The efficiency of Side Channel Attack （SCA） and the accuracy of key recovery are reduced by the high noise and dimension of energy trace data collected in SCA greatly. To solve these problems， a Correlation Power Analysis （CPA） method of Advanced Encryption Standard （AES） algorithm based on Uniform Manifold Approximation and Projection （UMAP） was proposed. In the proposed method， Euclidean distance was used as a basis to calculate the set of proximate points of energy traces. Firstly， in order to capture position relationships of the energy trace data to preserve local structural features of the data， a weighted adjacency matrix was obtained by constructing an adjacency graph and calculating the similarity among proximate nodes. Then， structure relationships of the adjacency graph were described using the Laplacian matrix， and the eigenvectors with small eigenvalues were extracted as the initialized low-dimensional data from the adjacency graph by feature decomposition. Meanwhile， in order to preserve global structural features of the data， the binary cross-entropy was used as optimization function to adjust position of the data in the low-dimensional space. Furthermore， in order to improve the computational efficiency， the force-directed graph layout algorithm was adopted in the gradient descent process. Finally， correlation power attacks were performed on the dimensional reduced data to recover the key. Experimental results show that UMAP method can preserve local and global structural features of the original energy trace data effectively； the proposed method can improve the correlation between energy trace data and assumed power leakage models， and reduce the number of energy traces required for key recovery，specifically， the number of energy traces required to recover a single key byte is 180， and the number of energy traces required to recover all 16 key bytes is 700 by the proposed method； compared to the ISOmetric MAPping （ISOMAP） dimension reduction method， the proposed method reduces the number of energy traces required to recover all key bytes by 36.4%.