Beyond existing multi-view clustering, this paper studies a more realistic
clustering scenario, referred to as incomplete multi-view clustering, where a
number of data instances are missing in certain views. To tackle this problem,
we explore spectral perturbation theory. In this work, we show a strong link
between perturbation risk bounds and incomplete multi-view clustering. That is,
as the similarity matrix fed into spectral clustering is a quantity bounded in
magnitude O(1), we transfer the missing problem from data to similarity and
tailor a matrix completion method for incomplete similarity matrix. Moreover,
we show that the minimization of perturbation risk bounds among different views
maximizes the final fusion result across all views. This provides a solid
fusion criteria for multi-view data. We motivate and propose a
Perturbation-oriented Incomplete multi-view Clustering (PIC) method.
Experimental results demonstrate the effectiveness of the proposed method.

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