MOTIVATION: We introduce a statistical approach for pattern recognition in multivariate spatial transcriptomics data. RESULTS: Our algorithm constructs a projection of the data onto a low-dimensional feature space which is optimal in maximizing Moran's I, a measure of spatial dependency. This projection mitigates non-spatial variation and outperforms principal components analysis for pre-processing. Patterns of spatially variable genes are well represented in this feature space, and their projection can be shown to be a denoising operation. Our framework does not require any parameter tuning, and it furthermore gives rise to a calibrated, powerful test of spatial gene expression. AVAILABILITY AND IMPLEMENTATION: The algorithm is implemented in the open source software R and is available at https://github.com/IMSBCompBio/SpaCo.