# Scatter Component Analysis: A Unified Framework for Domain Adaptation and Domain Generalization

arXiv: https://arxiv.org/abs/1510.04373 · HTML: https://mlsanity.com/paper/1510.04373/

## Key facts

- Cited by 96 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2015.

## Built on by (most cited first, 30 of 96)

- [Generalizing to Unseen Domains: A Survey on Domain Generalization](https://mlsanity.com/paper/2103.03097/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Towards Out-Of-Distribution Generalization: A Survey](https://mlsanity.com/paper/2108.13624/) (2021)
- [Domain Adaptation for Medical Image Analysis: A Survey](https://mlsanity.com/paper/2102.09508/) (2021)
- [A Fourier-based Framework for Domain Generalization](https://mlsanity.com/paper/2105.11120/) (2021)
- [Causality Inspired Representation Learning for Domain Generalization](https://mlsanity.com/paper/2203.14237/) (2022)
- [Open Domain Generalization with Domain-Augmented Meta-Learning](https://mlsanity.com/paper/2104.03620/) (2021)
- [Model-Based Domain Generalization](https://mlsanity.com/paper/2102.11436/) (2021)
- [AdaMatch: A Unified Approach to Semi-Supervised Learning and Domain Adaptation](https://mlsanity.com/paper/2106.04732/) (2021)
- [Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectives](https://mlsanity.com/paper/2208.07422/) (2022)
- [OoD-Bench: Quantifying and Understanding Two Dimensions of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.03721/) (2021)
- [NICO++: Towards Better Benchmarking for Domain Generalization](https://mlsanity.com/paper/2204.08040/) (2022)
- [Prompt Vision Transformer for Domain Generalization](https://mlsanity.com/paper/2208.08914/) (2022)
- [Rethinking Domain Generalization for Face Anti-spoofing: Separability and Alignment](https://mlsanity.com/paper/2303.13662/) (2023)
- [Improved Test-Time Adaptation for Domain Generalization](https://mlsanity.com/paper/2304.04494/) (2023)
- [Style Normalization and Restitution for Domain Generalization and Adaptation](https://mlsanity.com/paper/2101.00588/) (2021)
- [Out-of-distribution Generalization with Causal Invariant Transformations](https://mlsanity.com/paper/2203.11528/) (2022)
- [Semi-Supervised Domain Generalization with Stochastic StyleMatch](https://mlsanity.com/paper/2106.00592/) (2021)
- [Modeling the Data-Generating Process is Necessary for Out-of-Distribution Generalization](https://mlsanity.com/paper/2206.07837/) (2022)
- [Embracing the Dark Knowledge: Domain Generalization Using Regularized Knowledge Distillation](https://mlsanity.com/paper/2107.02629/) (2021)
- [Self-Adversarial Disentangling for Specific Domain Adaptation](https://mlsanity.com/paper/2108.03553/) (2021)
- [On Generalizing Beyond Domains in Cross-Domain Continual Learning](https://mlsanity.com/paper/2203.03970/) (2022)
- [Learning to Generalize across Domains on Single Test Samples](https://mlsanity.com/paper/2202.08045/) (2022)
- [Generalized Domain Conditioned Adaptation Network](https://mlsanity.com/paper/2103.12339/) (2021)
- [ManyDG: Many-domain Generalization for Healthcare Applications](https://mlsanity.com/paper/2301.08834/) (2023)
- [Controllable and Guided Face Synthesis for Unconstrained Face Recognition](https://mlsanity.com/paper/2207.10180/) (2022)
- [Domain Generalization under Conditional and Label Shifts via Variational Bayesian Inference](https://mlsanity.com/paper/2107.10931/) (2021)
- [Variational Disentanglement for Domain Generalization](https://mlsanity.com/paper/2109.05826/) (2021)
- [Toward cross-subject and cross-session generalization in EEG-based emotion recognition: Systematic review, taxonomy, and methods](https://mlsanity.com/paper/2212.08744/) (2022)
- [Not Just Pretty Pictures: Toward Interventional Data Augmentation Using Text-to-Image Generators](https://mlsanity.com/paper/2212.11237/) (2022)

## Abstract (arXiv)

This paper addresses classification tasks on a particular target domain in which labeled training data are only available from source domains different from (but related to) the target. Two closely related frameworks, domain adaptation and domain generalization, are concerned with such tasks, where the only difference between those frameworks is the availability of the unlabeled target data: domain adaptation can leverage unlabeled target information, while domain generalization cannot. We propose Scatter Component Analyis (SCA), a fast representation learning algorithm that can be applied to both domain adaptation and domain generalization. SCA is based on a simple geometrical measure, i.e., scatter, which operates on reproducing kernel Hilbert space. SCA finds a representation that trades between maximizing the separability of classes, minimizing the mismatch between domains, and maximizing the separability of data; each of which is quantified through scatter. The optimization problem of SCA can be reduced to a generalized eigenvalue problem, which results in a fast and exact solution. Comprehensive experiments on benchmark cross-domain object recognition datasets verify that SCA performs much faster than several state-of-the-art algorithms and also provides state-of-the-art classification accuracy in both domain adaptation and domain generalization. We also show that scatter can be used to establish a theoretical generalization bound in the case of domain adaptation.