Beyond Mapping : Domain-Invariant Representations via Spectral Embedding of Optimal Transport Plans

TL;DR

The paper addresses performance degradation due to distributional shifts by proposing Spectral Embedding of Optimal Transport Plans (SeOT) for domain adaptation. Rather than learning a direct mapping, SeOT treats smoothed OT plans $\gamma^*$ as adjacency graphs and applies spectral embedding on the resulting cross-domain graph to obtain domain-invariant, discriminative representations. A multi-source extension uses a Wasserstein barycenter to connect multiple sources and the target, building a unified graph for spectral analysis. Empirical evaluation on MSD, MGR, and CS-RT demonstrates competitive or superior gains over source-only baselines and several OT-based methods, highlighting the practical impact for acoustic and industrial sensing tasks. The approach offers a principled, graph-based interpretation of OT alignments that can be extended to out-of-sample data embedding and other cross-domain settings.

Abstract

Distributional shifts between training and inference time data remain a central challenge in machine learning, often leading to poor performance. It motivated the study of principled approaches for domain alignment, such as optimal transport based unsupervised domain adaptation, that relies on approximating Monge map using transport plans, which is sensitive to the transport problem regularization strategy and hyperparameters, and might yield biased domains alignment. In this work, we propose to interpret smoothed transport plans as adjacency matrices of bipartite graphs connecting source to target domain and derive domain-invariant samples' representations through spectral embedding. We evaluate our approach on acoustic adaptation benchmarks for music genre recognition, music-speech discrimination, as well as electrical cable defect detection and classification tasks using time domain reflection in different diagnosis settings, achieving overall strong performances.

Figures (2)

• Figure 1: Illustration of SeOT: (Left) Data from 3 labeled source domains and unlabeled target domain. (center-left) Domains connectivity through Wasserstein barycenter, where the lines connecting different domains refer to the optimal transport plans. (center-right) Constructed adjacency matrix ($\mathcal{A}$) derived from optimal transport plans between domains. (Right) Spectral embeddings of the unified graph representation, demonstrating that class clusters are well-separated in the latent space.
• Figure 2: The effect of embedding size $k$ on the spectral gap and the average classification accuracy for MSD dataset.