA under Rademacher principles of stability. KEMA exhibits very good performance over competing methods in synthetic examples, visual object recognition and recognition of facial expressions tasks.