In this paper, we propose a novel methodology for detecting systematic spatial failure patterns at wafer level for yield learning. Our proposed methodology takes the testing results (i.e., pass or fail) of a number of dies over different wafers, cluster all these wafers according to their failures, and eventually identify the underlying spatial failure patterns. Several novel machine learning algorithms, including singular value decomposition, hierarchical clustering, dictionary learning, etc., are developed in order to make the proposed methodology robust to random failures. The efficacy of our proposed approach is demonstrated by an industrial data set.