  Subspace clustering is a class of extensively studied clustering methods
where the spectral-type approaches are its important subclass. Its key first
step is to desire learning a representation coefficient matrix with block
diagonal structure. To realize this step, many methods were successively
proposed by imposing different structure priors on the coefficient matrix.
These impositions can be roughly divided into two categories, i.e., indirect
and direct. The former introduces the priors such as sparsity and low rankness
to indirectly or implicitly learn the block diagonal structure. However, the
desired block diagonalty cannot necessarily be guaranteed for noisy data. While
the latter directly or explicitly imposes the block diagonal structure prior
such as block diagonal representation (BDR) to ensure so-desired block
diagonalty even if the data is noisy but at the expense of losing the convexity
that the former's objective possesses. For compensating their respective
shortcomings, in this paper, we follow the direct line to propose Adaptive
Block Diagonal Representation (ABDR) which explicitly pursues block diagonalty
without sacrificing the convexity of the indirect one. Specifically, inspired
by Convex BiClustering, ABDR coercively fuses both columns and rows of the
coefficient matrix via a specially designed convex regularizer, thus naturally
enjoying their merits and adaptively obtaining the number of blocks. Finally,
experimental results on synthetic and real benchmarks demonstrate the
superiority of ABDR to the state-of-the-arts (SOTAs).

Machine Learning;Machine Learning