  This paper explores the problem of clustering ensemble, which aims to combine
multiple base clusterings to produce better performance than that of the
individual one. The existing clustering ensemble methods generally construct a
co-association matrix, which indicates the pairwise similarity between samples,
as the weighted linear combination of the connective matrices from different
base clusterings, and the resulting co-association matrix is then adopted as
the input of an off-the-shelf clustering algorithm, e.g., spectral clustering.
However, the co-association matrix may be dominated by poor base clusterings,
resulting in inferior performance. In this paper, we propose a novel low-rank
tensor approximation-based method to solve the problem from a global
perspective. Specifically, by inspecting whether two samples are clustered to
an identical cluster under different base clusterings, we derive a
coherent-link matrix, which contains limited but highly reliable relationships
between samples. We then stack the coherent-link matrix and the co-association
matrix to form a three-dimensional tensor, the low-rankness property of which
is further explored to propagate the information of the coherent-link matrix to
the co-association matrix, producing a refined co-association matrix. We
formulate the proposed method as a convex constrained optimization problem and
solve it efficiently. Experimental results over 7 benchmark data sets show that
the proposed model achieves a breakthrough in clustering performance, compared
with 12 state-of-the-art methods. To the best of our knowledge, this is the
first work to explore the potential of low-rank tensor on clustering ensemble,
which is fundamentally different from previous approaches.
