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

TL;DR

This paper introduces a spectral embedding method of optimal transport plans to create domain-invariant representations, improving performance across various domain adaptation tasks with distributional shifts.

Contribution

It proposes interpreting smoothed transport plans as bipartite graph adjacency matrices and deriving domain-invariant features via spectral embedding, addressing biases in traditional optimal transport methods.

Findings

Strong performance on acoustic adaptation benchmarks.

Effective in electrical cable defect detection.

Robust across multiple domain shift scenarios.

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.