Dimensionality Reduced ℓ⁰ -Sparse Subspace Clustering

Subspace clustering partitions the data that lie on a union of subspaces. ℓ⁰ -Sparse Subspace Clustering (ℓ⁰ -SSC), which belongs to the subspace clustering methods with sparsity prior, guarantees the correctness of subspace clustering under less restrictive assumptions compared to its ℓ¹ counterpart such as Sparse Subspace Clustering (SSC) [1] with demonstrated effectiveness in practice. In this paper, we present Dimensionality Reduced ℓ⁰-Sparse Subspace Clustering (DR-ℓ⁰-SSC). DR-ℓ⁰ -SSC first projects the data onto a lower dimensional space by linear transformation, then performs ℓ⁰-SSC on the dimensionality reduced data. The correctness of DR- ℓ⁰ -SSC in terms of the subspace detection property is proved, therefore DR-ℓ⁰-SSC recovers the underlying subspace structure in the original data from the dimensionality reduced data. Experimental results demonstrate the effectiveness of DR-ℓ⁰-SSC.