Guided Manifold Alignment with Geometry-Regularized Twin Autoencoders

Abstract--Manifold alignment (MA) involves a set of techniques for learning shared representations across domains, yet many traditional MA methods are incapable of performing out-of-sample extension, limiting their real-world applicability. We propose a guided representation learning framework leveraging a geometry-regularized twin autoencoder (AE) architecture to enhance MA while enabling generalization to unseen data. Our method enforces structured cross-modal mappings to maintain geometric fidelity in learned embeddings. By incorporating a pre-trained alignment model and a multitask learning formulation, we improve cross-domain generalization and representation robustness while maintaining alignment fidelity. We evaluate our approach using several MA methods, showing improvements in embedding consistency, information preservation, and cross-domain transfer . Additionally, we apply our framework to Alzheimer's disease diagnosis, demonstrating its ability to integrate multi-modal patient data and enhance predictive accuracy in cases limited to a single domain by leveraging insights from the multi-modal problem. Manifold learning encompasses a set of methods used to create a lower-dimensional representation, or an embedding, of higher-dimensional data. Such representations can form a key role in data visualization [1]-[5], dimensionality reduction as a preprocessing step for subsequent machine-learning or analytical tasks [6], or serve as a denoising mechanism [4]. In the context of multi-domain problems, where multiple types of data are considered, manifold learning becomes more challenging as data distributions across different domains or modalities may exhibit domain-specific variations while still sharing a common geometric structure. Manifold alignment (MA) seeks to address this problem. In some contexts, a common, shared representation of multi-modal data can be viewed as a natural extension of manifold learning. For example, cell samples of the same type but collected at a different time or using different methodologies should still share features in common, but differences in the measured features may occur due to batch effects [7], obscuring the similarities.