Soft subspace clustering is an important part and research hotspot in clustering research. Clustering in high dimensional space is especially difficult due to the sparse distribution of the data and the curse of dimensionality. By analyzing limitations of the existing algorithms, the concept of subspace difference and an improved initialization method are proposed. Based on these, a new objective function is given by taking into account the compactness of the subspace clusters and subspace difference of the clusters. And a subspace clustering algorithm based on k-means is presented. Theoretical analysis and experimental results demonstrate that the proposed algorithm significantly improves the accuracy.