  A new submodule clustering method via sparse and low-rank representation for
multi-way data is proposed in this paper. Instead of reshaping multi-way data
into vectors, this method maintains their natural orders to preserve data
intrinsic structures, e.g., image data kept as matrices. To implement
clustering, the multi-way data, viewed as tensors, are represented by the
proposed tensor sparse and low-rank model to obtain its submodule
representation, called a free module, which is finally used for spectral
clustering. The proposed method extends the conventional subspace clustering
method based on sparse and low-rank representation to multi-way data submodule
clustering by combining t-product operator. The new method is tested on several
public datasets, including synthetical data, video sequences and toy images.
The experiments show that the new method outperforms the state-of-the-art
methods, such as Sparse Subspace Clustering (SSC), Low-Rank Representation
(LRR), Ordered Subspace Clustering (OSC), Robust Latent Low Rank Representation
(RobustLatLRR) and Sparse Submodule Clustering method (SSmC).
