Extracting Common Components from Partially Observed Views Using Diffusion Geometry

TMLR Paper7837 Authors

Abstract: Data acquired from multiple sensors or modalities, commonly referred to as multiview data, is prevalent in real-world applications. A core problem in multiview data analysis is finding representations of common components across views while filtering out view-specific nuisance factors. A widely spread assumption in existing methods is that the views are fully aligned, where each sample has measurements from all views. However, in practice, data is often partially aligned, where some samples have missing measurements from one or more views, and only a subset of the samples are fully aligned. In this work, we propose ADM+, a multiview manifold learning algorithm that computes a low-dimensional embedding of common information from partially aligned data. ADM+ extends Alternating Diffusion Maps (ADM), an existing multiview manifold learning method, to the partial alignment setting by using fully aligned samples as anchor points for extracting common components for unaligned samples. Unlike existing methods, ADM+ does not require prior imputation of missing data or interpolation in the embedding space and makes use of all available data. We provide a computationally efficient implementation, improving upon the $O(N^3)$ time complexity of ADM, and a theoretical analysis showing that ADM+ approximates an anisotropic diffusion process that emphasizes common components. Empirical evaluations across three domains -- dynamical systems, synthetic multiview images, and real-world functional magnetic resonance imaging (fMRI) -- demonstrate that ADM+ achieves favorable performance compared to kernel- and manifold-based baselines. In addition, ADM+ shows robustness to distributional discrepancies between aligned and unaligned samples.

Submission Type: Regular submission (no more than 12 pages of main content)

Assigned Action Editor: ~Mehrtash_T._Harandi1

Submission Number: 7837