Sparse subspace clustering (SSC) and spectral clustering (SC) are both state-of-the-art methods to identify complex clusters in high-dimensional input space. However, there are few researches to discuss the relation between them. Therefore, in this paper, we provide an explicit theoretical connection between them from the respective of learning a data similarity matrix. We show that spectral clustering with Gaussian kernel can be viewed as sparse subspace clustering with entropy-norm (SSC+E). Compared to existing SSC algorithms, the SSC+E algorithm can obtain a sparse, analytical, symmetrical and nonnegative similarity matrix. Besides, it makes use of Gaussian kernel to compute the sparse similarity matrix of objects, which can avoid the complex computation of the sparse optimization program of SSC. Finally, we provide the experimental analysis to compare the efficiency and effectiveness of sparse subspace clustering and spectral clustering on ten benchmark data sets. The theoretical and experimental analysis can well help users for the selection of high-dimensional data clustering algorithms.