Large-scale Data Integration using Matrix Denoising and Geometric Factor Matching

Unsupervised integrative analysis of multiple data sources has become common place and scalable algorithms are necessary to accommodate ever increasing availability of data. Only few currently methods have estimation speed as their focus, and those that do are only applicable to restricted data layouts such as different data types measured on the same observation units. We introduce a novel point of view on low-rank matrix integration phrased as a graph estimation problem which allows development of a method, large-scale Collective Matrix Factorization (lsCMF), which is able to integrate data in flexible layouts in a speedy fashion. It utilizes a matrix denoising framework for rank estimation and geometric properties of singular vectors to efficiently integrate data. The quick estimation speed of lsCMF while retaining good estimation of data structure is then demonstrated in simulation studies.