Integration of simultaneously assayed modalities using Schema. a Schema is designed for assays where multiple modalities are simultaneously measured for each cell. The researcher designates one high-confidence modality as the primary (i.e., reference) and one or more of the remaining modalities as secondary. b Each modality’s observations are mapped to points in a multi-dimensional space, with an associated distance metric that encapsulates modality-specific similarity between observations. Across the three graphs, the dashed and dotted lines indicate distances between the same pairs of observations. c Schema transforms the primary modality space by scaling each of its dimensions so that the distances in the transformed space have a higher (or lower, as desired) correlation with corresponding distances in the secondary modalities; arbitrary distance metrics are allowed for the latter. Importantly, the transformation is provably guaranteed to limit the distortion of the original space, thus ensuring that information in the primary modality is preserved. d The new point locations represent information synthesized from multiple modalities into a coherent structure. To compute the transformation, Schema weights features in the primary modality by their importance to its objective; we have found this feature selection aspect very useful in biological interpretation of its results
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