To design geometrically motivated approaches for classifying the high-dimensional data, we propose to learn a discriminant subspace using Correlation Embedding Analysis (CEA). This novel algorithm enhances its discriminant power by incorporating both correlational graph embedding and Fisher criterion. In a geometric interpretation, it projects the high-dimensional data onto a hypersphere and preserves intrinsic neighbor relations with the Pearson correlation metric. After the embedding, resulting data pairs from the same class are forced to enhance their correlation affinity, whereas neighboring points of different class are forced to reduce their correlation affinity at the same time. The feature learned by CEA is tolerable to scaling or outlier. Experiments on face recognition demonstrate the effectiveness and advantage of the CEA.