  Low-Rank Representation (LRR) is arguably one of the most powerful paradigms
for Multi-view spectral clustering, which elegantly encodes the multi-view
local graph/manifold structures into an intrinsic low-rank self-expressive data
similarity embedded in high-dimensional space, to yield a better graph
partition than their single-view counterparts. In this paper we revisit it with
a fundamentally different perspective by discovering LRR as essentially a
latent clustered orthogonal projection based representation winged with an
optimized local graph structure for spectral clustering; each column of the
representation is fundamentally a cluster basis orthogonal to others to
indicate its members, which intuitively projects the view-specific feature
representation to be the one spanned by all orthogonal basis to characterize
the cluster structures. Upon this finding, we propose our technique with the
followings: (1) We decompose LRR into latent clustered orthogonal
representation via low-rank matrix factorization, to encode the more flexible
cluster structures than LRR over primal data objects; (2) We convert the
problem of LRR into that of simultaneously learning orthogonal clustered
representation and optimized local graph structure for each view; (3) The
learned orthogonal clustered representations and local graph structures enjoy
the same magnitude for multi-view, so that the ideal multi-view consensus can
be readily achieved. The experiments over multi-view datasets validate its
superiority.
