Structured data decomposition integrates clinical measurements with varying degrees of overlap. A) General approach description. Patients with MRSA bacteremia treated with vancomycin had samples collected at admission and then were monitored 5 days post-admission for clearance of MRSA from the bloodstream. Measurements of patient serum cytokine, plasma cytokine, and whole blood transcriptional profiles were assessed. These measurements were then reduced into overall factors describing patterns within the data, which in turn were used to assign disease outcomes, defined as resolving (RB) or persisting (PB) bacteremia. B) Overall structure of the data. Cytokine measurements from either plasma or serum can be arranged in a 3D tensor, wherein each dimension indicates patient, cytokine, or sample source, respectively. In parallel, gene expression measurements are aligned with cytokine measurements by virtue of sharing patients. C) Data reduction is performed by identifying additively separable components represented by the outer product of vectors along each dimension. The patient factors are shared across both the tensor and matrix reconstruction. D) Venn diagram of the variance explained by each factorization method. Canonical polyadic (CP) decomposition can explain the variation present within the cytokines tensor, or principal component analysis (PCA) could be used to reduce the gene expression matrix (9). Tensor partial least squares regression (tPLS) allows one to explain the shared variation between the matrix and tensor (15, 16). In contrast, here we wish to explain the total variation across both the tensor and matrix. This is accomplished with CMTF (11–13).