Skip to yearly menu bar Skip to main content


Co-manifold learning with missing data

Gal Mishne · Eric Chi · Ronald Coifman

Pacific Ballroom #267

Keywords: [ Unsupervised Learning ] [ Representation Learning ] [ Non-convex Optimization ] [ Dimensionality Reduction ] [ Convex Optimization ]


Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled structure to perform co-manifold learning: uncovering the underlying geometry of both the rows and the columns of a given matrix, where we focus on a missing data setting. Our unsupervised approach consists of three components. We first solve a family of optimization problems to estimate a complete matrix at multiple scales of smoothness. We then use this collection of smooth matrix estimates to compute pairwise distances on the rows and columns based on a new multi-scale metric that implicitly introduces a coupling between the rows and the columns. Finally, we construct row and column representations from these multi-scale metrics. We demonstrate that our approach outperforms competing methods in both data visualization and clustering.

Live content is unavailable. Log in and register to view live content