Matching and merging data from conflicting sources is the bread and butter of data integration, which drives search verticals, e-commerce comparison sites and cyber intelligence. Schema matching lifts data integration - traditionally focused on well-structured data - to highly heterogeneous sources. While schema matching has enjoyed significant success in matching data attributes, inconsistencies can exist at a deeper level, making full integration difficult or impossible. We propose a more fine-grained approach that focuses on correspondences between the values of attributes across data sources. Since the semantics of attribute values derive from their use and co-occurrence, we argue for the suitability of canonical correlation analysis (CCA) and its variants. We demonstrate the superior statistical and computational performance of multiple sparse CCA compared to a suite of baseline algorithms, on two datasets which we are releasing to stimulate further research. Our crowd-annotated data covers both cases that are relatively easy for humans to supply ground-truth, and that are inherently difficult for human computation.