# When Unsupervised Domain Adaptation Meets Tensor Representations

arXiv: https://arxiv.org/abs/1707.05956 · HTML: https://mlsanity.com/paper/1707.05956/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2017.

## Built on by (most cited first, 7 of 7)

- [Seeking Similarities over Differences: Similarity-based Domain Alignment for Adaptive Object Detection](https://mlsanity.com/paper/2110.01428/) (2021)
- [Learning to Relate Depth and Semantics for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2105.07830/) (2021)
- [Domain-Specific Suppression for Adaptive Object Detection](https://mlsanity.com/paper/2105.03570/) (2021)
- [Improving speech recognition models with small samples for air traffic control systems](https://mlsanity.com/paper/2102.08015/) (2021)
- [Deep Learning Techniques for Visual Counting](https://mlsanity.com/paper/2206.03033/) (2022)
- [Deep Image Semantic Communication Model for Artificial Intelligent Internet of Things](https://mlsanity.com/paper/2311.02926/) (2023)
- [Visually Similar Pair Alignment for Robust Cross-Domain Object Detection](https://mlsanity.com/paper/2504.06607/) (2025)

## Abstract (arXiv)

Domain adaption (DA) allows machine learning methods trained on data sampled from one distribution to be applied to data sampled from another. It is thus of great practical importance to the application of such methods. Despite the fact that tensor representations are widely used in Computer Vision to capture multi-linear relationships that affect the data, most existing DA methods are applicable to vectors only. This renders them incapable of reflecting and preserving important structure in many problems. We thus propose here a learning-based method to adapt the source and target tensor representations directly, without vectorization. In particular, a set of alignment matrices is introduced to align the tensor representations from both domains into the invariant tensor subspace. These alignment matrices and the tensor subspace are modeled as a joint optimization problem and can be learned adaptively from the data using the proposed alternative minimization scheme. Extensive experiments show that our approach is capable of preserving the discriminative power of the source domain, of resisting the effects of label noise, and works effectively for small sample sizes, and even one-shot DA. We show that our method outperforms the state-of-the-art on the task of cross-domain visual recognition in both efficacy and efficiency, and particularly that it outperforms all comparators when applied to DA of the convolutional activations of deep convolutional networks.