  Multi-view data clustering attracts more attention than their single view
counterparts due to the fact that leveraging multiple independent and
complementary information from multi-view feature spaces outperforms the single
one. Multi-view Spectral Clustering aims at yielding the data partition
agreement over their local manifold structures by seeking
eigenvalue-eigenvector decompositions. However, as we observed, such classical
paradigm still suffers from (1) overlooking the flexible local manifold
structure, caused by (2) enforcing the low-rank data correlation agreement
among all views; worse still, (3) LRR is not intuitively flexible to capture
the latent data clustering structures. In this paper, we present the structured
LRR by factorizing into the latent low-dimensional data-cluster
representations, which characterize the data clustering structure for each
view. Upon such representation, (b) the laplacian regularizer is imposed to be
capable of preserving the flexible local manifold structure for each view. (c)
We present an iterative multi-view agreement strategy by minimizing the
divergence objective among all factorized latent data-cluster representations
during each iteration of optimization process, where such latent representation
from each view serves to regulate those from other views, such intuitive
process iteratively coordinates all views to be agreeable. (d) We remark that
such data-cluster representation can flexibly encode the data clustering
structure from any view with adaptive input cluster number. To this end, (e) a
novel non-convex objective function is proposed via the efficient alternating
minimization strategy. The complexity analysis are also presented. The
extensive experiments conducted against the real-world multi-view datasets
demonstrate the superiority over state-of-the-arts.
