  Multi-view anchor graph clustering selects representative anchors to avoid
full pair-wise similarities and therefore reduce the complexity of graph
methods. Although widely applied in large-scale applications, existing
approaches do not pay sufficient attention to establishing correct
correspondences between the anchor sets across views. To be specific, anchor
graphs obtained from different views are not aligned column-wisely. Such an
\textbf{A}nchor-\textbf{U}naligned \textbf{P}roblem (AUP) would cause
inaccurate graph fusion and degrade the clustering performance. Under
multi-view scenarios, generating correct correspondences could be extremely
difficult since anchors are not consistent in feature dimensions. To solve this
challenging issue, we propose the first study of the generalized and flexible
anchor graph fusion framework termed \textbf{F}ast \textbf{M}ulti-\textbf{V}iew
\textbf{A}nchor-\textbf{C}orrespondence \textbf{C}lustering (FMVACC).
Specifically, we show how to find anchor correspondence with both feature and
structure information, after which anchor graph fusion is performed
column-wisely. Moreover, we theoretically show the connection between FMVACC
and existing multi-view late fusion \cite{liu2018late} and partial view-aligned
clustering \cite{huang2020partially}, which further demonstrates our
generality. Extensive experiments on seven benchmark datasets demonstrate the
effectiveness and efficiency of our proposed method. Moreover, the proposed
alignment module also shows significant performance improvement applying to
existing multi-view anchor graph competitors indicating the importance of
anchor alignment. Our code is available at
\url{https://github.com/wangsiwei2010/NeurIPS22-FMVACC}.
