Genetic regulation of gene expression, revealed by expression quantitative trait loci (eQTLs), exhibits complex patterns of tissue-specific effects. Characterization of these patterns may allow us to better understand mechanisms of gene regulation and disease etiology. We develop a constrained matrix factorization model, sn-spMF, to learn patterns of tissue-sharing and apply it to 49 human tissues from the Genotype-Tissue Expression (GTEx) project. The learned factors reflect tissues with known biological similarity and identify transcription factors that may mediate tissue-specific effects. sn-spMF, available at https://github.com/heyuan7676/ts_eQTLs, can be applied to learn biologically interpretable patterns of eQTL tissue-specificity and generate testable mechanistic hypotheses.