# Learning an Invariant Hilbert Space for Domain Adaptation

arXiv: https://arxiv.org/abs/1611.08350 · HTML: https://mlsanity.com/paper/1611.08350/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2016.

## Built on by (most cited first, 17 of 17)

- [Meta-Learning for Multi-Label Few-Shot Classification](https://mlsanity.com/paper/2110.13494/) (2021)
- [From Big to Small: Adaptive Learning to Partial-Set Domains](https://mlsanity.com/paper/2203.07375/) (2022)
- [Adaptive Betweenness Clustering for Semi-Supervised Domain Adaptation](https://mlsanity.com/paper/2401.11448/) (2024)
- [Differentially Private Transferrable Deep Learning with Membership-Mappings](https://mlsanity.com/paper/2105.04615/) (2021)
- [Attention Regularized Laplace Graph for Domain Adaptation](https://mlsanity.com/paper/2210.08170/) (2022)
- [Discriminative Noise Robust Sparse Orthogonal Label Regression-based Domain Adaptation](https://mlsanity.com/paper/2101.04563/) (2021)
- [Heterogeneous Domain Adaptation with Adversarial Neural Representation Learning: Experiments on E-Commerce and Cybersecurity](https://mlsanity.com/paper/2205.07853/) (2022)
- [Normed Spaces for Graph Embedding](https://mlsanity.com/paper/2312.01502/) (2023)
- [Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent](https://mlsanity.com/paper/2407.04335/) (2024)
- [Robust Importance Sampling for Error Estimation in the Context of Optimal Bayesian Transfer Learning](https://mlsanity.com/paper/2109.02150/) (2021)
- [Beyond Batch Learning: Global Awareness Enhanced Domain Adaptation](https://mlsanity.com/paper/2502.06272/) (2025)
- [Information Theoretic Evaluation of Privacy-Leakage, Interpretability, and Transferability for Trustworthy AI](https://mlsanity.com/paper/2106.06046/) (2021)
- [ISTRBoost: Importance Sampling Transfer Regression using Boosting](https://mlsanity.com/paper/2204.12044/) (2022)
- [Cross-Domain Label Propagation for Domain Adaptation with Discriminative Graph Self-Learning](https://mlsanity.com/paper/2302.08710/) (2023)
- [SIDE: Self-supervised Intermediate Domain Exploration for Source-free Domain Adaptation](https://mlsanity.com/paper/2310.08928/) (2023)
- [Decision Boundary Optimization-Informed Domain Adaptation](https://mlsanity.com/paper/2502.06498/) (2025)
- [Model Recycling Framework for Multi-Source Data-Free Supervised Transfer Learning](https://mlsanity.com/paper/2508.02039/) (2025)

## Abstract (arXiv)

This paper introduces a learning scheme to construct a Hilbert space (i.e., a vector space along its inner product) to address both unsupervised and semi-supervised domain adaptation problems. This is achieved by learning projections from each domain to a latent space along the Mahalanobis metric of the latent space to simultaneously minimizing a notion of domain variance while maximizing a measure of discriminatory power. In particular, we make use of the Riemannian optimization techniques to match statistical properties (e.g., first and second order statistics) between samples projected into the latent space from different domains. Upon availability of class labels, we further deem samples sharing the same label to form more compact clusters while pulling away samples coming from different classes.We extensively evaluate and contrast our proposal against state-of-the-art methods for the task of visual domain adaptation using both handcrafted and deep-net features. Our experiments show that even with a simple nearest neighbor classifier, the proposed method can outperform several state-of-the-art methods benefitting from more involved classification schemes.