  Low-Rank Representation (LRR) highly suffers from discarding the locality
information of data points in subspace clustering, as it may not incorporate
the data structure nonlinearity and the non-uniform distribution of
observations over the ambient space. Thus, the information of the observational
density is lost by the state-of-art LRR models, as they take a constant number
of adjacent neighbors into account. This, as a result, degrades the subspace
clustering accuracy in such situations. To cope with deficiency, in this paper,
we propose to consider a hypergraph model to facilitate having a variable
number of adjacent nodes and incorporating the locality information of the
data. The sparsity of the number of subspaces is also taken into account. To do
so, an optimization problem is defined based on a set of regularization terms
and is solved by developing a tensor Laplacian-based algorithm. Extensive
experiments on artificial and real datasets demonstrate the higher accuracy and
precision of the proposed method in subspace clustering compared to the
state-of-the-art methods. The outperformance of this method is more revealed in
presence of inherent structure of the data such as nonlinearity, geometrical
overlapping, and outliers.
