Diverse, high-dimensional modalities collected in large cohorts present new opportunities for the formulation and testing of integrative scientific hypotheses. Similarity-driven multi-view linear reconstruction (SiMLR) is an algorithm that exploits inter-modality relationships to transform large scientific datasets into smaller, more well-powered and interpretable low-dimensional spaces. SiMLR contributes an objective function for identifying joint signal, regularization based on sparse matrices representing prior within-modality relationships and an implementation that permits application to joint reduction of large data matrices. We demonstrate that SiMLR outperforms closely related methods on supervised learning problems in simulation data, a multi-omics cancer survival prediction dataset and multiple modality neuroimaging datasets. Taken together, this collection of results shows that SiMLR may be applied to joint signal estimation from disparate modalities and may yield practically useful results in a variety of application domains.