Kernel Manifold Alignment

TL;DR

This paper presents KEMA, a kernel-based manifold alignment method that handles multiple data sources with minimal supervision, offering robustness, flexibility, and invertibility for domain adaptation and data synthesis.

Contribution

KEMA is a novel kernel method that generalizes manifold alignment, enabling alignment of diverse data sources without paired samples, and introduces a reduced-rank version for efficiency.

Findings

KEMA outperforms competing methods in synthetic and real-world tasks.

It effectively aligns manifolds of different complexities and dimensions.

KEMA demonstrates robustness to nonlinear feature deformations.

Abstract

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible which allows transfer across-domains and data synthesis. We also present a reduced-rank version for computational efficiency and discuss the generalization performance of KEMA under Rademacher principles of stability. KEMA exhibits very good performance over competing methods in synthetic examples, visual object recognition and recognition of facial expressions tasks.